STEREOCHEMISTRY OP ALKANES AND NON-CONJUGATED …

STEREOCHEMISTRY

ALKANES

NON-CONJUGATED ALKENES

A T h e s i s presen ted , fo r

t h e d e g r e e o f D octor o f P h i lo so p h y

i n th e

F a c u l t y o f S c ie n c e

o f th e

U n iv e r s i t y o f Glasgow

Moira Jane M C a f fe r

September 1977

ProQuest Number: 13804129

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ACKNOWLEDGEMENTS

I w ish t o acknow ledge my in d e b t e d n e s s t o D r .D .N .J .W h ite

and P r o f e s s o r G.A.Sim f o r t h e i r i n t e r e s t and d i r e c t i o n th rou gh ou t

t h i s p e r io d o f r e s e a r c h . I am a l s o g r a t e f u l t o o th e r members o f

t h e X - ra y a n a l y s i s group o f t h e U n i v e r s i t y o f Glasgow, p a r t i c u l a r l y

D r .C .J .G i lm o r e ,D r .P .M a l l in s o n and M r.A#A.Freer f o r h e l p f u l

d i s c u s s i o n s and a d v i c e .

Thanks are due t o t h e s t a f f o f t h e c h e m is tr y and com puting

departm ents and t o t h e p h o to g r a p h e r , Mr.R.Munro, who a s s i s t e d me i n

my r e s e a r c h .

F i n a n c i a l supp ort from t h e S c ie n c e R esearch C ou n c il i s

g r a t e f u l l y acknow ledged .

F i n a l l y , I am v e r y g r a t e f u l t o my husband w ith o u t whose

h e lp and encouragement %I c o u ld not have com p leted t h i s p r o j e c t .

G lasgow, 1977 M .J.M °Caffer

- iii -

CONTENTS

Summary 1

Chapter one - M olecu lar m ec h a n ic s : An i n t r o d u c t i o n 5

1 . 1 I n t r o d u c t io n 6,

1 . 2 P o t e n t i a l f u n c t i o n s and f o r c e f i e l d s 10

1 .3 D e te r m in a t io n o f h e a t s o f fo r m a t io n 20

1*4 P a r a m e t r iz a t io n o f f o r c e f i e l d s 24

1*5 Energy m in im is a t io n 27,

1 .6 R e f e r e n c e s 37

C hapter two - The developm ent o f a m o le c u la r f o r c e 39

f i e l d f o r c a l c u l a t i o n s on a lk a n e s and

n o n -c o n ju g a te d a lk e n e s

2 .1 I n t r o d u c t io n 40

2 .2 The f o r c e f i e l d 41

2 .3 R e s u l t s and d i s c u s s i o n f o r compounds in c lu d e d 55

i n t h e p a r a m e t r iz a t io n

2*4 Some a p p l i c a t i o n s o f t h e W h i t e - B o v i l l f o r c e 71

f i e l d

2 .5 R e f e r e n c e s 8 l

Chapter t h r e e - A p p l i c a t i o n o f t h e W h i t e - B o v i l l 86

f o r c e f i e l d t o t h e c o n fo r m a t io n a l

a n a l y s i s o f c y c l i c h y d r o c a r b o n s ,C ^ -C ^

3 .1 I n t r o d u c t io n 87

3 .2 The e f f e c t o f in t r o d u c in g a d ou b le bond i n t o 90

cycloalkanes,C^-C-^Q

3 .3 The e f f e c t o f in t r o d u c in g a secon d d o u b le 92

bond i n t o c y c l o a l k e n e s ,C g - c^q

C on ten ts ( c o n t d . )

3*4 C onform ations o f t h e i n d i v i d u a l c y c l e n e s 101

3*5 R e fe r e n c e s 148

Chapter fou r - M olecu lar m echan ics c a l c u l a t i o n s on 152

t h e s t a b i l i t y o f b r id g eh ea d o l e f i n s i n

b i c y c l o ( m . n . l ) a l k - l - e n e sy stem s

4 .1 I n t r o d u c t io n 153

4 - 2 R eview 154

4*3 M olecu lar m echan ics c a l c u l a t i o n s and r e s u l t s 159

4*4 D i s c u s s i o n I 69

4*5 R e fe r e n c e s 183

Chapter f i v e - P r e d i c t i o n o f t h e s t e r e o s e l e c t i v i t y I 85

o f h in d e r e d s u b s t r a t e s

5*1 I n t r o d u c t io n 186

5*2 P r e d i c t i o n o f t h e s t e r e o s e l e c t i v i t y i n t h e 191

h y d r o b o r a t io n o f h in d e r e d c y c lo h e x e n e s u s in g

m o le c u la r m echan ics o a l c u l a t i o n s and s t e r i c

c o n g e s t i o n c a l c u l a t i o n s

5*3 D i s c u s s i o n 199

5 .4 R e f e r e n c e s 203

Chapter s i x - The c o r r e l a t i o n o f Raman o p t i c a l a c t i v i t y 204

i n m ethyl t o r s i o n modes w ith m o le c u la r

m echanics c a l c u l a t i o n s o f c h i r a l h in d

e r in g p o t e n t i a l s

6 . 1 I n t r o d u c t io n 205

6 .2 M o lecu la r m ech an ics c a l c u l a t i o n s 213

C o n te n ts ( c o n t d . )

6 .3 D i s c u s s i o n 225

6 .4 R e fe r e n c e s 229

Chapt er s e v e n - Some a s p e c t s o f c r y s t a l lo g r a p h y 230

7 .1 H i s t o r i c a l 231

7 .2 C o r r e c t io n s t o t h e measured i n t e n s i t i e s 232

7 .3 S t r u c tu r e f a c t o r s 235

7 . 4 S t r u c tu r e f a c t o r s and t h e e l e c t r o n d e n s i t y

d i s t r i b u t io n

7-5 D ir e c t m ethods o f phase d e te r m in a t io n 239

7 .6 F o u r ie r s y n t h e s i s 246

7 .7 L east sq u a res r e f in e m e n t 247

Chapter e ig h t - X -ray a n a l y s i s o f 1 , 8 - d i m e t h y l - 2 -

n ap h th y l a c e t a t e

8 .1 I n t r o d u c t io n 253

8 .2 E xp er im en ta l 256

8 . 3 R e s u l t s 260

8 .4 D i s c u s s i o n o f r e s u l t s 291

8 .5 R e fe r e n c e s 301

Chapter n in e - The c r y s t a l s t r u c t u r e o f b i c y c l o ( 4 * 4 . l ) - 302

* u n d e c a n e -1 , 6 - d i o l

9 -1 I n t r o d u c t io n 303

9 .2 E xp er im enta l 307

9 .3 R e s u l t s 310

9 . 4 D i s c u s s i o n o f r e s u l t s 346

9-5 R e fe r e n c e s 357

SUMMARY

M olecu lar f o r c e f i e l d s , which were d e v e lo p e d b e f o r e 1973

t o d e a l w ith c a l c u l a t i o n s on a lk a n e s a n d /o r n o n -c o n ju g a te d a l k e n e s ,

were each known t o have c e r t a i n d e f e c t s i n t h a t t h e y c o u ld not

a d e q u a t e ly rep rod u ce a l l th e e x p e r im e n ta l d a t a . The p a r a m e t r iz a t io n

o f 9, new and improved f o r c e f i e l d f o r c a l c u l a t i o n s on a lk a n e s and

n o n -c o n ju g a te d a lk e n e s was t h e r e f o r e u n d er ta k e n . The f o r c e f i e l d ,

which was s u b s e q u e n t ly -d e v e lo p e d ( r e f e r r e d t o a s t h e W h i t e - B o v i l l

f o r c e f i e l d or YfBFF, f o r s h o r t ) , in c o r p o r a te d i n t o i t s p a r a m e t r iz a t io n

l a r g e amounts o f r e c e n t l y p u b l i s h e d e x p e r im e n ta l d a ta c o n c e r n in g

t h e thermodynamic and s t r u c t u r a l p r o p e r t i e s o f a c a r e f u l l y

s e l e c t e d group o f 75 compounds and was found t o be more g e n e r a l

and r e l i a b l e th an t h e p r e v io u s l y d e v e lo p e d f o r c e f i e l d s . The

f i n a l form o f th e YIBFF c o n s i s t e d o f 22 param eters f o r a l i p h a t i c

f u n c t i o n s and 18 param eters f o r d o u b le bonds and i t s s u r r o u n d in g s .

The mean d e v i a t i o n betw een t h e c a l c u l a t e d and e x p e r im en ta l

e n t h a l p i e s o f 60 compounds was 0 .5 5 k c a l . / m o l e and. t h e c o r r e s p o n d in g

f i g u r e s f o r g e o m e tr ic p r o p e r t i e s were 0 .0 0 9 0 . 6 ° and 0 . 9 ° in

bond l e n g t h s , , bond a n g le s and t o r s i o n a n g l e s .

M olecu lar mechanics(MM) c a l c u l a t i o n s , u t i l i s i n g t h e WBFF,

were th e n und ertaken on a s e r i e s o f c y c l e n e s which had. one d o u b le

bond, i n t h e r i n g , r a n g in g from - C^q and w ith two d o u b le bonds

i n t h e r i n g , r a n g in g from Cg - s o t h a t d e t a i l e d knowledge

o f t h e r e l a t i o n s h i p betw een c o n fo r m a t io n a l s t r u c t u r e and en ergy

would be o b t a in e d . The WBFF produced e x tr e m e ly r e l i a b l e r e s u l t s

f o r g e o m e t r ie s , h e a t s o f fo rm a t io n and h e a t s o f h y d r o g e n a t io n o f

a number o f medium r i n g compounds so t h a t i t was p o s s i b l e t o

p l a c e a c e r t a i n d e g r e e o f c o n f id e n c e in t h e r e s u l t s from t h i s

i n v e s t i g a t i o n o f t h e p l e t h o r a o f co n fo rm a t io n s and t r a n s a n n u la r

i n t e r a c t i o n s ex h ib ite d , by medium r i n g s . In a d d i t i o n , t h e minimum

en ergy co n fo rm a t io n (KEC) o f c i s t c i s , c i s - l t 5 t 9 - c y c l o d o d e c a t r i e n e

was a s s ig n e d on t h e b a s i s o f MM c a l c u l a t i o n s and an NMR a n a l y s i s ,

A s e r i e s o f KM c a l c u l a t i o n s was perform ed on a c a r e f u l l y

s e l e c t e d group o f s i x t e e n b i c y c l i c b r id g eh ea d o l e f i n s w ith th e

aim o f a s s e s s i n g t h e l i m i t s o f th e a p p l i c a t i o n o f t h e r u l e s ,

proposed by B red t , F aw cett and. YJiseman, r e g a r d in g t h e s t a b i l i t y

o f b r id g e h e a d o l e f i n s and p r o v id in g g u i d e l i n e s or r u l e s f o r

s i t u a t i o n s not c o v e re d by th e p r e v io u s r u l e s . The e x p e r im en ta l

d a t a , which were m o s t ly o f a q u a l i t a t i v e n a tu r e , were s a t i s f a c t

o r i l y reproduced by t h e WBFF.and i t was found t h a t , w i t h in a

g i v e n s k e l e t o n , sy stem s w ith a d ou b le bond p la c e d in t h e secon d

l a r g e s t b r id g e w i l l be l e s s s t r a i n e d th a n t h o s e w ith a d o u b le

bond l o c a t e d in t h e l a r g e s t b r id g e , which in tu r n a re l e s s s t r a i n e d

th a n t h o s e w ith a d o u b le bond s i t u a t e d i n t h e s m a l l e s t b r i d g e .

The r e c e n t p u b l i c a t i o n o f r e s u l t s o f a s e r i e s o f

h y d r o b o r a t io n /o x id a t io n exp er im en ts on h in d e r e d 1 , 3 , 5 wkr i “ a hd

t e t r a - s u b s t i t u t e d a lk y lc y c lo h e x e n e s p r o v id e d r e f e r e n c e d a ta f o r

t e s t i n g t h e a p p l i c a t i o n o f summed atom c e n tr e d c o n g e s t i o n r a t i o s

( based on t h e Wipke and Gund c o n g e s t io n a lg o r i th m ) in t h e

p r e d i c t i o n o f t h e outcome o f s t e r e o s e l e c t i v e a d d i t io n s t o

h in d e r e d d ou b le bonds s i n c e h y d r o b o r a t io n i s known t o be s e n s i t i v e

t o t h e b a la n c e o f s t e r i c h in d r a n c e t o t h e two f a c e s o f t h e d ou b le

bond. The agreem ent betw een t h e p r e d ic t e d and e x p e r im e n t a l ly

o b serv ed s t e r e o s e l e c t i v i t y was fa v o u r a b le ( w i t h i n 15/& o f each

o th e r ) when s t e r i c c o n t r o l dom in ates t h e r e a c t i o n .

I t has been s u g g e s te d t h a t Raman o p t i c a l a c t i v i t y in

m ethyl t o r s i o n modes o f v i b r a t i o n in c h i r a l m o le c u le s can be

c o r r e l a t e d w ith t h e c h i r a l p a r t o f t h e e l e c t r o n i c p o t e n t i a l

b a r r ie r h in d e r in g t h e r o t a t i o n o f t h e m ethyl g r o u p . In a

perturbed, harm onic o s c i l l a t o r a p p r o x im a tio n , t h e c h i r a l p art i s

p r o p o r t io n a l t o t h e d isp la c e m e n t o f th e e q u i l ib r iu m p o s i t i o n o f

t h e m ethy l group from t h e sym m etric p o s i t i o n . MM c a l c u l a t i o n s

o f t h i s d isp la c e m e n t in ( + ) - 3 -m e th y lc y c lo h e x a n o n e , ( + ) - 3 - m e t h y l -

c y c lo p e n ta n o n e , ( - ) - l im o n e n e , ( + ) - c a r v o n e and ( - ) -m enthol was

found t o c o r r e l a t e in s i g n , and a p p r o x im a te ly in m agnitude,, w ith

t h e o b se r v ed Raman o p t i c a l a c t i v i t y i n bands a s s ig n e d t o m ethyl

t o r s i o n modes.

A s t r u c t u r e a n a l y s i s o f 1 ,8 - d im e t h y l - 2 - n a p h t h y l a c e t a t e

was c a r r i e d out as p a r t o f a s e r i e s o f i n v e s t i g a t i o n s , by D r .J .

Carnd.uff, i n t o t h e a u t o x id a t i o n o f 2 - n a p h t h o l s . On th e b a s i s o f

t h e r a t e s o f a u t o x id a t i o n r e a c t i o n s , t h e 1 ,8 - d im e t h y l d e r i v a t i v e

was e x p e c te d t o be more s t r a i n e d th a n th e 1 - i s o p r o p y l d e r i v a t i v e ,

w h ic h , in t u r n , sh o u ld be more s t r a i n e d th an t h e 1 -m eth y l d e r i v a t i v e .

T h is h y p o t h e s i s was su p p o rted by t h e c o r re sp o n d in d s t r u c t u r e

a n a l y s e s and, from a com parison o f s t r u c t u r a l d a ta f o r e ig h t Cl

a n d /o r C8 s u b s t i t u t e d n a p h th a le n e s , t h e o n ly c o n s i s t e n t i n d i c a t o r s

o f s t e r i c crow ding a r e t h e C1-C9-C8 v a le n c e a n g le and C 1 . . . .C 8

nonbonded d i s t a n c e .

An X -ray c r y s t a l s t r u c t u r e a n a l y s i s o f b i c y c l o ( 4 » 4 » l ) -

u n d .e c a n e - l ,6 -d . io l was u nd ertaken t o d e term in e t h e MEC o f th e

b ic y c lo (4 * 4 « l)u n d .e c a n e system and t h e c o n fo rm a t io n o f th e 1 0 -

membered r i n g and t o o b t a in s t r u c t u r a l d e t a i l s o f t h e MEC o f

c y c lo h e p t a n e . The X -ray r e s u l t s r e v e a l t h a t t h e b i c y c l o ( 4 * 4 * l ) “

undecane r i n g system c o n s i s t s o f two c y c lo h e p ta n e r i n g s , bo th in

t h e C^- sym m etric t w i s t - c h a i r c o n fo r m a t io n , fu s e d b a c k - to - b a c k in

a 1 , 3-m anner. MM c a l c u l a t i o n s on a number o f p l a u s i b l e conform

a t i o n s o f t h e b i c y c l o ( 4 « 4 * l ) lindecane system con firm th e X -ray

r e s u l t s . The c o n fo rm a t io n o f t h e 10-membered r i n g i n th e

b i c y c l o ( 4 . 4 . l ) u n d e c a n e - l , 6 - d i o l was o f i n t e r e s t on accou n t o f t h e

- 4 -f a c t t h a t i t b e lo n g s t o a c l a s s which had not y e t been c o n s id e r e d

i n MM c a l c u l a t i o n s or d i f f r a c t i o n s t u d i e s o f t h e lo w -e n e r g y

c o n fo r m a t io n s o f c y c lo d e c a n e .

CHAPTER ONE

M olecu lar m ec h a n ic s : An i n t r o d u c t i o n

1 .1 I n t r o d u c t i o n

Through c h e m i s t r y , i n c o n j u n c t i o n w i t h a l l t h e o t h e r

s c i e n c e s and t e c h n o l o g i e s , c i v i l i z a t i o n has made tremendous

headway d u r i n g th e l a s t c e n t u r y . I n c h e m i s t r y , t h e s u c c e s s

o f John D a l t o n ' s a tomic t h e o r y and th e c o n c e p t o f i som er ism ,

p ro po sed hy B e r z e l i u s l e d to r a d i c a l changes o f method.

C h e m is t ry cea sed to he the s c i e n c e o f ' m a t e r i a l p r i n c i p l e s ’

and was t r a n s fo rm e d i n t o th e s c i e n c e o f 'm o l e c u l a r s t r u c t u r e * .

B e fo re D a l to n , t h e r e had heen no way o f l a b e l l i n g th e

c o n s t i t u t i o n s o f c h em ica l s u b s t a n c e s , e x c e p t by r e f e r e n c e

t o t h e i r l a r g e - s c a l e o b s e r v a b le p r o p e r t i e s . But now a new

p hase b eg an : by p a y in g c l o s e a t t e n t i o n t o t h e i r m o le c u la r

w e ig h t s and r e a c t i o n s , one cou ld e s t a b l i s h th e u n d e r l y i n g

m o le c u l a r s t r u c t u r e s o f ch em ica l s u b s t a n c e s d i r e c t l y . The

deve lopm ent o f th e c o n c e p t o f v a l e n c y was d e c i s i v e , f o r i t

l e d to r u l e s g o v e rn in g th e w r i t i n g o f s t r u c t u r a l f o r m u la e .

A n o th e r c o n c e p tu a l scheme of g r e a t s i g n i f i c a n c e f o r

i d e a s o f s t r u c t u r e o f m a t t e r was th e i d e a o f Le Bel and

v a n ' t Hoff (187U) o f th e t h r e e - d i m e n s i o n a l a r rangem en t o f

a to m s . This i d e a d id n o t r e a l i s e i t s f u l l impetus u n t i l

1950 when D.H.R. B a r to n p u b l i s h e d h i s p i o n e e r i n g p a p e r

on c o n f o r m a t i o n a l a n a l y s i s , r e l a t i n g c h e m ic a l r e a c t i v i t y

o f s t e r o i d s and p o l y c y c l i c t e r p e n o i d s to c o n f o r m a t i o n .

S ince t h e n , th e o r g a n ic c h e m is t has been co nce rned w i t h

t h e p h y s i c a l and c h em ica l p r o p e r t i e s and r e a c t i v i t y o f

o r g a n ic m o le cu le s i n g r e a t e r d e p th and t h e r e f o r e he w i l l

u t i l i s e e x p e r i m e n t a l and t h e o r e t i c a l m ethods , which

s u p p ly d e t a i l e d i n f o r m a t i o n of th e geometry and thermo

dynamic p r o p e r t i e s o f m o le c u l e s , and which a re s i m p le ,

r e l i a b l e and e c o n o m ic a l .

When s t r u c t u r a l f e a t u r e s o f th e m o lecu le (bond

a n g l e s , bond l e n g t h s , t o r s i o n a l a n g l e s , nonbonded d i s t a n c e s )

d e p a r t from t h e i r o p t im a l v a l u e s , t h e m olecu le i s s a i d to

be s t r a i n e d . O f te n , f u n c t i o n a l u n i t s a re th e s t a n d a r d s o f

c h o ic e and, f o r example , n o n - l i n e a r c a rb o n - c a rb o n

t r i p l e bo n ds , t w i s t e d o l e f i n i c l i n k a g e s , and n o n p la n a r

benzene r i n g s a r e f e a t u r e s i n d i c a t i n g m o le c u la r s t r a i n .

While s t r a i n i s q u a l i t a t i v e l y an i n t u i t i v e and s im p le

s u b j e c t , a good d e a l o f c o m p le x i ty e n t e r s when q u a n t i t

a t i v e r e s u l t s a r e d e s i r e d e . g . i n th e s t u d y o f c h em ica l

r e a c t i v i t y o r when com par ison be tw een f o r m a l l y u n r e l a t e d

m o le c u le s i s a t t e m p t e d , and, as a r e s u l t , d a t a c o n c e rn in g

m o le c u l a r s t r a i n i s r e l a t i v e l y s c a r c e .

E x i s t i n g e x p e r i m e n t a l t e c h n iq u e s f o r d e t e r m i n i n g

m o le c u l a r s t r u c t u r e and e n e rg y e . g . s p e c t r o c o p y (NMR, IR,

ORD/CD), d i f f r a c t i o n ( X - r a y s , e l e c t r o n s , n e u t r o n s ) ,

c a l o r i m e t r y and e l e c t r o c h e m i s t r y a l l have t h e i r l i m i t a t i o n s

and d raw b ac k s . A l l a r e t im e-consum ing a t b e s t and , w i th

t h e e x c e p t i o n o f d i f f r a c t i o n , g iv e r i s e t o in co m p le te

d e s c r i p t i o n s o f geometry a n d / o r e n e r g y , w h i l e th e d i f f

r a c t i o n methods g iv e no i n f o r m a t i o n r e g a r d i n g e n e r g i e s .

F o r many y e a r s , c h e m is t s have a t t e m p te d to overcome

e x p e r i m e n t a l d i f f i c u l t i e s by c a l c u l a t i n g th e geometry and

e n e rg y o f a g iv e n m olecu le u s i n g d i f f e r e n t a p p ro a c h e s .

One ap p ro a ch in v o lv e s th e c a l c u l a t i o n o f m o le c u la r

p r o p e r t i e s e . g . e n e r g y , geom etry , e l e c t r o n d e n s i t y , by

quantum m ec h an ic s . A l though a b - i n i t i o quantum m echan ica l

c a l c u l a t i o n s a re t h e o r e t i c a l l y sound , t h e y a re i m p r a c t i c a l

f o r m o le cu le s o f about more th a n tw en ty atoms as t h e y use

v a s t amounts o f computer t ime - the t ime r e q u i r e m e n t goes

up as n^ where n i s t h e number o f o r b i t a l s . A l t e r n a t i v e l y ,

s e m i - e m p i r i c a l ( s i m p l i f i e d ) quantum m ec h a n ic a l t r e a t m e n t s

(EHT, CNDO, MINDO) co u ld be used b u t the r e s u l t s o b t a i n e d

a re r a t h e r r e s t r i c t e d b eca u se o f th e u n c e r t a i n t i e s i n t r o

duced by th e v a r i o u s a p p r o x i m a t i o n s .

M o lecu la r mechanics c a l c u l a t i o n s ( o r e m p i r i c a l

f o r c e - f i e l d c a l c u l a t i o n s ) , on th e o t h e r hand , a r e l e s s

t im e-consum ing t h a n th e quantum m echan ica l c a l c u l a t i o n s -

t h e computer t ime r e q u i r e m e n t goes up by where N i s the

number o f atoms and a r e r e l a t i v e l y e a s y t o p e r fo rm . I n

a d d i t i o n , th e r e s u l t s o b ta in e d by t h i s method, u n de r

s u i t a b l e c o n d i t i o n s , c an be h i g h l y r e l i a b l e and t h e i r

a c c u r a c y i s comparab le to t h a t o b t a i n e d by many o f th e

e x p e r i m e n t a l t e c h n i q u e s . U n f o r t u n a t e l y , t h e s u c c e s s o f

t h i s t e c h n iq u e depends on th e e x i s t e n c e o f a l a r g e body

o f good e x p e r i m e n t a l d a t a f o r t h e i n i t i a l p a r a m e t r i s a t i o n

o f an assumed f o r c e - f i e l d , which s u b s e q u e n t l y p r o v i d e s

i n f o r m a t i o n on f u r t h e r compounds, some o f which may be

new o r u n o b s e rv e d , by a p r o c e s s o f e x t r a p o l a t i o n .

I n th e p a s t few y e a r s , m o le c u la r mechanics c a l c u l

a t i o n s have been used to i n v e s t i g a t e f e a t u r e s o f th e

bORN-OPPENHEIMER s u r f a c e o f a wide c l a s s o f o r g a n i c mole

c u l e s and have th us h e lp e d c o n s i d e r a b l y i n th e u n d e r s t a n d i n g

o f v a r i o u s a s p e c t s o f o r g a n i c c h e m is t r y i n c l u d i n g m o le c u la r

c o n f o r m a t i o n s , m o le c u la r thermodynamic, p r o p e r t i e s , r e a c t i o n

mechanisms, k i n e t i c s , v i b r a t i o n a l s p e c t r a and th e i n t e r

p r e t a t i o n o f dynamic NMR s p e c t r a . At p r e s e n t r e l i a b l e

c a l c u l a t i o n s can o n ly be made f o r a l i m i t e d ran g e o f

compounds c o m p r i s in g a l k a n e s , a l k e n e s , a ld e h y d e s , k e t o n e s ,

e s t e r s and p e p t i d e s w i t h up to UO to 50 atoms p e r m o le c u le .

There a r e many rev ie w s on m o le c u la r mechanics2 - 8

c a l c u l a t i o n s which a r e r e l e v a n t to t h e p r e s e n t d i s c u s s i o n .

- 10 -

1 . 2 P o t e n t i a l F u n c t io n s and Force F i e l d s

A l though t h e r e a re o f t e n c o n s i d e r a b l e d i f f e r e n c e s

i n th e d e t a i l e d t e c h n i q u e s , a l l methods e x p re s s the

m o le c u l a r s t r a i n en e rg y as a sum o f c o n t r i b u t i o n s from

i n t e r a c t i o n s such as b o n d - s t r e t c h i n g , v a l e n c e a n g le

d e f o r m a t io n s and nonbonded c o n t a c t s .

geom etry i s u s u a l l y s p e c i f i e d by a s e t o f o r d i n a r y

c r y s t a l o r o r th o g o n a l c o - o r d i n a t e s . I t i s assumed t h a t

t h e r e i s a n a t u r a l ( o r s t r a i n - f r e e ) bond l e n g t h be tw een

two atoms bonded t o g e t h e r and a n a t u r a l bond a n g le be tween

a g iv e n s e t o f a tom s. D e v i a t i o n s c ause e n e rg y changes

d e f i n e d by i n t e r a c t i o n p o t e n t i a l s . S i m i l a r l y t o r s i o n and

van d e r W aa l ' s p o t e n t i a l s can be r e l a t e d to s t a n d a r d

v a l u e s . A computer program now moves atoms by a s p e c i f i e d

in c re m e n t ( u s u a l l y 0.00001 A), d e r i v e s the t o t a l r e s u l t a n t

e n e rg y and c o n t i n u e s u n t i l i t f i n d s a minimum o f e n e r g y .

Using i n t e r a c t i o n p o t e n t i a l s , d e r i v e d i n p a r t e x p e r i m e n t a l l y ,

one c an c a l c u l a t e the. e n e r g i e s o f o r g a n i c m o le cu le s as a

f u n c t i o n o f v a r i o u s g e o m e tr ic p a r a m e t e r s .

e n e r g y ) , V_, o f a m olecu le i s g iv e n by th e sum o f s i x5

components , which a re assumed to be i n d e p e n d e n t o f one

a n o t h e r i n th e s i m p l e s t t r e a t m e n t s and which a r e model

dependen t

I n v a le n c e f o r c e - f i e l d m ethods , th e m o le c u la r

The t o t a l m o le c u la r p o t e n t i a l e n e rg y ( o r th e s t e r i c

' U I T * x q rV and a re t h e components o f

where V.

- 11 -

e n e r g y which r e s u l t s from bond l e n g t h d e f o r m a t i o n , bond

a n g le d e f o r m a t io n (Baeyer s t r a i n ) , t o r s i o n a l s t r a i n

( P i t z e r s t r a i n ) , o u t - o f - p l a n e d e fo r m a t io n s a t t r i g o n a l

a to m s , coulombic i n t e r a c t i o n s and nonbonded i n t e r a c t i o n s

r e s p e c t i v e l y .

I n th e above t r e a t m e n t , c r o s s terms which a cc o u n t

f o r c o u p l i n g between th e components e . g . s t r e t c h - s t r e t c h t e rm ,

s t r e t c h - b e n d term and bend-bend terms a re n e g l e c t e d as

t h e y u s u a l l y a re v e r y s m a l l .

( a ) Bond L eng th D efo rm at ions

I n t u i t i v e l y , a chem ica l bond may be e n v i s io n e d as

a s p r i n g and th u s t h e r e i s a ”n a t u r a l " bond l e n g t h . The

p o t e n t i a l en e rgy s t o r e d i n a m o lecu le due to bond l e n g t h

d e f o r m a t i o n may be computed u s in g Hooke’s Law.

V, = I ? k (1 - l o ) 2 (2 )1

where ^ i s th e u n s t r a i n e d l e n g t h , 1 i s t h e obse rved

l e n g t h and i s the f o r c e c o n s t a n t depend ing on th e

s t i f f n e s s o f th e bond .

T h is term w i l l be s i g n i f i c a n t i f t h e r e a r e , i n th e

m o le c u le , one o r more bonds which a re f o r c e d by t h e i r

en v iro n m en t to have u n n a t u r a l bond l e n g t h s . D e fo rm a t io n

o f bond l e n g t h s i s an e n e r g e t i c a l l y c o s t l y p r o c e s s e . g .o

t o s t r e t c h o r compress a s i n g l e bond by o n ly 0 .0 3 A

c o s t s 0 . 3 k c a l . / m o l e .

(b) Bond Angle D efo rm a t ion

The use o f Hooke’s law t o d e s c r i b e bond a n g le

d e f o r m a t i o n s i s o n ly a good a p p ro x im a t io n f o r s m a l l a n g u la r

- 12 -

d i s p l a c e m e n t s b eca u se o f th e anharraonic n a t u r e o f m o le c u le s .

I n o r d e r to q u a n t i f y l a r g e d e fo r m a t io n s ( £ a . 2 5 ° ) , i t i s

n e c e s s a r y to i n t r o d u c e a d d i t i o n a l terms i n t o th e harmonic

e x p r e s s i o n . This i s u s u a l l y i n the form o f a c u b ic term

and th e f o l l o w i n g type of e x p r e s s i o n i s b e s t s u i t e d to 9

o u r model .

Ve = I H e (Ao2 - k1e A e 3 ) , (3)e

where A e = e - e Q» e b e in g obse rved bond a n g l e , e Q i s th e

e q u i l i b r i u m bond a n g l e , k i s the f o r c e c o n s t a n t d e pend ing©1on the s t i f f n e s s o f the v a l e n c y a n g le s and k i s th e c u b ic©

f o r c e c o n s t a n t .

Bond a n g le d e f o r m a t i o n i s an e n e r g e t i c a l l y cheap

p r o c e s s e . g . to deform a C-C-C bond a n g le by 1° from i t s

p r e f e r r e d lo w e s t e n e rg y v a lu e c o s t s o n ly abou t 0.01 k c a l /

mole and th u s bond a n g le v a r i a t i o n i s common.

( c ) T o r s i o n a l s t r a i n

A c o n c e p t , l o n g l a b e l l e d as P i t z e r s t r a i n , a r i s e s

f rom 1 , 2 i n t e r a c t i o n s 'be tween groups a t t a c h e d t o

c o n t ig u o u s c a rb o n a tom s. V a r i a t i o n s o f t o r s i o n a n g le s

from t h e i r most e n e r g e t i c a l l y f a v o u r a b l e p o s i t i o n i s t a k e n

i n t o acco un t i n th e f o l l o w i n g manner -

v, . = Zi . (1 + s cos n i o ) , (4 )U) OJ w

where k ^ i s the b a r r i e r t o f r e e r o t a t i o n , S assumes the

v a l u e o f - 1 f o r C =C-C-C and OG-C-H r o t a t i o n s i . e .

where th e minimum i s an e c l i p s e d c o n f o r m a t io n , and the

v a l u e o f +1 f o r a l l r o t a t i o n s around s i n g l e b o n d s , n i s

t h e p e r i o d i c i t y i . e . t h e no . o f t im es th e same conform

a t i o n o c c u r s i n one r e v o l u t i o n , and CO i s th e ob se rved

d i h e d r a l a n g l e .

- 13 -

This e x p r e s s i o n assumes t h a t th e h a r r i e r h e i g h t i s

i n s e n s i t i v e to th e changes i n th e n a t u r e o f th e s u b s t i t u e n t

and t h a t e ach e c l i p s i n g i n t e r a c t i o n makes an e q u a l c o n t r i b

u t i o n t o th e b a r r i e r . The e n e rg y b a r r i e r s have been fo u n d ,

e x p e r i m e n t a l l y , to be d e p e n d e n t , t o some e x t e n t , on th e

number o f s u b s t i t u e n t s b u t r e a s o n a b l y i n s e n s i t i v e to t h e i r

n a t u r e •

The t o r s i o n a n g le s a re s ig n e d q u a n t i t i e s c o r r e s

pond ing to th e P r e l o g - I n g o l d c o n v e n t io n which i s adopted

by c o n f o r m a t i o n a l a n a l y s i s t s (as opposed t o s p e c t r o -

s c o p i s t s ) :/

. /view N\

A must be r o t a t e d

c lo c k w ise to e c l i p s e D

and th e t o r s i o n a n g le i s

p o s i t i v e •

A must be r o t a t e d a n t i

c lo c k w is e t o e c l i p s e E

and th e t o r s i o n a n g le i s

n e g a t i v e .

Theory , to accoun t f o r th e o r i g i n o r p h y s i c a l

phenomena from which th e r o t a t i o n a l b a r r i e r a r i s e s i s f a r10

from mute and i s f i l l e d w i t h a p p a r e n t c o n c e p tu a l c o n f l i c t s .

The quantum m ec h an ica l r e s u l t s a r e c o n s i s t e n t w i t h

t h e view t h a t th e b a r r i e r a r i s e s from i n t e r a c t i o n s among

atoms n o t f o r m a l l y bound t o one a n o t h e r and i t i s t h e r e f o r e

- 14 -

n e c e s s a r y t o c o n s i d e r r e p u l s i o n ene rg y be tw een s u b s t i t u e n t s ,

e l e c t r o n i c k i n e t i c e n e r g y , e l e c t r o n - e l e c t r o n r e p u l s i o n and

n u c l e a r - e l e c t r o n i c a t t r a c t i o n . Whatever the e x p l a n a t i o n ,

t h e o m is s io n o f t h i s term from th e model , i n t r o d u c e s

g rave e r r o r s .

( d ) Out - o f - P lane D efo rm a t ion

When f o u r g roups ( o r a toms) a t t a c h e d t o an o l e f i n i c

l i n k a g e o r two groups ( o r a toms) a t t a c h e d t o a c a r b o n y l

group d e v i a t e s i g n i f i c a n t l y from c o p l a n a r i t y w i t h th e

t r i g o n a l c e n t r e s , the TT-bond i s weakened due t o p oo r o v e r

l a p , Out - o f - p l a n e ben d in g p o t e n t i a l s , i n a d d i t i o n t o

p u re t o r s i o n a l p o t e n t i a l s , must be added t o e n s u r e p r o p e r

geometry and e n e rg y r e p r e s e n t a t i o n o f e t h y l e n i c compounds

and k e t o n e s . The p o t e n t i a l e n e rg y s t o r e d i n th e m o lecu le

as a r e s u l t o f t h i s d e f o r m a t io n i s a ccoun ted f o r i n th e

f o l l o w i n g manner.

Vx = I i k x (180 - X )2 (5)X

where k ^ i s th e o u t - o f - p l a n e b e n d in g f o r c e c o n s t a n t and X i s th e im proper t o r s ion- a n g le a t t r i g o n a l a tom s.

( e ) Coulombic I n t e r a c t i o n Energy

Coulombic (o r e l e c t r o s t a t i c ) i n t e r a c t i o n s i n f l u

ence s t e r i c r e p u l s i o n s i n m o lecu le s which p o s s e s s a d i p o l e

e . g . k e t o n e s , am ides , and c o n s e q u e n t ly must be t a k e n i n t o

a c c o u n t i n any q u a n t i t a t i v e t r e a t m e n t o f m o le c u la r

c o n fo r m a t io n and e n e r g y . Accord ing t o c l a s s i c a l e l e c t r o

s t a t i c t h e o r y , th e e l e c t r o s t a t i c i n t e r a c t i o n e n e rg y Vq i s

g iv e n b y : -

Vq = Qi q-j , (6 )

where D i s th e e f f e c t i v e d i e l e c t r i c c o n s t a n t f o r i n t e r

a c t i o n s be tween ch a rged a tom s, q , q-j i s th e c h a rg e on

- 15 -

atoms i and j and r . . i s th e d i s t a n c e be tween atoms i, and

( f ) Nonbonded I n t e r a c t i o n E n e r g i e s

Non-bonded i n t e r a c t i o n s a r e th e most t ro u b le so m e

components o f th e s t e r i c en e rg y and a re th e a t t r a c t i v e and

r e p u l s i v e f o r c e s t h a t e x i s t be tween two atoms o r groups

o f atoms s u f f i c i e n t l y c l o s e i n space ( e i t h e r i n t r a - o r

i n t e r m o i e c u l a r ) b u t n o t d i r e c t l y bonded t o one a n o t h e r .

These f o r c e s a r e q u a l i t a t i v e l y a p p a r e n t from th e e x i s t e n c e

o f l i q u i d s and s o l i d s on one hand and from t h e i r r e l a t i v e

i n c o m p r e s s i b i l i t y on th e o t h e r .

F o r an i s o l a t e d p a i r o f s p h e r i c a l l y symmetric atoms

( o r m o l e c u l e s ) , th e p o t e n t i a l e n e rg y i s a f u n c t i o n o f th e

s e p a r a t i o n o f th e a tomic (o r m o le c u l a r ) c e n t r e s and has the

a p p ro x im a te form, i l l u s t r a t e d be low .

E q u il ib r iu m s e p a r a t io n

- 16 -

F o r n o n - s p h e r i c a l atoms ( o r m o l e c u l e s ) , th e p o t e n t i a l

e n e rg y depends a l s o on the o r i e n t a t i o n o f the atoms (o r 11 12m o le c u le s ) 9 and would t h e r e f o r e r e q u i r e an a d d i t i o n a l

p a r a m e t e r i n th e p o t e n t i a l f u n c t i o n , b u t t h i s problem has

n o t as y e t been so lved*

The f o r c e s be tween atoms (o r m o le c u le s ) may be

o b t a i n e d from th e g r a d i e n t o f th e p o t e n t i a l ene rg y curveo

and f o r s m a l l s e p a r a t i o n s ( l e s s th an 3A), the f o r c e s a reo

r e p u l s i v e and f o r l a r g e r s e p a r a t i o n s ( g r e a t e r than i+ A ) ,

t h e y a re a t t r a c t i v e *

I n p r i n c i p l e , the p o t e n t i a l cu rve ( a l s o r e f e r r e d to

as van d e r Waals p o t e n t i a l ) f o r any p a r t i c u l a r p a i r o f

atoms can be c a l c u l a t e d from a c o n s i d e r a t i o n o f the

d e v i a t i o n o f th e c o r r e s p o n d in g gas from i d e a l b eh av io u r*

However, i n p r a c t i c e , th e p o t e n t i a l c u rv e s have proved

d i f f i c u l t t o measure e x p e r i m e n t a l l y and a c c u r a t e van d e r1 3Waals p o t e n t i a l s a re a v a i l a b l e o n ly f o r r a r e g a se s and

a few s p e c i a l c a s e s e . g . N2 and CH^. This i s u n f o r t u n a t e

s i n c e t h e y a r e r e s p o n s i b l e f o r a l a r g e p r o p o r t i o n o f the

s t r a i n - c a u s i n g d e f o r m a t io n s i n m o le cu le s and c o n s e q u e n t l y ,

s t r o n g l y i n f l u e n c e m o le c u la r geom etry , v i b r a t i o n a l

f r e q u e n c i e s and e n t h a l p y .

The f u n c t i o n a l form Vr which d e s c r i b e s i n t r a m o l e c

u l a r nonbonded i n t e r a c t i o n s i s u s u a l l y t a k e n o v e r from

known o r assumed i n t e r a t o m i c o r i n t e r m o l e c u l a r i n t e r a c t i o n 1Up o t e n t i a l s . A l though t h e r e i s no c l e a r p h y s i c a l b a s i s

f o r t h i s e x t r a p o l a t i o n , t h i s method has proved t o be

s a t i s f a c t o r y and r e a s o n a b l y s u c c e s s f u l even a l t h o u g h i t

n e g l e c t s t h e n a t u r e o f th e m a t e r i a l be tw een th e a tom s.

The two most w id e ly used ty p e s o f i n t e r m o l e c u l a r i n t e r

a c t i o n p o t e n t i a l s which have "been used to d e s c r i b e i n t r a

m o le c u l a r nonbonded i n t e r a c t i o n s a r e the two - p a ra m e te r

L e n n a rd - J o n e s p o t e n t i a l (7) and t h r e e - p a r a m e t e r Buckingham

p o t e n t i a l ( 8 ) .

V ( r ) = A/RK - B/R , w i t h H = 12 o r 9 (7)

V ( r ) = A exp ( - ER) - C/R^ ( 8 )

I n b o t h (7) and ( 8 ) , th e f i r s t term d e s c r i b e s th e

r e p u l s i v e s h o r t range f o r c e s which o c c u r when th e d i s t a n c e

be tw een th e c e n t r a l atoms i s l e s s t h a n the sum o f the

v a n d e r Waals r a d i i and which r e s u l t from a b a l a n c e be tw een

n u c l e a r r e p u l s i o n s , e l e c t r o n i c k i n e t i c e n e r g i e s , e l e c t r o n i c

r e p u l s i o n s and n u c l e a r - e l e c t r o n i c a t t r a c t i o n s * The

second term i n (7) and ( 8) i s e a s i e r to e s t i m a t e and

a c c o u n t s f o r th e London d i s p e r s i o n f o r c e s .

The p r e c i s e form o f the p o t e n t i a l which was used i n

th e development o f th e W h i t e - B o v i l l a l k a n e / a l k e n e f o r c e -9 15f i e l d » was d e r i v e d by W il l iams by a l e a s t - s q u a r e s

p r o c e d u r e t o r e p r e s e n t i n t e r m o l e c u l a r i n t e r a c t i o n s i n

c r y s t a l l i n e hy d ro ca rbo n s e . g . h e a t s o f s u b l i m a t i o n , l a t t i c e

c o n s t a n t s and s t r u c t u r a l d e t a i l s and has th e f o l l o w i n g form,

Vr = Z £ ( - 2/cxJ* + exp (1 2 (1 - o c ) ) ) ( 9 )r

where th e e x p r e s s i o n s i s summed o v e r a l l p a i r s o f non

bonded atoms s e p a r a t e d by t h r e e o r more bonds ( d i f f e r e n t

c o n v e n t io n s a re adopted by o t h e r w orkers i n th e f i e l d ) .

Bond s t r e t c h i n g p o t e n t i a l s t ake a cc o u n t o f th e van d e r

Waals i n t e r a c t i o n be tw een atoms t h a t a re bonded t o each

- 18 -

o t h e r , w h i l e bond a n g le bend ing p o t e n t i a l s a l lo w f o r

nonbonded i n t e r a c t i o n s be tween atoms bound to a common

T his e x p r e s s i o n ( 9 ) assumes t h a t th e t o t a l van d e r

Waals i n t e r a c t i o n e n e rg y i s e q u a l t o the sum o f th e e n e r g i e s

o f each p a i r o f ( s p h e r i c a l ) atoms ( “p a i r w i s e a d d i t i v e

f o r m u l a t i o n " ) . I t has been shown t h a t t h i s method g iv e s

some i n c o r r e c t r e p r e s e n t a t i o n s , p a r t i c u l a r l y i f i n t e r

a c t i n g sys tem s a re n o t l o c a l i s e d , b u t , a t p r e s e n t , t h e r e i s

no s a t i s f a c t o r y a l t e r n a t i v e and i t i s hoped t h a t some o f

t h e s e a p p ro x im a t io n s may be averaged ou t o r ab so rb ed i n

th e p a r a m e t r i z a t i o n o f th e f o r c e - f i e l d , p a r t i c u l a r l y i f

c a r e i s t a k e n i n th e e v a l u a t i o n o f a d j u s t a b l e p a ra m e te r s

(c*and £ ) i n ( 9 ) , f o r example , by i n c l u d i n g e x p e r i m e n t a l

d a t a w i t h sm a l l s e p a r a t i o n s s i n c e p o t e n t i a l f u n c t i o n s a re

l e a s t r e l i a b l e i n t h i s a r e a .

In ( 9 ) ol i s a f u n c t i o n o f th e d i s t a n c e c o - o r d i n a t ep

a lo n e and i s e q u a l to ------------ where r i s van d e r Waals* *r 1 r 2d i s t a n c e be tween atoms '1 and 2 , and r^ * and r ^ * a r e the

van d e r Waals r a d i i o f atoms 1 and 2 . £ i s a f u n c t i o n o f

t h e e n e rg y c o - o r d i n a t e and i s a p a ra m e te r which v a r i e s w i th

t h e s i z e o f th e atom, s i n c e i t i s c l e a r l y more d i f f i c u l t to

push two l a r g e a tom s, l i k e i o d i n e , t o g e t h e r to some sm a l l

v a l u e o f t h a n i t i s to push two sm a l l atoms to th e same

v a lu e o f 0 6 . I n some f o r c e f i e l d s , th e v a lu e o f £ f o r a

p a i r o f d i s s i m i l a r atoms i s t a k e n to be th e g e o m e t r i c mean

o f th e v a l u e s f o r i d e n t i c a l p a i r s o f th e d i f f e r e n t atoms

- 19 -

i n t e r a c t i n g , w h i l e i n o t h e r s , £ i s an i n d e p e n d e n t p a r a m e t e r .

However, i n v iew o f th e a fo re m en t io n e d a p p r o x i m a t i o n s , i t

would a p p e a r more s e n s i b l e to have as many in d ep e n d en t non

bonded p a ra m e te r s as p o s s i b l e and use th e g e o m e tr ic mean

as th e s t a r t i n g v a lu e o f £ i n p a r a m e t r i s a t i o n s i n such

c a s e s •

Some te rm s which w i l l a p p e a r i n f u t u r e d i s c u s s i o n s

c o n c e r n i n g nonbonded p o t e n t i a l f u n c t i o n s and p a ra m e te r s

a r e d e f i n e d as f o l l o w s .

a " h a r d ” atom i s one f o r which th e p l o t o f th e f o r c e

v e r s u s d i s t a n c e shows a s t e e p s l o p e ,

a " s o f t " atoms i s one f o r which th e p l o t o f f o r c e

v e r s u s d i s t a n c e shows a g e n t l e s l o p e ,

a " b i g g e r " atoms i s one where th e e q u i l i b r i u m

s e p a r a t i o n i s s l i d f u r t h e r to th e r i g h t ,

a " s m a l l e r " atom i s one where the e q u i l i b r i u m

s e p a r a t i o n i s s l i d f u r t h e r to th e l e f t .

The r e f e r e n c e g e o m e t r i e s , f o r c e c o n s t a n t s and the

e x p r e s s i o n s f o r th e p o t e n t i a l e n e rg y components o f th e

s t e r i c e n e rg y a re r e f e r r e d to c o l l e c t i v e l y as th e f o r c e

f i e l d . The m ajor ty p e s o f f o r c e f i e l d used i n v i b r a t

i o n a l a n a l y s i s and m o le c u la r mechanics a r e th e v a l e n c e

f o r c e f i e l d (VFF), which i s d e s c r i b e d above, and the

U re y -B ra d le y f o r c e f i e l d (UBFF). The UBFF c o n t a i n s

c o n t r i b u t i o n s due to bond s t r e t c h i n g , bond r o t a t i o n and

a n g le b e n d in g , i n c l u d e s a l l nonbonded i n t e r a c t i o n s > even

th o s e be tw een atoms s e p a r a t e d by two bonds i . e . 1 , 3

i n t e r a c t i o n s and om its c r o s s t e r m s .

- 20 -

The VPF i s more g e n e r a l and can always he m od if ied

i n such a way as to a c h ie v e a b e t t e r f i t be tw een observed

and c a l c u l a t e d q u a n t i t i e s , however, t h e r e a r e computer

programming c o m p l e x i t i e s a s s o c i a t e d w i t h th e i n t r o d u c t i o n

o f c r o s s te rm s and th e t im e-consum ing e f f o r t t o a s s e s s

them. The UBFF i s , however , l e s s c o m p l ica te d t h a n th e

There i s a n o th e r type o f f o r c e f i e l d , the c e n t r a l

f o r c e f i e l d , which assumes t h a t m o lecu le s a re h e ld t o g e t h e r

by f o r c e s a c t i n g a lo ng l i n e s be tween each p a i r o f a tom s,

b u t t h i s ty pe o f f o r c e f i e l d i s r a r e l y u s e d .

1 . 3 D e t e r m in a t io n o f H eats o f Fo rm a t ion

The e n e rg y m in im i s a t i o n program used i n f o r c e f i e l d

c a l c u l a t i o n s , m in im ises th e en e rgy w i th r e s p e c t to the

c a r t e s i a n c o - o r d i n a t e s and s u p p l i e s the d e t a i l e d geom etry ,

t h e s t e r i c e n e rg y components and the t o t a l s t e r i c e n e r g y ,

Vs , o f d i f f e r e n t c o n f o r m a t i o n a l minima o f a m o le c u le .

The s t e r i c e n e rg y , Vs , c o r r e s p o n d s to an i s o l a t e d m olecu le

i n a " h y p o t h e t i c a l m o t i o n l e s s s t a t e a t 0°K" I n o r d e r

t o compare th e c a l c u l a t e d s t e r i c e n e rg y , Vs, ( o f a

m o le c u le ) w i t h an e x p e r i m e n t a l q u a n t i t y , u s u a l l y th e h e a t

o f f o r m a t i o n , A H 0f (which i s d e f i n e d as t h e h e a t ab so rbed

o r r e l e a s e d upon f o r m a t i o n o f th e compound from the

s t a n d a r d s t a t e s o f th e e le m e n ts composing i t . ) i t i s n e c e s s a r y

t o t a k e a cc o u n t o f t h e e n t h a l p i e s o f v i b r a t i o n , r o t a t i o n and

t r a n s l a t i o n and th e v i b r a t i o n a l zero p o i n t e n e r g y .

These can be induced by making e m p i r i c a l c o r r e c t i o n s

- 21 -

(g roup o r bond c o n t r i b u t i o n s ) o r v i a s t a t i s t i c a l m e c h an ic s .

The f i r s t app roach e . g . group in c rem en t scheme,

assumes t h a t , w i t h i n l i m i t s , m o le c u la r s t r u c t u r a l groups

have t h e same c o n t r i b u t i o n to th e h e a t o f f o r m a t i o n r e g a r d

l e s s o f t h e n a t u r e o f th e t o t a l m o le c u la r s t r u c t u r e .

T h is i s n o t an u n r e a s o n a b le a s su m p t io n ( se e T ab le 1 ) i f

i t i s remembered t h a t e x p e r i m e n t a l h e a t s o f f o r m a t i o n a re

th e m se lv e s u n c e r t a i n t o a few t e n t h s o f a k c a l . / m o l e . The

e n t h a l p y o f f o r m a t i o n o f a m olecu le

Table 1

Compound AH °f ( g a s , 25°C) k c a l . / m o l e .

In c re m e n t , k c a l . / m o l e •

° 2H6 - 2 0 . 21+ - 4 . 5 9

o- 2 4 .8 3 - 5 . 5 3

S H10 -3 0 .3 6 - 4 .7 4

C5H12 - 3 5 .1 0 - 4 . 8 2

c 6H11+ - 3 9 .9 2 - 4 . 9 3

V i s • ' - 4 4 .8 5 -5 .01

° 8H1 8 - 4 9 .8 6 - 4 . 8 0

C9H20 - 54.66 - 4 .9 6

C10H22 - 5 9 .6 2

i s c a l c u l a t e d by add ing th e s t e r i c e n e rg y , Vs, to th e sura

o f a p p r o p r i a t e group e n t h a l p y i n c r e m e n t s , which c an be

o b t a i n e d from th e s t e r i c e n e r g i e s and e x p e r i m e n t a l

e n t h a l p i e s by a l i n e a r i e a s t - s q u a r e s p ro c e d u re e . g .

f o r 5 - e t h y l i d e n e no^bornene -

- 22 -

A H ° f. ( g a s , 25°C) = E + 3 I ( = CH)+ 1 l ( = C)+ 1 1 (- C H J + 21i s j(- CH2 )+ 21 (- CH) (10)

Bond in c rem en t schemes a re adopted i n a s m i l a r

f a s h i o n . These group and bond e n t h a l p y in c rem en t schemes

a r e more c o n v e n ie n t t h a n t h e s t a t i s t i c a l mechanics scheme

and t h e y a l s o t a k e i n t o accoun t e r r o r s which e x i s t i n th e

p a r a m e t r i z a t i o n .

I n th e a l t e r n a t i v e s t a t i s t i c a l mechanics ap p ro a ch ,

i t i s n e c e s s a r y to add to th e c a l c u l a t e d s t e r i c e n e rg y , th e

r o t a t i o n a l and t r a n s l a t i o n a l e n t h a l p i e s (= 3RT), th e

v i b r a t i o n a l e n t h a l p y and z e ro p o i n t e n e rg y i n o r d e r to

o b t a i n th e c a l c u l a t e d h e a t o f f o r m a t i o n . The 3N - 6

v i b r a t i o n a l f r e q u e n c i e s , V ^ , n e c e s s a r y f o r th e e v a l u a t i o n

o f th e l a t t e r two components , c an be o b t a in e d by d i a g o n a l -—-5- ——

i s i n g th e m a t r i x , M 2 B M~2 , where B i s t h e m a t r i x o f th e

p o t e n t i a l e n e rg y second d e r i v a t i v e s and M i s th e d i a g o n a l

m a t r i x o f th e a tomic m as se s . The v i b r a t i o n a l z e ro p o i n to 3N-6e n e r g y , , i s g iv e n by E y ^ o = £ h y v . > where h

2 i =1 1i s P l a n c k ' s c o n s t a n t , w h i le a t Tem pera ture T, th e

v i b r a t i o n a l e n t h a l p y , *s c a l c u l a t e d as3N-6

HVIB = kT l ^ O - e x p ( - h V ^ / k T ) ) ,

where k i s B o l tzm an’s c o n s t a n t and h i s P l a n c k ' s

c o n s t a n t •

- 23 -

I f th e e n t h a l p i e s o f v i b r a t i o n a re e v a l u a t e d f o r

th e d i f f e r e n t c o n f o r m a t i o n a l minima o f one m o le c u le , i t

i s found t h a t th e v a l u e s seldom d i f f e r by about more t h a n

1 k c a l / m o l e , which im p l i e s t h a t d i f f e r e n c e s i n s t e r i c

e n e r g i e s can be equa ted w i t h c o n f o r m a t i o n a l e n e r g i e s .

I t i s im p o r t a n t t h a t c a r e shou ld be t a k e n when

e q u a t i n g d i f f e r e n c e s i n s t e r i c e n e r g y , d i f f e r e n c e s i n

e n t h a l p y and d i f f e r e n c e s i n f r e e e n e r g y . Energy i s more

i n t u i t i v e l y c o n v e n ie n t w h i l e e n t h a l p y i s more e x p e r i m e n t

a l l y and th e rm o d y n am ica l ly c o n v e n ie n t and t h e y a re

i n t e r r e l a t e d by P A v te r m s ,

A h = Ae + p Av , (11)

u s u a l l y th e e r r o r s inv o lv e d i n t h e s e terms a r e sm a l l

u n d e r th e c o n d i t i o n s o f i n t e r e s t : 25°C (298K) and

1 a t m . p r e s s u r e .

F r e e e n e rg y ( AG) i s the thermodynamic v a r i a b l e

which d e te r m in e s r e l a t i v e s t a b i l i t y :

A g = A h - tA s = -RT I n K

where A h i s th e e n t h a l p y c h a n g e , A S i s th e e n t r o p y and

K i s th e e q u i l i b r i u m c o n s t a n t . From t h i s e q u a t i o n , i t i s

e v i d e n t t h a t t h e f r e e e n e rg y i s composed o f an e n t h a l p y

( o r en e rg y ) term as w e l l as an entropy term ( A s ) .

Whereas A h i s e s s e n t i a l l y t e m p e r a tu r e in d e p e n d e n t ,

i n c r e a s i n g the t e m p e r a tu re i n c r e a s e s the e n t r o p y te rm .

I n most c a s e s , n e a r ambient t e m p e r a t u r e s , the e n t h a l p y

term d o m in a t e s . As su c h , i t i s u s u a l l y s a f e t o assume

- 24 -

t a c i t l y t h a t i n f o r m a t i o n abou t A h i s c o n c e p t u a l l y

e q u i v a l e n t to t h a t a bou t A g . I n any c a s e , i t i s AH

d i f f e r e n c e s t h a t d e f i n e s t r a i n e n e rg y and AG d i f f e r e n c e s

t h a t d e f i n e r e l a t i v e thermodynamic s t a b i l i t y .

From a knowledge o f th e f r e e en e rg y d i f f e r e n c e be tw een

two co n fo rm ers a t a p a r t i c u l a r t e m p e r a t u r e , i t i s p o s s i b l e

to deduce th e e x t e n t t o which th e c o n fo rm ers a r e p r e s e n t

e . g . A G° f o r t h e change gauche to a n t i b u t ane i s - 0 . 3 9

k c a l / m o l e , which c o r r e s p o n d s to an e q u i l i b r i u m c o n s t a n t

K v a l u e o f 1 . 9 . Thus a t 300°K, b u ta n e i s a p p ro x im a te ly

65% a n t i and 35% g a u c h e .

1 P a r a m e t r i z a t i o n o f Fo rce F i e l d s

As p r e v i o u s l y m en t ioned , t h e f o r c e c o n s t a n t s ,

r e f e r e n c e g e o m e t r i e s and th e p o t e n t i a l f u n c t i o n s a re

r e f e r r e d t o c o l l e c t i v e l y as a f o r c e f i e l d , which t h e r e

f o r e ' d e s c r i b e s th e r e s t o r i n g f o r c e s which o c c u r i n a

m o lecu le when th e geometry o f minimal p o t e n t i a l e n e rg y i s

d i s t u r b e d ' ^ . I t i s t h e r e f o r e n e c e s s a r y to d e r i v e

optimum v a l u e s f o r th e f o r c e f i e l d p a ra m e te r s i n such a

manner t h a t th e r e s u l t a n t f o r c e f i e l d w i l l c o r r e c t l y

p r e d i c t t h e g eo m e tr ic a n d / o r s p e c t r o s c o p i c a n d /o r

thermodynamic p r o p e r t i e s o f a l a r g e v a r i e t y o f m u l t i fo rm

m o le c u l e s , w i t h i n th e l i m i t s o f e x p e r i m e n t a l e r r o r .

In o r d e r t o a c h ie v e t h i s s u c c e s s , i t i s e s s e n t i a l

t o have a v a i l a b l e a l a r g e body o f e x p e r i m e n t a l d a t a

which i s b o t h d i v e r s e and , e q u a l l y i m p o r t a n t , a c c u r a t e and

a l s o t o use th e minimum number o f n e c e s s a r y a d j u s t a b l e

p a r a m e t e r s e . g . t o omit n e g l i g i b l e c r o s s - t e r m s , o t h e r w i s e

s e r i o u s problems r e s u l t i n g from o v e r p a r a m e t r i z a t i o n w i l l

- 25 -

a r i s e •

I n i t i a l e s t i m a t e s f o r f o r c e c o n s t a n t s and p o t e n t i a l

f u n c t i o n s f o r bond s t r e t c h i n g , a n g le b e n d ing and o u t - o f

p l a n e b en d in g a re u s u a l l y borrowed from v i b r a t i o n a l a n a l y s i s

w h i l e bond l e n g t h s and a n g le s a r e c h osen from e l e c t r o n

d i f f r a c t i o n , microwave o r X - ray r e s u l t s . I n bond ang le18 19d e f o r m a t i o n , i t has been proved 9 t h a t to rep ro d u c e

a c c u r a t e l y e x p e r i m e n t a l e n e r g i e s as w e l l as g e o m e t r i e s

t h a t i t i s v i t a l l y im p o r ta n t t o use d i f f e r e n t s t r a i n -

f r e e a n g le s f o r d i f f e r e n t s u b s t i t u t i o n o f the c e n t r a l

c a r b o n i n th e f o r c e f i e l d . The s t a r t i n g f o r c e c o n s t a n t and

p o t e n t i a l f u n c t i o n f o r t o r s i o n a l i n t e r a c t i o n s a r e t a k e n

from microwave a n a l y s i s o f r o t a t i o n a l b a r r i e r d a t a .

An a c c u r a t e d e s c r i p t i o n o f van d e r Waals c u rv e s

f o r nonbonded i n t e r a c t i o n s i s most e s s e n t i a l , b u t t h e y

a r e now known o n ly i n th e c r u d e s t way and c o n s e q u e n t ly th e

nonbonded e n e r g i e s a r e th e most d i f f i c u l t t o p a r a m e t r i z e

f o r . S in c e th e L e n n a rd -J o n e s and Buckingham type p o t e n t i a l s

a r e known t o be l e a s t r e l i a b l e a t sm a l l i n t e r a t o m i c s e p a r

a t i o n , i t i s v i t a l t o i n c l u d e as much e x p e r i m e n t a l d a t a

which e x h i b i t t h i s f e a t u r e as p o s s i b l e .

I n p r a c t i c e , i t i s p o s s i b l e to o b t a i n numerous s e t s

o f o p t im i s e d p a ra m e te r s e ach o f which w i l l g iv e e s s e n t i a l l y

t h e same r e s u l t s , b u t ex treme c a r e must be t a k e n w i t h th e

b a la n c e be tw een th e f u n c t i o n s and w i t h t h e i n t e r p r e t a t i o n

o f th e r e s u l t s .

Most w orke rs adop t one o f two methods t o d e r i v e

- 26 -

optimum v a l u e s f o r f o r c e f i e l d p a r a m e te r s - (a ) t r i a l - a n d -

e r r o r method o r (b) l e a s t - s q u a r e s p r o c e d u r e .

I n method ( a ) , t h e f o r c e f i e l d p a ra m e te r s a r e a l t e r e d

i n a t r i a l - a n d - e r r o r manner i n an a t t e m p t to f i n d optimum

v a l u e s . T h is method consumes l a r g e amounts o f human and

com pute r r e s o u r c e s as i t i s d i f f i c u l t t o p r e d i c t a c c u r

a t e l y th e e f f e c t o f a p a ra m e te r change on th e o v e r a l l

geom etry and en e rg y o f a l l m o lecu le s in v o lv e d i n th e

p a r a m e t r i z a t i o n .

Method (b) was implemented by Lifeon and W arshel i n201968 and i n v o lv e s an e l a b o r a t e l i n e a r l e a s t - s q u a r e s

p ro c e d u re to f i n d th e b e s t p o s s i b l e v a l u e s f o r th e f o r c e

f i e l d p a ra m e te r s from s t r u c t u r a l , thermodynamic and

v i b r a t i o n a l d a t a by m in im is in g th e s q u a r e s o f th e d i f f e r

ences be tw een e x p e r i m e n t a l and c a l c u l a t e d p r o p e r t i e s w i t h

r e s p e c t to f o r c e f i e l d p a ra m e te r s and p roduce a

CONSISTENT FORCE FIELD. The squ a red term i s u s u a l l y w e igh ted

by an amount which i s i n v e r s e l y p r o p o r t i o n a l t o th e sq u a re

o f th e s t a n d a r d d e v i a t i o n o f th e c o r r e s p o n d i n g e x p e r i m e n t a l

o b s e r v a t i o n . T h is method has th e adv an tag e o f g i v i n g

i n f o r m a t i o n c o n c e rn in g th e o m is s io n o f p a r a m e te r s ( i . e . ones

which do n o t d i f f e r s i g n i f i c a n t l y from z e r o ) and th e

dependence o r independence w i t h i n groups o f p a r a m e te r s

b u t . b e c a u s e o f th e need t o e v a l u a t e th e second d e r i v a t i v e s

o f p o t e n t i a l e n e rg y i n the c a l c u l a t i o n o f v i b r a t i o n a l

f r e q u e n c i e s , t h i s method r e q u i r e s th e a v a i l a b i l i t y o f l a r g e

amounts o f computer t im e . The agreem ent w i t h e x p e r i m e n t a l21d a t a i s r e l i a b l e - Ermer and L If son d ev e lo ped an a lk e n e

c o n s i s t e n t f o r c e f i e l d where t h e a v e rage a b s o l u t e d i f f e r

ences be tween obse rved and c a l c u l a t e d bond l e n g t h s , bond

- 27 -

a n g le s and t o r s i o n a n g le s used i n th e o p t i m i s a t i o n a re

0*003 X, 0*5° and 1 .0 ° r e s p e c t i v e l y o v e r a t o t a l o f JL+2+

s t r u c t u r a l q u a n t i t i e s , be tween ob se rved and c a l c u l a t e d

h e a t s o f h y d r o g e n a t io n 0*92 k c a l /m o l e o v e r 10 thermo

c h e m ic a l q u a n t i t i e s and be tw een observed and c a l c u l a t e d_-i

f r e q u e n c i e s 15»U cm o v e r 259 v i b r a t i o n a l f r e q u e n c i e s .

^ t i s n o te w o r th y t h a t method (a ) p roduces e q u a l l y good

r e s u l t s . .

An a l t e r n a t i v e method, which may be r e g a r d e d as a

h y b r id o f methods (a ) and ( b ) , may be used and i t i s a

consequence o f th e f a c t t h a t i t i s more d i f f i c u l t t o

r e p r o d u c e p r o p e r t i e s a s s o c i a t e d w i t h th e e n e rg y o f

m o le c u le s t h a n th o se a s s o c i a t e d w i th th e geometry i . e .

e n e rg y p a ra m e te r s a r e more f o r c e f i e l d dependen t t h a n

g e o m e t r i c p a r a m e t e r s . To overcome t h i s problem e f f i c i e n t l y

th e f o r c e c o n s t a n t s i n th e f o r c e f i e l d i . e . k^ , k^ , k ^

and £ may be in c lu d e d i n a l i n e a r l e a s t - s q u a r e s

o p t i m i s a t i o n a lo n g w i t h th e group e n t h a l p y i n c r e m e n t s .

1 . 5 Energy M in im is a t io n

G e n e r a l l y th e c o - o r d i n a t e s o f a m o le c u le , which

a r e i n i t i a l l y used i n a m o le c u la r mechanics s t u d y a r e

o n ly app rox im ate a s , f o r example , t h e y have been d e r i v e d

from m o le c u la r m ode ls . In o r d e r to o b t a i n i n f o r m a t i o n

r e g a r d i n g th e e q u i l i b r i u m p r o p e r t i e s o f a m o le c u le , i t i s

n e c e s s a r y t o a dop t an en e rgy m i n i m i s a t i o n scheme which

w i l l m in im ise th e s t e r i c e n e rg y o f th e m o le c u le , Vs, w i t h

r e s p e c t to th e c o - o r d i n a t e s by s y s t e m a t i c a l l y a d j u s t i n g

th e p o s i t i o n s o f th e atoms and which w i l l a l s o p roduce

- 28 -

r e s u l t s which a re "both c o n s i s t e n t and r e l i a b l e . At p r e s e n t ,

t h e r e i s no s i n g l e scheme which i s g e n e r a l l y a c c e p te d as

a l l t h e m in i m i s a t i o n methods which a re u s e d , have known 22sh o r t c o m in g s , However, th e s u c c e s s o r f a i l u r e o f one

scheme depends l a r g e l y on the p o s i t i o n on the p o t e n t i a l

e n e rg y h y p e r s u r f a c e t h a t th e model m o lecu le l i e s .

The i n p u t c o - o r d i n a t e s a r e u s u a l l y c a r t e s i a n s i n c e

t h e y a re s i m p l e r to u se and e a s i e r to programme th a n

i n t e r n a l c o - o r d i n a t e s which a r e , however , i n d i s p e n s a b l e

f o r m o le cu le s composed o f more t h a n 60 a tom s.

The most w id e ly used e n e rg y m in im i s a t i o n schemes

w i l l be d i s c u s s e d i n th e f o l l o w i n g s e c t i o n s , a l t h o u g h the

o v e r a l l m in i m i s a t i o n method, which i s a d o p te d , i s o f t e n

a c o m b in a t io n o f two d i f f e r e n t schemes.

At a p o t e n t i a l en e rg y minimum, th e n e t f o r c e

a c t i n g on any one atom i s ze ro i . e . a n e c e s s a r y c o n d i t i o n

f o r an e n e rg y minimum i s t h a t th e p a r t i a l d e r i v a t i v e s o f

t h e e n e rg y w i t h r e s p e c t t o each c o - o r d i n a t e e q u a l z e r o ,

I . e . d v s (x ) = o , i = 1 , 2 , 3N

6 x iwhere N i s t h e number o f atoms i n th e m olecu le and x i s

a c o - o r d i n a t e v e c t o r .

The p o t e n t i a l e n e rg y o f the t r i a l model can be

expanded i n a T a y lo r s e r i e s ( t r u n c a t e d a f t e r th e l i n e a r

te rm ) abou t an e n e rg y minimum:

- 29 -

v 0 ( x + 6 x ) y = v = v j x ) ^ + X ( f s , ^ ) . A x i■S i=1 (d x A )

x=x s(1 2 )

where x i s a g iv e n s t a r t i n g p o i n t n o t f a r from th e sminimum.

I n o r d e r to s a t i s f y the c o n d i t i o n f o r an e n e rg y

minimum, th e d e r i v a t i v e s o f th e ene rg y w i t h r e s p e c t to each

o f t h e 3N c o - o r d i n a t e s a r e t a k e n :

3N ^ 3N£ V (x+ 6 x)) = z ( ^VS (x))

3=1 (“ T ^ )x=x 3=1 ( ^ x 3 )x=xs

I I < <32v s ( x >) _ A x ± = o (13)3=1 1=1 ( 1 7 J T I ~ ) x'=x

sE q u a t io n (13) i s e q u i v a l e n t , i n m a t r i x n o t a t i o n t o :

V V (x + 6 x ) = V v (x ) + P 8 x = o (1 4 )D O D O 5

where VV i s th e g r a d i e n t o f V, and F i s th e m a t r i x o f th e ssecond d e r i v a t i v e s o f V. From (14)> i t c an he deduced

t h a t

6 * = -Fs “1. ^ Vs ^ Xs^ ( 1 5 ) ,

where F i s th e i n v e r s e o f F .

( a ) Scheme 1 : S t e e p e s t Descen t

T h is was th e f i r s t g e n e r a l scheme t o he i n t r o d u c e d23i n t o m o le c u l a r mechanics c a l c u l a t i o n s , hy Wiherg , i n

1965 and i t i n v o lv e s c h a n g in g , i n t u r n , e ach c o - o r d i n a t e o f

t h e m o lecu le hy a s m a l l i n c r e m e n t , c a l c u l a t i n g the

- 30 -

c o r r e s p o n d i n g e n e rg y change and th e n r e s t o r i n g th e c o

o r d i n a t e to i t s i n i t i a l v a l u e . A f t e r t h i s p ro c e d u re has

b e en a p p l i e d to each c o - o r d i n a t e i n th e m o le c u le , th e

c o - o r d i n a t e s a r e t h e n each moved hy an amount p r o p o r t i o n a l

t o i t s p a r t i a l d e r i v a t i v e o f en e rg y w i th r e s p e c t t o th e

c o - o r d i n a t e , i n a d i r e c t i o n which low ers th e e n e r g y . This

p ro c e d u re i s r e p e a t e d u n t i l the d i f f e r e n c e i n e n e rg y from

one c y c l e to th e n e x t i s l e s s t h a n a s t i p u l a t e d v a l u e .

To o b t a i n a m a th e m a t i c a l d e s c r i p t i o n o f th e

s t e e p e s t d e s c e n t method, i t i s n e c e s s a r y to s u b s t i t u t e a•4

d i a g o n a l m a t r i x D w i t h where L i s a s c a l i n g

c o n s t a n t , f o r F i n e q u a t i o n (15)> which g i v e s :

5 x , = -L ( ^ V ( x ) ) (1 6 )< W s

2UBixon and Lifeon d e te r m in e the c o n s t a n t L from a g iv e n

v a lu e f o r t h e r o o t - m e a n - s q u a r e change of th e C a r t e s i a n

c o - o r d i n a t e s ( <JQ)

L = ° 0 (3N £ , i & r >

The v a lu e o f ' G must be p r o p e r l y c hosen d u r i n g

t h e v a r i o u s s t a g e s o f th e m in i m is a t i o n p r o c e s s , o t h e r

w ise th e co nvergence i s u n n e c e s s a r i l y s low ,

A l l i n g e r and o t h e r workers have found t h a t t h i s

m i n i m i s a t i o n method a v o id s the d i f f i c u l t y o f g e t t i n g

s t u c k i n a s a d d l e p o i n t on th e h y p e r s u r f a c e and t h a t i t

i s most e f f i c i e n t ( i . e . r a p i d m i n i m i s a t i o n ) when th e

e n e r g y and geometry o f th e m olecu le a r e f a r removed

from i t s minimum b u t becomes l e s s e f f i c i e n t as the

- 31 -

minimum i s ap p ro a ch e d . A no the r d i s a d v a n t a g e , a p a r t from

t h e s c a l i n g p rob lem s , i s t h a t t h i s method f i n d s b o t h

g l o b a l and l o c a l minima as w e l l as maxima. The f i n a l

a b s o l u t e p a r t i a l d e r i v a t i v e a t t a i n e d by t h i s method i s about

0.1 k c a l mole” £ 1 .

0>) Scheme 2: P a t t e r n S e a rc h

2 PT h is method which was f i r s t a p p l i e d to m o le c u la r

m echanics c a l c u l a t i o n s by S c h l e y e r , i s s i m i l a r t o th e

s t e e p e s t d e s c e n t method. I t d i f f e r s from s t e e p e s t d e s c e n t

i n t h a t th e p e r t u r b e d c o - o r d i n a t e i s no t r e t u r n e d to i t s

s t a r t i n g p o i n t , i f i t i s a f a v o u r a b l e e n e rg y change , so

t h a t th e p a t t e r n s e a r c h method does n o t r e q u i r e the

e v a l u a t i o n o f d e r i v a t i v e s and i s s c a l e i n v a r i a n t . The

m i n i m i s a t i o n i s accom pl ished by a c o m b in a t io n o f e x p l o r

a t o r y moves and p a t t e r n moves t o g e n e r a t e a sequence of

im prov ing a p p r o x i m a t i o n s . E x p l o r a t o r y moves examine th e

l o c a l b e h a v io u r o f th e f u n c t i o n and s e e k t o l o c a t e th e

d i r e c t i o n o f any s l o p i n g v a l l e y s p r e s e n t ; p a t t e r n moves

u t i l i z e th e i n f o r m a t i o n y i e l d e d by th e e x p l o r a t i o n s by

p r o g r e s s i n g a lo n g any such v a l l e y s . T h is method has th e

ad v an tag e t h a t th e r a t e o f d e s c e n t down v a l l e y s i s more

r a p i d th a n i n th e s t e e p e s t d e s c e n t method.

2S c h l e y e r ’s m o d if ied p a t t e r n - s e a r c h method , has

g iv e n lo w er e n e rg y and more r e a s o n a b l e d i s t r i b u t i o n o f

s t r a i n t h a n th e s t e e p e s t d e s c e n t method, b u t l i k e th e

s t e e p e s t d e s c e n t method, f i n d s l o c a l minima and

convergence n e a r minimum i s r e l a t i v e l y s lo w . The d i f f i c u l t y

- 32 -

o f th e o c c u r r e n c e o f l o c a l minima can he p a r t i a l l y

e l i m i n a t e d hy employing a v a r i e t y o f s t a r t i n g g e o m e t r i e s ,

when f l e x i b l e m o lecu le s a r e h e in g c o n s i d e r e d , which w i l l

h o p e f u l l y converge to the same geometry and e n e r g y .

Convergence i s assumed and the s e a r c h t e r m in a t e d when th e

e x p l o r a t i o n s t e p s have h een reduced helow some s p e c i f i e d

l i m i t ( e . g . 10 ^ 2 ) .

The p a t t e r n s e a r c h method i s c l e a r l y a s im p le

s t r a t e g y which i s e a s i l y programmed, r e q u i r e s v e r y l i t t l e

computer s t o r a g e and hence f a s t e r t h a n th e s t e e p e s t

d e s c e n t method and l i k e th e s t e e p e s t d e s c e n t method, i s

r e l a t i v e l y t o l e r a n t o f th e approx im ate t r i a l s t r u c t u r e .

( c ) Scheme 3: Newton - Raphson method

This p ro c e d u re was f i r s t used i n d e p e n d e n t l y hy19 26J a c o h , Thompson and B a r t e l l , Boyd and L i f s o n and

20W arshe l and was found to he v e r s a t i l e and t o p roduce

r e s u l t s which were r e p r o d u c i b l e and r e l i a b l e .

I n e q u a t i o n (15)> F i s th e m a t r i x o f second

d e r i v a t i v e s o f V i . e ' .

p = d \S J p x i

2I f P i s s e t e q u a l to 3 V : i , j 4 3 f o r e ach atoms

dx. 6 x ,0 7 o A

i . e . P i s t h e n e q u a l to t h e b l o c k d i a g o n a l m a t r i x 9 ,

t h i s overcomes th e s c a l i n g problems e n co u n te re d i n th e

s t e e p e s t d e s c e n t method. This b l o c k d i a g o n a l a p p ro x

i m a t io n method i s , however , l e s s t o l e r a n t o f the

ap p ro x im a te t r i a l s t r u c t u r e t h a n th e s t e e p e s t d e s c e n t and

- 33 -

p a t t e r n s e a r c h m ethods , h u t i t i s more e f f e c t i v e f o r

b r i n g i n g a c r u d e , t r i a l c o n fo rm a t io n i n t o th e v i c i n i t y

o f th e minimum. A f t e r 50 - 100 i t e r a t i o n s , t h e f i r s t

d e r i v a t i v e s o f p o t e n t i a l en e rg y w i t h r e s p e c t t o the

c a r t e s i a n c o - o r d i n a t e s a r e reduced to abou t 0.1 k c a l .-1 o-1mole A , b u t t h e r e a f t e r convergence i s s low . More

gr e c e n t l y i t has been found t h a t th e b lo c k d i a g o n a l

method i s , i n f a c t , l e s s t o l e r a n t o f th e t r i a l s t r u c t u r e

t h e n th e pu re d i a g o n a l a p p ro x im a t io n i . e . where F =

^ 2v p. f o r each atom, a l t h o u g h th e convergence p r o p e r t i e s

a r e r o u g h ly th e same. I t would t h e r e f o r e seem t o be more

a d v an tageou s to u se th e pu re d i a g o n a l app roach which

would use l e s s computer t im e .

R e g a r d l e s s o f w h e th e r th e pure o r b l o c k d i a g o n a l

a p p ro a ch i s adopted i n t h e i n i t i a l s t a g e s o f m in i m i s a t i o n ,

i t becomes n e c e s s a r y i n l a t e r s t a g e s to u se a method which

h a s b e t t e r convergence p r o p e r t i e s . Such a method i s theQ

f u l l - r n a t r i x Newton-Raphson i . e . where P = 6 V :i x l d x i

i , j = 1 , 3N 0 (18)

The m a t r i x P i s s i n g u l a r w i th s i x eigenvalues z e ro

b e c a u se r o t a t i o n s and t r a n s l a t i o n s have n o t b e en e x c lu d ed ,

and so t h e s e t o f e q u a t i o n s (15)cann o t be s o lv e d d i r e c t l y .

Two methods a r e a v a i l a b l e f o r i n v e r t i n g F . The

f i r s t " g e n e r a l i s e d i n v e r s e " method2 ^ r e q u i r e s th e

d i a g o n a l i s a t i o n o f F : -

- 34 -

F + = E d i a g (1 / A )E*

where F + i s th e g e n e r a l i s e d i n v e r s e o f F , X and E a re

e i g e n v a l u e s and e i g e n v e c t o r s o f F r e s p e c t i v e l y . The

second a p p ro a c h , sometimes c a l l the " red u ced F - m a t r ix

t e c h n iq u e " o r R a o ' s method^’ ^ , in v o lv e s k eep in g s i x

c o - o r d i n a t e s c o n s t a n t hy removing th e c o r r e s p o n d i n g rows

and columns from th e m a t r i x and s o l v i n g the r em a in in g s e t

o f e q u a t i o n s hy s t a n d a r d m ethods .

However, a l t h o u g h t h i s second method i s s i g n i f i c a n t l y

f a s t e r t h a n th e f i r s t , i t does n o t p roduce th e un ique

g e n e r a l i s e d i n v e r s e F + - i n s t e a d i t y i e l d s a non un ique

F1*2 g e n e r a l i s e d r e c i p r o c a l , where F1*2 i s a m a t r i x which i s

a two c o n d i t i o n g e n e r a l i s e d r e c i p r o c a l m a t r i x , s a t i s f y i n g

c o n d i t i o n s (l ) and ( 2 ) , d i s c u s s e d h e l o w ^ F o r any

m a t r i x P, sq u a r e o r r e c t a n g u l a r , t h e r e e x i s t s a un ique

m a t r i x Q s a t i s f y i n g the c o n d i t i o n s

PQP = P (1 )

QPQ = Q (2)

(PQ)*= PQ (3)

(QP)*= «P <*>F u r th e r m o r e , the un ique g e n e r a l i s e d i n v e r s e m a t r i x o f P i s

a m a t r i x Q = P+, which s a t i s f i e s the c o n d i t i o n s (1) - (U)*

Th is sh o r tc o m in g o f th e second method i s m a n i f e s te d hy th e

o b s e r v a t i o n t h a t the convergence o f th e p r o c e s s depends

on th e o r i e n t a t i o n o f th e m olecu le i n th e f r a m e , a l t h o u g h ,

i n th e c a s e o f m o le c u la r m echan ics , th e d i f f e r e n c e i n

- 35 -

r e s u l t s f o r one o r i e n t a t i o n and a n o t h e r i s u s u a l l y no t

s i g n i f i c a n t .

T h is q u a d r a t i c a l l y c o n v e rg en t Hewton-Raphson

p r o c e s s has to he i t e r a t i v e ( s e r i e s o f s u c c e s s i v e a p p ro x

i m a t io n s ) beca u se o f the l i n e a r r e l a t i o n s h i p be tw een the

f i r s t d e r i v a t i v e s o f V and the c a r t e s i a n c o - o r d i n a t e s ,sim p l ied hy (15) and b ecau se o f th e t r u n c a t i o n o f th e

T a y l o r s e r i e s . The f u l l - m a t r i x m i n i m i s a t i o n method has

good convergence p r o p e r t i e s as i t c o n v e r g e s , a f t e r about

3 c y c l e s , w i t h th e f i r s t d e r i v a t i v e s b e in g lowered to-10 -10-110 k c a l mole A • The geom etry , m o s t ly t o r s i o n a n g l e s ,

w i l l u s u a l l y he changed s i g n i f i c a n t l y , and t h i s method th u s

g i v e s a b e t t e r r e p r e s e n t a t i o n ' o f th e t r u e m o le c u la r

geom etry and i t s i n h e r e n t symmetry t h a n any o f th e methods

p r e v i o u s l y d i s c u s s e d , an accoun t of th e f a c t t h a t th e f u l l -

m a t r i x method t a k e s i n t o c o n s i d e r a t i o n th e i n t e r a c t i o n o f

e a c h atom w i t h a l l th e o t h e r atoms i n the m o le c u le . The

e n e r g y , on the o t h e r hand , i s n o t u s u a l l y s i g n i f i c a n t l y

a l t e r e d on go ing t o th e f u l l - m a t r i x from th e b l o c k - d i a g o n a l

method. S ince th e f u l l - m a t r i x method r e q u i r e s a good i n i t i a l

e s t i m a t e o f th e t r i a l s t r u c t u r e , i t i s o n ly used i n the

second s t a g e s o f m in i m i s a t i o n - s t e e p e s t d e s c e n t , p a t t e r n

s e a r c h , b l o c k d i a g o n a l o r pure d i a g o n a l methods may be used

i n t h e f i r s t s t a g e s . One m ajor d i s a d v a n t a g e i s th e n e c e s s i t y

o f s o l v i n g a s e t o f l i n e a r e q u a t io n s a t e ach i t e r a t i o n ,

which r e q u i r e s v a s t amounts o f computer r e s o u r c e s , b u t t h i s

i s n o t a v e r y s e r i o u s prob lem , due t o th e a v a i l a b i l i t y o f

- 36 -

v e r y f a s t computers w i t h l a r g e c o re s t o r e s .

The m a t r ix e le m e n ts F j j , c a l c u l a t e d f o r the

e q u i l i b r i u m s t r u c t u r e , c o r re sp o n d t o t h e mass in d ep e n d en t

g e n e r a l i s e d f o r c e c o n s t a n t s o f the sy s te m . The f o r c e

c o n s t a n t s c o r r e s p o n d in g t o th e normal v i b r a t i o n s o f the

m o lecu le a r e th e e ig e n v a l u e s o f the m a t r ix w i t h e le m en ts

(G j jF [j ) where G i s th e m a t r ix o f reduced masses and so

normal modes o f v i b r a t i o n and thermodynamic v a r i a b l e s can

be e a s i l y d e r i v e d . Second d e r i v a t i v e schemes g ive a c c e s s

t o b o th m in i m is a t i o n and m a x im is a t io n and p r o v i d e s a means

o f d i s t i n g u i s h i n g be tween the two p o s s i b i l i t i e s .

( d ) Numerica l v e r s u s a n a l y t i c a l d e r i v a t i v e s ^ .

A n a l y t i c a l s a r e f a s t e r i n computer e x e c u t i o n t ime

b u t nu rne r ica ls a r e e a s i e r to program and more v e r s a t i l e .

T h is l a t t e r f e a t u r e can be v i t a l l y i m p o r t a n t e . g . when a

f o r c e - f i e l d i s i n th e p r o c e s s o f b e in g p a r a m e t r i z e d . During

th e p a r a m e t r i z a t i o n , i t i s u s u a l l y n e c e s s a r y to change

t h e form o f one o r more o f the p o t e n t i a l forms i n the

f o r c e - f i e l d . In a scheme u t i l i s i n g n u m e r ic a l d e r i v a t i v e s ,

i t i s n e c e s s a r y to change o n ly a few l i n e s i n th e p rogram ,

w h e r e a s , when a n a l y t i c a l d e r i v a t i v e s a re used th e new

e x p r e s s i o n s f o r t h e s e must be d e r i v e d and i n c o r p o r a t e d

i n t o th e program which must be amended s u b s t a n t i a l l y to

accommodate the c h a n g e s . F o r p r o d u c t i o n work, t h e r e i sq

p r e f e r e n c e f o r a n a l y t i c a l d e r i v a t i v e s , s i n c e t h e y use

l e s s computer t im e .

- 37 -

1 ,6 R e f e r e n c e s

1 . D.H.R. B a r to n , E x p e r i e n t i a 6 , 316 (1 95 0 ) .

2 . J .D . W i l l i a m s , P . J . S tang and P . von R. S c h l e y e r ,

Annu. Rev. P h y s . Chem. , 1 9 . 531 (19 6 8 ) .

3 . E.M. E n g l e r , J .D . Andose and P. von R. S c h l e y e r ,

J . Amer. Chem. S o c . t 95 . 8005 (1973)«

4 . C. A l to n a and D.H. F a h e r , Topics in C u r r a n t C h e m i s t r y ,

1 (1974) .

5* J .D . D u n i tz and H.B. Burgi i n , I n t e r n a t i o n a l Review

o f S c i e n c e . P h y s i c a l C h e m is t ry S e r i e s Two. ,

B u t t e r w o r t h s , London, V o l . I I , Ch. 4 ( 1 9 7 6 ) .

6 . N.L. A l l i n g e r , Advances in P h y s i c a l Organic C h e m i s t r y .

1 3 , 1 (1 97 6 ) .

7 . 0 . Ermer, S t r u c t u r e and Bonding . 2 7 . 161 (1 9 7 6 ) .

8 . D .N .J . W hite , Computers in C h e m i s t r y , (1 9 7 7 ) , i n p r e s s .

9* D .N .J . White and M.J. B o v i l l , J . Chem. S o c . P e r k i n I I .

i n p r e s s .

1 0 . J . P . Lowe, S c i e n c e , 1 7 9 . 527 (1 97 3 ) , p r e s e n t s a comp

a r i s o n o f the e x p l a n a t i o n s f o r e t h a n e .

1 1 . H. Margenau, P h y s .*R ev . , 6 3 . 385 (19 4 3 ) ; 6i±, 131

(191+3); 66, 303 (191+1+).

1 2 . L . P a u l i n g , The N a tu re o f th e Chemical Bond. C o r n e l l

U n i v e r s i t y P r e s s , 1940.

13- I* Amdur and E.A. Mason, J . Chem. P h y s . . 22, 670 (1 9 54 ) .

14* F o r a r ev ie w see G.C. Mait land and E .B . Sm i th , Chem.

Soc . Rev . . 2 , 181 (19 7 3 ) .

15* a) D.E. W i l l i a m s , J . Chem. P h y s . . 4 5 . 3770 (1 9 6 6 ) .

h ) D.E. W i l l i a m s , i b i d . . 4 J , 4680 (19 6 7 ) .

- 38 -

1 6 . S. Chang, D. McNally, S. S h a ry -T e h ran y , M.J. H ickey

and R.H. Boyd, J . Amer. Chem. S o c . . 9 2 . 3109 (197 0 ) .

17* H.L. L ip so n and W. Cochran , The C r y s t a l l i n e S t a t e .

Ed. W.L. Bragg, V o l . I l l , 340 (1 9 6 6 ) .

1 8 . N.L. A l l i n g e r , J .A . H i r s c h , M.A. M i l l e r , I . Tyminsk i ,

and F.A. van C a t l e d g e , J . Amer. Chem. S o c . . 9 0 .

1199 (19 6 8 ) .

1 9 . E . J . J a c o b , H.B. Thompson, L .S . B a r t e l l , J . Chem. P h y s . .

kZ» 3736 (1 9 6 7 ) .

2 0 . S. L i f s o n and A. W arsh e l , J . Chem. P h y s . . 4 9 . 5116(1 968) .

2 1 . 0 . Ermer and S. L i f s o n , J . Amer. Chem. S o c . . 9 5 .

4121 (19 7 3 ) .

22 . W. Murray ( e d . ) i n Numerical Methods f o r U n c o n s t ra in e d

O p t i m i z a t i o n , London, Academic P r e s s (1 97 2 ) .

23* K.B. Wiberg, J . Amer. Chem. S o c . , 8 7 , 1070 (1 9 65 ) .

24 . I* S u z u k i , B u l l . Chem. Soc. J a p a n , 3 5 . 540 (1962 ) ;

1279 (1 96 2 ) .

25* Hooke and T.A. J e e v e s , J . Assoc . Computing

M ach ine ry , 8, 212 (1 961 ) .

2 6 . R.H. Boyd, J . Chem. P h y s . 4 3 , 2574 (19 6 8 ) .

27* D .N .J . White and G.A. Sim, T e t r a h e d r o n . 29 , 3933 (1 9 73 ) .

2 8 . N.L. A l l i n g e r and G.A. Lane, J . Amer. Chem. S o c . .

2 6 , 2937 (1974 ) •

29* A. Warshel and S. L i f s o n , J . Chem. P h y s . . 5 3 . 5 8 2 (19 7 0 ) .

30 . C.R. Rao, Sankhya , 1 ^ , 253 (19 5 5 ) .

31 • D .N .J . Y/hite , Acta C r y s t , (A) , i n p r e p a r a t i o n .

32. A.L. Mackay, Acta C r y s t . , A33, 212 (1 9 7 7 ) .

- 39 -

CHAPTER TWO

The developm ent o f a m o le c u la r f o r c e f i e l d

f o r c a l c u l a t i o n s on

a lk a n e s and non-con.jugat ed. a lk e n e s

- 40 -

2.1 I n t r o d u c t i o n-j 2 7 |i

By 1973> t h e r e were s e v e r a l f o r c e - f i e l d s 9 i n

e x i s t e n c e which were developed to d e a l w i t h c a l c u l a t i o n s on

a lk a n e s a n d /o r n o n -c o n ju g a te d a l k e n e s . U n f o r t u n a t e l y , each

one o f t h e s e f o r c e f i e l d s was known t o have c e r t a i n

d e f e c t s i n t h a t t h e y could n o t a d e q u a te ly r e p ro d u c e a l l the

a v a i l a b l e e x p e r im e n ta l d a t a e . g . h e a t s o f f o r m a t i o n of5

p o l y c y c l i c h y d ro ca rb o n s . Such sh o r tc o m in g s a r e u s u a l l y

a r e s u l t o f a b i a s e d s e l e c t i o n o f m o le cu le s in c lu d e d i n th e

p a r a m e t r i z a t i o n o f th e f o r c e f i e l d , u n n e c e s s a r y o v e r p a r a -

m e t r i z a t i o n , l a c k o f e x p e r im e n ta l d a t a and i n c o r r e c t

d e r i v a t i o n o f th e b a la n c e be tw een non-bonded i n t e r a c t i o n

p o t e n t i a l s and o t h e r c o n t r i b u t i o n s t o th e s t e r i c e n e r g y .

S ince an a l k a n e / a l k e n e f o r c e - f i e l d can form th e

b a s i s f o r o t h e r f o r c e f i e l d s d e s c r i b i n g a l l o t h e r f u n c t i o n a l

ty p e s o f m o le cu le s e . g . c a r b o n y l compounds, h a l o g e n s , i t i s

im p o r t a n t t h a t t h e b a s i c a l k a n e / a l k e n e f o r c e f i e l d i s a

r e l i a b l e one , o th e r w i s e v a s t amounts o f human and computer

r e s o u r c e s a r e w a s t e d .

S ince 1973t a number o f p a p e r s , s u p p l y i n g p o t e n t

i a l l y u s e f u l e x p e r im e n ta l d a t a , have appea red i n th e

l i t e r a t u r e . This d a t a i n c l u d e h e a t s o f f o r m a t i o n o f

p o l y c y c l i c h y d r o c a r b o n s ^ ' h e a t s o f h y d r o g e n a t io n o fQ

medium r i n g d i e n e s and t r i e n e s and s t r u c t u r a l d a t a e . g .9

n e u t r o n d i f f r a c t i o n s t u d y o f a c y c lo d ec an e d e r i v a t i v e and

X - ra y and e l e c t r o n d i f f r a c t i o n s t u d i e s o f medium r i n g d i e n e s .

The t ime was t h e r e f o r e c o n s i d e r e d to be r i g h t f o r the

p a r a m e t r i z a t i o n o f a new and improved f o r c e f i e l d which would

be more g e n e r a l and r e l i a b l e t h e n th e p r e v i o u s l y deve loped

- 41 -

f o r c e f i e l d s .

2 . 2 . The Force F i e l d

The f o r c e f i e l d which was s u b s e q u e n t l y deve loped

( r e f e r r e d to as th e W hite - B o v i l l f o r c e f i e l d o r WBFF, f o r

s h o r t ) , i n c o r p o r a t e d i n t o i t s p a r a m e t r i z a t i o n l a r g e amounts

o f e x p e r i m e n t a l d a t a c o n c e rn in g the thermodynamic and

s t r u c t u r a l p r o p e r t i e s o f a c a r e f u l l y s e l e c t e d group o f abou t

75 compounds, which range from th e s i m p l e s t a l k e n e , e th y l e n e

t h r o u g h o t h e r s t r a i g h t and b ranched c h a i n compounds, c y c l i c

compounds from - C1 2 > b i c yc l i c > p o l y c y c l i c and h i g h l y

s t r a i n e d h y d r o c a r b o n s ^ .

I n o r d e r t o keep th e f o r c e f i e l d as s im p le as p o s s i b l e ,

a t r u n c a t e d ( i . e . no c r o s s - t e r m s u sed ) v a le n c e f o r c e f i e l d

m odel , i d e n t i c a l i n form to t h a t used i n S c h l e y e r ’s a lk a n e

f o r c e f i e l d (SFF) was a d o p te d . The H H p o t e n t i a l s i n

SFF were found too ’hard* and were t h e r e f o r e r e v i s e d . As

d e s c r i b e d i n C h a p te r 1 , th e s t e r i c e n e rg y , Vs, f o r a l k a n e s /

a lk e n e i s composed o f 5 c o m p o n e n ts : -

Vs = z * k i ( 1 - V 2 + Z ? k e ( a e 2 - k 1 G a e 3 ) +1 6

J"l>k (1 + s cos n oo) + 2 L £ ( - 2 / b 6 ^ + exp CO r

(1 2 (1 - o c ) ) ) (180 - X )24* 4s Y

where o(.= r / ( r + r 2

The t r i a l f o r c e c o n s t a n t s were c a r e f u l l y a d j u s t e d i n

a t r i a l and e r r o r manner u n t i l th e f i t be tw een a l l the

c a l c u l a t e d and o bse rved p r o p e r t i e s was s a t i s f a c t o r y -

h e a t s o f f o r m a t i o n , h e a t s o f h y d r o g e n a t i o n , c o n f o r m a t i o n a l

e n e r g i e s , b a r r i e r h e i g h t s be tween c o n fo r m a t io n s and

- 42 -

g e o m e t r i e s o f m o le c u le s .

The f i n a l form o f th e f o r c e f i e l d c o n s i s t e d of

22 p a ra m e te r s f o r a l i p h a t i c f u n c t i o n s and 18 p a ra m e te r s

f o r doub le bonds and i t s s u r r o u n d in g s and i s g iv e n i n

T ab le 1• A Group e n t h a l p y in c rem en t scheme was adopted to

o b t a i n h e a t s o f f o r m a t io n and h y d r o g e n a t io n w i t h th e

i n c re m e n t s b e in g de te rm in ed from th e s t e r i c e n e r g i e s and

e x p e r i m e n t a l h e a t s o f f o r m a t io n by a l i n e a r l e a s t - s q u a r e s

p r o c e s s . The v a l u e s o f t h e inc re m e n ts and t h e i r e . s . d ' s

( e s t im a t e d s t a n d a r d d e v i a t i o n s ) a re r e p o r t e d i n T ab le 2 ,

I n t o t a l , 60 e x p e r im e n ta l e n th a lp h y v a l u e s were used

i n th e p a r a m e t r i z a t i o n and the f i n a l mean d e v i a t i o n

be tw een th e c a l c u l a t e d and e x p e r im e n ta l e n t h a l p i e s was

0 ,5 5 k c a l /m o le which compares f a v o u r a b l y w i t h t h e 0.61

k c a l /m o le o v e r 39 compounds, 0 .72 k c a l /m o le o ve r 391

compounds and 0 .92 o v e r 10 compounds ob ta ined by S c h l e y e r ,2 3A l l i n g e r and Ermer and L i f s o n r e s p e c t i v e l y . The

c o r r e s p o n d i n g f i g u r e s f o r g e o m e tr ic p r o p e r t i e s a r e 0 .0 0 9

£ , 0 . 6 ° and 0 .9 ° i n bond l e n g t h s , bond a n g le s and t o r s i o n

a n g le s r e s p e c t i v e l y o v e r a s e t o f 93 o b s e r v a t i o n s . The

e n th a l p h y and g e o m e tr ic d a t a on the i n d i v i d u a l m o lecu le s a re

l i s t e d i n T ab les 3 and U r e s p e c t i v e l y . I t can th u s be s e e n

t h a t t h e s e r e s u l t s a r e w i t h i n th e a c c e p t a b l e l i m i t s o f

e x p e r i m e n t a l e r r o r and a re more r e l i a b l e t h a n th e a f o r e

ment ioned f o r c e f i e l d s and hence a c e r t a i n amount o f con

f i d e n c e c an be p lac ed i n th e r e s u l t s f o r compounds, no t

i n c lu d e d i n th e p a r a m e t r i z a t i o n b u t whose s t r u c t u r a l

f e a t u r e s a r e r e p r e s e n t e d i n i t .

The energy m in i m i s a t i o n scheme was a tandem q u a s i -

Newton ( b lo c k D iag o na l fo l lo w e d by F u l l M a t r ix ) m in im is -

- 43 -

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- 44 -

-ST ' CDin in tnCL* CT\ CTVo o oI—I I—I I—I

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id D' cm in o• • • * »

CO rH ! CO O CL*r H CM O H Or-H i—I i—I i—I i—1

ID IDIDVDVDVOIDVDCOCT» 00 O'* O'. CL* O'* O'* O'* CT\o o o o o o o o oo o o o o o o o o o o0 0 0 0 0 6 0 0 0 0 0

inoOQcocMoocooOOi n i D \ D C M r o r - c o c o c r > c r v C MO O O r H C M O O O O O r HO O O O O O O O O O O

• • • • • • • • • • »O O O O O O O O O O O

CO0P i rH CM CO CO CO rH CM CO CM CO CO >1

0& , c m c m c m c m c m c o c o c o c o c o c o >1

eo•pid

rHIdu•pp0u0

Go•r |•p

•p•rl•pinAp0mo

00nOft0

0X i+>

+>0o•rlG

•r |

+»a•Huo0p0cupw

0Q*>1tH

rHrHrHCM CO rH rH rH CM CM CO

- 45 -

o o o o o o o o o o o o o o o o o opj • ♦ » » » • * • • » » » » » » • • «c m c m c m c o c o c o c o c o c o c o c o c o c o c o c o c o c o c o

O O O O O O O O O O O O O O O O O OrH rH i—I i—I i—I i—! rH r—< r—{ i—I r—I i-H r—| i—1 i—) (—I rH r—il i t : t t

OOOr'-r^r'~<x>oro\cr>cnG'>OOOOc^c7> • 3 OOOvovowncmcnincmcnOOOOnw M i n i n i o r o n n ^ w i f l ^ v o v o H H H o i o v o HC N M t N H H H O O O O O O H H H O O O

v o v o v o o O O O O O O O O O O O O O O .HC*

rHCOCOrHCMCOrHCMCOrHCMCOrHCMCOCMCOCO O04>1EH

CO COo04>1Eh

cmcmcmcocococococococococococooococo Q)04EH

a)04Eh

O04>iEh

CM<MCMCMCM<MCMCMCMCMCMCM<OCOCOCOCOCO

~i i—I CO «—1 i—I i—I CM CM CM CO CO CO i—I «—I i—[ CM CM CO

0•H CM»d0 <Do 04!>iEh<Da<drHp4tH rH0 Q)•p 040 >io Eh

Sil.'InijciOi;I

j jr'i.--i'j

mZ 1 l‘ Vl

. j• cn -•L_i r

fv Cv i -nV (£ I*-.

c c c r .

• • ■ •7 ~ ..7> tV —— f I I

CM CO CM

C_- <_ L_ w” C' C_ t_ It It IS I I I I

oI->~4

- 47 -

8 8 8 8 8 8 8. • CM CM CM CM CM CM CMu.LJ 8 8 8 8 8 8 0 8 8

<9 0 8 (Vi CM CO

SODIfiGTrctVITrNV^ina 'OMODMnOO'. ESIOCM^®• • • • • ■ • • • • • • • • • • • • • • • • • • • • AQ r j C i E C Q D Q Q D a n Q Q O C ^ D a c a w Q O Q D D

S • I I I I I I ! K

CO CO 8 ID CD —* ID C\J CM "1

CM CO ID O r o r o r o cm

C IT O IO CM FO

o o a o 3 3 o o r o o n n o+1 *H + l -H +1 -H «*-» + | + | -H -H -H -H

r s , c o —• h v f O i n s n —« ir > c * C M —*r,D O M > r o o o > O T r c \ i F ' ^ u o c o m c c ^ k c c — i r c ^ - ^ k n i o c c N - s c c f v K r t r c v i c c • • • « • • • • • • • • • » • • • • • • • » • •w xr s *■i c \ i ^ r o o \ o c ; i o < C M i O ( O K i n i n M T ? r o o - « o i f t C \ j

♦ I I I I I I • »-* »H I l f »”• r 4 w* CM CJ »-•l i l t I I I I I I I I

OID ct: ID

• • •(Mfiin- • cm cm I I

K ^ i *hC\1D»h <CO - CHOG ©NC\fN-<(0ifi»C^N.ir-H0'0''C '00 )” 0 0 ) 'O C J-* D M O 'in S 'O O ^ C O » 4 ^ 0 D O -* D N '^ 0 • • • • « • • • • • • • • • • • • • • • • • • • • • •

w xr c <h ca n co «o g tt o ^ n o n lti- io v m n o ro ri in•*« I I I I I I «-• »-* *-* *-« I I I «-* * »-t •—• CM CM CM «-* * -* CM CM

t i l l I I I I I I I I I I

• H ^ E a - c o t f ) © o D K - H C ( \ i n c o 'o w N - 4 S ( c n c o D c c n o• ^ 'T O O 'O c o ^ O i L O ' r c v o o w o O j O ^ O r H x r o t r H ' f c j ^ 3 8 Q «-■ 3 3 —• - * C M C M M C M - « < M O C M r O C \ I C M C M C M r D ,3 ^ C M - < C D

LJ LJ LJz z zr. z :

LJlj rrZZ L i LJ *—a 33 EDtr iCl_- «“•

3 CM I I

CM C O I ”CO <»-*trc _ j»— »-«

LJ I 3 _JWij > -

Eli L . 3CO I

U D Z D Z CT C. (Z LJ 1 I «

-r-l CM —‘ Z* I * l> I

cr _ j _ s _* ! > - > - > -

V *— I—- I— i L i LJ L ,

JZ *-A »—» *-* i - Q O Q LJ I I I" n o nI * H *

CM CM CM r>

LJ LJ LJ LJ

r u z—I »~ 3

UJC. Z Clr i u iLJ cv a CM

U H I I Iz r w Ci «

. a.. L~ ii_ ...» I Z* Z F- D < CT < LJ ZT I C m Cl

I - Li CM I - (-J I— I J Z C . I I I trz lj iLJ CL CJ > - > - > - > - h I I I I I I Z (\J O H h - H I—LJ I 2* LJ LJ L i LJ

T»-cr T V 7 V—* L> f— cm cm r> -m-

LJ I—

LJ LJ I— CL r i. ■- iC. I i _ j

O* L iI I Z

_ ! »- LJ> U Mz : r c

- J L L L J L i C C I -T>- r

h I L i0 a1 - ir r m t

t UXLJ

. Li. LJl j i t a z u oLl. » - _■ X Q L )u < . >-r : x c>I L i J

O l z > - I I ~

t o 3 »—LJ

l > —• n

- 48 -

«—k

. •U_UJ

—ai n

aKS CD CO CM

a aB E C S E C C —H

—ai n

o or i n i n i n » n L O i n i n i n i n i noi nCO «

aCO o ro co ov ro as. hs. cm ro K Ka* l m ^ m - cm r o cj CD —a 4*o o * • • • • • a a a a»—» < G E C w w O Q O O r *o •*- 1 • 1 I—< CO i n i n S CO

a CD i n —a CM CMz o i n • • • a •o t—s • ZD ZD ZD O ZD*-l CO O +1 -H -4-1 +1 -Ma— r> <£ W + 1 3 0 0 5 0 TT cm rv•< CD CD (V vC O IT O — ro ro CM CDT~ —. V-» • a a a • a a a a aor k O H- oc o t v a <o « - d t o CO COo z

<I CM TO t - a CM CJ I

U- c I 1 1 Iu

II.oCO •a— __s< o u z :

o_J■«o

t o<1 i n (V —a K —a m cm ro o ^r \ o N H i O W O >* ro t ■o LO

. • w a a a a a a a a a a_ j _ j O s - CO CD —* CD Df> —a •TD O co ro<1 <C I • CM ID 1 - a CM CM |+ - <_> <1 1 1 1 Kz : i c11 i Vi

»-» (A (ACl IO -4 LO is. CC K N . CD M K

t? Nr ro ccCO - a ro o

c : u j UJ . a a. a a a a a a a aUJ « ^ fM fM TO fD CM CM ro co i nCL CO X UJ UJ 1-4

DC LJ ■< DI

LJCLJ (_>»—< K _J UJ D »— (_> CO _ J<C CD

i t j . u : »-

. • -X

LJ LJ»— i— L i

LJ UJ <CL CL Xd C . UJ

LJ _J _2 ID— U J U O M

LJDC UJ UJ DT

Vb-fcUJ Mit c . err <j

_ j xCJ LJ

4-s _J y > y z _ ; r >- D <z uu<0 ZD H U U < ( J ^ u o 1—■ 1—

w tJ c D X > X _J _■ Cl CLr o _ j ~T u > - > - . a o ' J '>- L» LJ LJ

< ID o r r u i D > ~*~ ~UJ o O D H H O > - O I - U o 3_J CL _J Li LJ _I D _J LJ 1 _* _uCD Q TI U D D T J h - O rz t L> _>■C DT O >- 1 1 > L > 1 a >- >-a- <c t_> U ’a r D O Z - a -a- CJ CJ

i naoCO

ad —• c v r o - c c v i n

( 0 » * C ^ f 0 ^ M 0 ® 0 v » 0 C » * ^ « H n c C^ n M O Q D O O w 3 ^ r < N O a N N

a a a a a a a a a a a a a a a a aCD CD CD CD O —a —a O CD —a CD —a —a d j —a CD CMI I I « I I I • •

JOf j i n i o o c n w G c c o E e c m i c t n N ^ ^ - C M n i o c o ' O L O r o i n o t o i n K

• • • • • • • • • • • • • • •a O O D O D D D D D D O C ! D H a - l - H + l + 4 + 4 - H - H - H - H - H a H - H - H a - l - H

K-rt CJ r ; (Nl uT N vO n ^ r o ^ lO N O T j ^ T r c c c c ^ i r c ^ i r ^ i r v c c c ^ T r r ,

• • * * • • • • • » » • • • • • •l O v f w ^ r c i n N G . w n K c x r r i n v ^ o r j n ^ r o ' O w n ' T n r o r o n c j

i ■ i a i i i t i i i t i

n e w - > cr—► c (Mfiin<on»HC\cc,ioD o. N N -• K .O ^ O 'J -7 D ^ n ’T 'T 0 3 a a a a a a a a a a a a a a a a a

o n ^ n ^ o o in k o n rj ct d n i: co ■ •—• it. ro c\ j ro n ' C - ' n v n v ( \ r o w

i i a a i i a i i a a t i

c g n ( \i f\.’ n ^ - f n c e r x c c N X NCOO^'OCJO'IOMK-OONnNDC'i• • • • • • • • • • • • • • • • a

c v c o —• ii> - a —» c j cd —i n . rv co o> cs. —• cow t CM —< —* —a C\j rH «h

u jDC•<

C jUJ UJ UJ UJ■ C —1 . _ ~ zCL UJ UJ > - UJ U l u u <r

UJ c DT DT ~T~ TT TT' - o DT oDT CL C <T r - •< <r •< <L C LJ

L J u l CL I— »— L J LJ 1— + - 1— TT TT C i+- C DT DT DT DT dt DT r—>

. U'k U . L 3 1 <11 LJ DI •5 »H I— ~z •C < : »~4 *o rod J L H L U C U h •< L H H H (T a aO * JD CD - - --C •rj ►— — TT C CD C l f — r o ro_j >- ■< C »—i _ J ■’ 1 <C C _J _: <3cj CJ ~~ TT _ j i— > - > - ho a *— > - > - •>- , y 3 ZD> 1 CL CL > _T - a c — zz TD C - J _JL) c.o ZD 3 < 1— +— LO 3 < 1— 1— 1— >~ L> c_>1 ~~ — lt »- T~ L_I LJ a t - C UJ u L-. T_ > Vco - i 11 r LJ " ~ ~~ ro 3 < tt TT ~z _J CJ

CL o c 1 c . 1 1 a CC H « V 1 UJ *—t MD H UO - a CM - a r > - a CL TO a

- 49 -

UJX»-

2*-< 2UJ» • UJ XU- 2 XUJ OCC CD co co CO CO 00 Q

QUJ*~oroo o> tt CM 00 K <7v o» X a.1 Oi Q <o o K N UJo • • • • • • • or or

< <—1 INca•o

kAOo•Q

o —• G ou_k—uUJor

0CO • UJui co nr co uj <r

UJ ^ to 2 U < 7 LJ LJ OCO ■H -H O 1u (0 IU or m Z •—aCD Q vO vO CM rO to o Q O Z hc N• cm• c• AC• AC• N• L) •-( C HtU Jh-H L

X ro IO ro K ro O x <r k- or< m ID CM CM TT T3" k- k— x <c o1 • cr x u_

o to U_ O LJUJ U C I l U IlQ z> o ao _j >- u. or• c < J O O Oo > 2 >- k-—1 • O H Z <•< CO GO TT K CM _J 2 <t UJo K CO —• o» IS- in o Z U L U• • • • • • X *—■C X c:r Cv CJ ro CM uo N. k—*-« _J< C\j in CM CM TT TJ . • < k~ uj k~ <I _l<cLJ

< Z < H Z K k J Z 1-4 X UJCO «o Hl in CO «C 1C Ll X X Xtf) rj ro JO CM -4 CCh U hta . • • • • • • u_ lj x orCO CO •<T -3- K OA CO O 1— • H LI1 1 1 1 • UJ

CJ I—LJ CO Clo t c r x•

< T_1_J c c »-» uj

LJ LJUj 7* UJ 1 1 LJ ~T~ X CO LlX o LZ * LI < T* O <C • XUJ X UJ L1T~" LJ »—1 LT CO k—*-« a UJ H LJ LJ LJ -* 02 ^ ctJa X x X LJ O 1 Oh- i— cOu .2 X•c u u < o LJ O < X C*- >- X CJ _J C: _J LJ <1 UJ ^ LlL> CJ 3 UJ L> 3 L> LJ LJ LJ 7771— I XO 1 X c >- _1 > O y X _J *—i z • < zO o c CJ LJ LJ < D c O CO <c cr U O 1 c.—I _1 • >- 1 LJ ' LJ »-» C: 1- LJ 1-4 __ w K-(LJ LJ (J U LJ o O O LJ LJ LJ 1— TT 777 X u > > r 1 %C. >- c- < X UJ X H U • <LI CJ. UJ»—r CJi CJ. U» — COI — Cl LJ ~ i *— X x . U.A U. (_)» H->l1 k- i 1 I LJ 1 L‘ 1 t _J > CL M U_ CO _J >Si CJ CODO o _u CO•-"I CO LJ o LJ U X n •

. IIOD M < U% C H ►—» « r~ T"*1cr ~~~ > V X X LJ ~ CO X LJ Xw-t o CJ -Z A—< vj —• LJ o /■ o u_X 1 _JT A s

D' D t 1 X X h C U O t XfO CJ A” 1 k- 1 CO 1 cr- u UI t— _i -~<yX’ h~1>- K- V*' i—■■ V i —1 *-1 1 < vO. X X CL -<d » <o LJ CJ CJ "TOO COUJ CO_J o LJ Q LJ _J c x ii n oc. h 1 UJ *■ 1 ~7 X x cr ,~T~ C UJ < o O--X LOco co *-» CO CO -X LJ COUJ < UJ *— to :i CO 1 | to »-» M *—«cr CZ cr »—(M »—» r- > CJ u *—u U L X J H O L J H a H to o 10 • 13 o<J<j *>

- 50 -

Table 4: Experimental and Calculated Structural Parameters

Compound Structure Expt Calc. CSlc’ Ref.Expt

Ethylene

Propene

cis-1- Butene

■ " A

*230123

'23'123

'123234

1.335 1.336 0.001 55

1.090 1.089 -0.001121.7 121.3 -0.4

1.336 1.337 0.001 56

1.501 1.505 0.004124.3 123.6 -0.7

126.7 125.5 -1.2 18

114.8 115.4 0.6

skew-l-Butene

Isobutene

■ " A — .

'123234

125.4 123.6 -1.7 18

112.1 111.5 -0.6

115.3 116.2 0.9 57

trans-2-Butene\

2-Methyl-s k ev,T-1 - Bu t e n e

'23'12

•1234

1.508 1.506 -0.002 22

1.347 1.338 -0.009123.8 123.6 -0.2

72.7±5.0

71.5 -1.2 58

- 51 -

T a b le 4 (co n td )

Compound S t r u c t u r e Expt Calc . Calc . - E xp t Ref.

*12 1 .5 1 1 1 .5 1 1 0 .0 0 0 59

*23 1.353 1 .3 4 6 - 0 . 0 0 7

012 113 .2 114 .4 1 .2

^1534 156 .7 1 6 0 .9 4 .2 60

*1234 - 1 5 . 2 - 1 5 . 3 - 0 . 1 61

*2345 44 .9 4 5 .4 0 . 5

*3456 - 6 0 . 2 - 6 2 . 2 - 2 . 0

*12 1 .326 1 .3 4 0 0 .0 1 4 62

*23 1.506 1 .5 1 0 0 . 0 0 4

0123 128 .2 1 2 7 .0 - 1 . 2

0345 114 .1 1 13 .6 - 0 . 5

$1234 - 1 1 4 .7 - 1 1 5 . 5 - 0 . 8

*2345 58 .2 5 9 .5 1 .3

*12 1 .5 3 5 1 .5 1 0 - 0 . 0 2 5 63/4

*23 1 .343 1 .3 3 7 - 0 . 0 0 6

0174 9 4 .1 9 4 .3 0 . 2

:*1?> 1 .544 1 .52 6 - 0 . 0 1 8

*2145 115 .6 1 1 6 .3 0 . 7

2 , 3-Dimethyl* 2 -B u te n e W/"A.

C y c lo p e n te n e

C yc loh ex en e

c i s / c i s - l , 6 - C y c lo d e c a d i e n e

N o r b o r n a d ie n e

- 52 -

Expt Calc . Ca lc . - E x p t Ref

$6143 1 2 1 .2 120. 4 - 0 . 8 64

$1234 0 . 0 0 . 0 0 . 0

^2145 123.4 123 .4 0 , 0 64

*1784 0 . 0 0 . 0 0 . 0

*12 1 .334 1 .3 3 8 0 .0 0 4 65

*16 1.496 1 .5 0 9 0 .0 1 3 -

9234 113 .3 1 1 3 .2 - 0 . 1

0345 123 .5 123 .4 0 . 1

^1234 0 . 0 0 . 0 0 . 0

*12 1 .34 1 .3 4 0 . 0 0 66

0176 112 ± 3 108 -4

0123 118 ± 3 118 0

8217 118 ± 3 119 1

e i , 2 , 10 126 125 - 1

*4365 146 ± 8 142 -4

*cc 1 .528 1 .5 3 0 0 . 0 0 2 67,6E

0 C C C 111 .3 1 1 1 . 3 0 . 0

$c c c c 55 .2 5 5 .2 0 . 0

Compound S t r u c t u r e

B i c y c l o [ 2 . 2 , 2 ] O c te n e

B i c y c l o [ 2 , 2 . 2 ] /O c t a d i e n e /

EL 4 \

V1 , 4 - C y c lo h e x a d ie n e .

2 - P i n e n et o

Cyclohexans

- 53 -

Compound S t r u c t u r e E xp t Calc. Cg^p*t Ref*

C y c lo d e c a n e (C2h a v e r a g e )

Adamantane

D iamantane

® 345 1 18 .0 117 .9 - 0 . 1

e 456 1 18 .1 117 .6 - 0 . 5

0567 114 .7 11 4 .9 0 . 2

pLO, 1 , 2 , 3 •152 -152 0

^1234 55 55 0

^2345 66 68 2r(H6 * *-H9) 2 .08 2 .07 - 0 . 0 1

r (H2- • -H6) 1 .94 1 .9 4 0 . 0 0

0123 1 10 .0 1 1 0 .0 0 . 0

e 234 109 .2 1 0 9 .2 0 . 0

<*■00* 1.534 1 .5 3 6 0 .0 0 2

<^ c c > 1 .5 3 5 1 .5 3 7 0 .0 0 2

<0c c c > 109 .5 1 0 9 .4 - 0 . 1

011 ,12 ,13 108.8 1 0 9 .2 0 .4

05 , 1 3 , 12 110 .2 1 1 0 .0 - 0 . 2

06 , 5 ,13 110 .2 1 0 9 .9 - 0 . 3

0561 108 .7 1 0 9 .0 0 . 3

- 54 -

T a b l e 4 (co n td )

Compound S t r u c t u r e E xpt C a lc .Calc . -

E xp t

*12 1 .341 1 .3 4 0 - 0 . 0 0 1

*23 1 .5 0 2 1 .5 1 2 0 .0 1 0

*34 1 .554 1 .5 3 0 - 0 . 0 2 4

0123 127 .8 127. 8 0 . 0

0234 1 16 .8 1 1 5 .8 - 1 . 0

r ( C l - - *C5) 3 .3 0 3 .3 9 0 .0 9

r ( C l - - • C6) 3 .05 3 .08 0 .0 3

r (C2 - - * C6) 3 .32 3 .31 - 0 . 0 1

r ( C 3 • - • C7) 3 .82 3 .8 1 - 0 . 0 1

H o • • • o 3 .19 3 .1 9 0 . 0 0

r (C4 * • -C8) 3 .13 3 .05 - 0 . 0 8

*23 1 .54 1 .53 - 0 . 0 1

*34 1 .4 9 1 .5 1 0 . 0 2

*45 1 .3 2 1 .3 4 0 . 0 2

0234 1 11 .1 1 1 2 .1 1 . 0

0345 124 .1 1 2 3 .5 - 0 .6

^1234 63.4 6 1 .6 - 1 . 8

*2345 - 1 1 6 . 5 - 1 1 5 . 0 1 . 5

*3456 178 .0 1 7 7 .9 - 0 . 1

c i s , c i s - l , 5 - C y c l o o c t a d i e n e

t r a n s , t r a n s , t r a n s - 1 , 5 , 9 - C y c lo - d o d e c a t r i e n e (D^ a v e r a g e )

- 55 -

a t i o n which u t i l i z e d n u m e r ic a l f i r s t and second d e r i v a t i v e s .

A l l compounds were minimised u n t i l ^ V g/ ^ ) x was 10 ® k c a l /

mole .

2 . 3 R e s u l t s and D i s c u s s io n f o r compounds in c lu d e d i n th e P a r a m e t r i z a t i o n

( a ) The E f f e c t o f non bonded p o t e n t i a l s onc a l c u l a t e d m o le c u la r c o n fo rm a t io n s and s t e r i c e n e r g i e s

Many d i f f e r e n t f o r c e f i e l d models have emerged s i n c e 1 2 31970 9 9 . I n g e n e r a l , t h e y have rep ro d u c ed g e o m e tr ic and

thermodynamic p r o p e r t i e s o f a lk a n e s and a lk e n e s in many

i n s t a n c e s and th e r e s u l t s o f d i f f e r e n t f o r c e f i e l d s a re

i n f a i r a g re em en t . These f o r c e f i e l d s , de pend ing on the

manner o f th e p a r a m e t r i z a t i o n and th e s p e c i f i c r e a s o n f o r

th e p a r a m e t r i z a t i o n , c o n t a i n a d i v e r s e "balance of non-

bonded p o t e n t i a l f u n c t i o n s super imposed on t r u n c a t e d v a le n c e1 11f o r c e f i e l d s . Some workers ’ have t a k e n t h i s to mean t h a t

d i f f e r e n c e s be tw een nonbonded p o t e n t i a l s can be o f f s e t , i n

p a r t a t l e a s t , by s u i t a b l e m o d i f i c a t i o n o f th e v a l e n c e

f o r c e f i e l d , w h i l s t m a i n t a i n i n g a p p ro x im a te ly s p e c t r o s c o p i c

v a l u e s f o r th e v a l e n c e f o r c e c o n s t a n t s .

1 0During th e p a r a m e t r i z a t i o n o f WBFF , one i n t e r e s t i n g

p o i n t t h a t emerged was t h a t th e range o f v a l u e s t h a t an

a c c e p t a b l e c h o ic e of p a ra m e te r s f o r H . . .H f u n c t i o n (and

hence C . . . C , as th e two a re h i g h l y c o r r e l a t e d ) can assume

i s somewhat n a r ro w er and l i m i t e d th a n p r e v i o u s l y b e l i e v e d

and t h a t , i n f a c t , t h e f i r s t d e r i v a t i v e o f th e H . . . . H

p o t e n t i a l w i th r e s p e c t t o t h e i n t e r n u c l e a r s e p a r a t i o n should

- 56 -

-1 o~1n o t exceed 8 k c a l mole A and the en e rg y p e r H . . .H

i n t e r a c t i o n a t 2 .oS shou ld n o t exceed 1 .5 k c a l mole ^

T able 5 shows th e v a lu e s o f the above f u n c t i o n s c a l c u l a t e d1 2by e i g h t f o r c e f i e l d s . I n v e s t i g a t i o n s have r e v e a l e d t h a t

i t i s v i t a l t o employ an a c c e p t a b l e b a l a n c e o f f o r c e s

be tw een th e d i f f e r e n t f u n c t i o n s i n t h e f o r c e f i e l d ,

o t h e r w i s e th e consequences can be s e r i o u s - i n c o r r e c t

p r e d i c t i o n o f geom etry , h e a t s o f f o r m a t i o n , c o n f o r m a t io n a l

e n e r g i e s (and hence minimum energ y c o n fo r m a t io n s ) and

i n c o r r e c t i n t e r p r e t a t i o n o f t r e n d s i n m o le c u l a r p r o p e r t i e s .

These p o i n t s w i l l be i l l u s t r a t e d i n th e f o l l o w i n g s e c t i o n s .

As an example o f such d e f e c t s , i t i s known t h a t

1 - b iadam antane has 6 s h o r t H . . .H c o n t a c t s o v e r th e

c e n t r a l bond and i t has b een found e x p e r i m e n t a l l y t h a t the

c e n t r a l bond (C1 - C1 ) i s 1 .578& which i s c o n s i d e r a b l y3 3l o n g e r t h a n a Csp - Csp bond i n an ’u n s t r a i n e d 1 m olecu le

e . g . 1 . 5 3 3 f t i n p r o p a n e . This s t r e t c h i n g can be i n t e r p r e t e d

as a means o f r e l i e v i n g th e s t r a i n due to H . . . H c o n t a c t s

and hence a f u n c t i o n o f th e h a rd n e s s o f th e H . . . H p o t e n t i a l 11used • The h a r d e r th e H . . .H p o t e n t i a l used i n a f o r c e

f i e l d , t h e more th e c e n t r a l bond l e n g t h i s o v e r e s t i m a t e d .17 1 A l l i n g e r and S c h l e y e r c a l c u l a t e t h i s bond l e n g t h to be

1 .6 1 7 X and 1 .5 8 3 S r e s p e c t i v e l y , th e c o r r e s p o n d in g—"I o —1

d e r i v a t i v e s a r e 21 . 5 and 9*5 k c a l mole A , s u g g e s t i n g

t h a t th e e r r o r i n c r e a s e s r a p i d l y w i t h th e v a lu e o f th e f i r s t

d e r i v a t i v e and t h a t th e H . . . H nonbonded p o t e n t i a l i n t h e s e

two f o r c e f i e l d s a re too ’h a r d 1.

- 57 -

T ab le 5

The ene rg y ( k c a l mol”*' ) p e r H . . .H i n t e r a c t i o n a t 2.0&, and

i t s f i r s t d e r i v a t i v e w i t h r e s p e c t t o H . . .H d i s t a n c e (k c a l

mol X ) , f o r the p o t e n t i a l f u n c t i o n from a s e l e c t i o n

o f c u r r e n t f o r c e f i e l d s .

F o rc e F i e l d V d V /d ra

A l l i n g e r and Sprague ( 2 ) 4 . 4 3 -2 1 .U 9

S c h l e y e r and c o -w ork e rs (1) 2 . 2 6 - 9 .1 * 8

Ermer and L i f s o n (3) 1 . 3 2 - 6 . 6 0

B a r t e l l and co -w o rk e rs (13) 1 . 1 2 - 5 . 3 8

Montgomery and co -w o rk e rs (14) 1 . 0 8 - 5 . 1 0

Boyd and co -w o rk e rs (15) 1 . 0 6 - 4 . 3 1

H end r ic k so n (16 ) 0 . 9 5 - 3 . 8 8

White and B o v i l l (10) 0 . 6 9 - 3 . 0 5

aA d i r e c t measure o f the " h a r d n e s s ” o f th e f u n c t i o n .

- 58 -

(b ) 1 - Butene

Two minimum en erg y c o n fo rm a t io n s o f 1 - b u t e n e a re the

gauche form ( I ) and th e e c l i p s e d form ( I I ) .

\ __ /Me

E x p e r im e n ta l e v id e n ce i m p l i e s t h a t th e two forms a re of18 19a p p r o x im a te ly th e same en e rg y * •

F o rc e f i e l d c a l c u l a t i o n s u s in g A l l i n g e r ' s a lk e ne

f o r c e f i e l d (AFF) and an ex tended v e r s i o n o f S c h l e y e r ’s

a lk a n e f o r c e f i e l d to d e a l w i t h a lk e n e s (SFF/E) o v e r e s t i m a t e

t h e s t e r i c en e rgy o f th e e c l i p s e d form by o v e r 1 k c a l /m o l e .

T h is i s a d i r e c t consequence o f u s i n g "h a rd" H . . .H p o t e n t i a l s

( s e e T able 5)> which t h e r e f o r e e x a g g e r a t e the two r e p u l s i v e

i n t e r a c t i o n s i n th e e c l i p s e d form . The WBFF, on the

o t h e r hand , c a l c u l a t e s th e gauche form ( i ) to be more

s t a b l e t h a n th e e c l i p s e d form ( I I ) by o n ly o ,6 k c a l /m o l e ,

which i s e q u i v a l e n t to a 70^:30% m ix t u r e ,

( c ) 2 - Butene

The most s t a b l e c o n fo rm a t io n o f p ropene has a methyl

hydrogen e c l i p s i n g th e doub le bond, and two su ch e c l i p s i n g

i n t e r a c t i o n s a r e p r e s e n t i n t r a n s - 2 -b u te n e ( i l l ) , which i s

e s s e n t i a l l y s t r a i n f r e e w i t h r e s p e c t to s t e r i c i n t e r f e r e n c e

be tween the hydrogen a tom s. However i n c i s - 2 - b u t e n e (IV)

m ain tenance o f two such e c l i p s i n g i n t e r a c t i o n s would p l a c e

nonbonded hydrogens o n ly 1 .8 0 X a p a r t i n an i d e a l geom etry .

- 59 -

Thus p o t e n t i a l l y d e s t a b i l i s i n g i n t e r a c t i o n i s , i n l a r g e

m ea su re , r e l i e v e d by open ing o f the C=C-C__3 andSPH-Cgp^— ^sp2 ang l e s * s t r a i n i n c i s - 2 - b u t e n e r e l a t i v e

20t o t r a n s i s found e x p e r i m e n t a l l y to be o n ly 1 .2 4 k c a l /m o le21A cco rd in g t o th e microwave spec t rum , c i s - 2 - b u t e n e

p o s s e s s e s C2y -sym m etry w i th e c l i p s e d methyl g r o u p s .

I— H

IVI I I

O v e r e s t i m a t i o n o f H . . .H i n t e r a c t i o n s , i n t h i s c a s e ,

h a s t h r e e co n seq u e n ce s ; th e c i s / t r a n s en e rg y d i f f e r e n c e i s

c a l c u l a t e d to be too h i g h , the C=C-C v a l e n c y a n g le s too

l a r g e i n t h e c i s i som er and p o s s i b l y an i n c o r r e c t p r e

d i c t i o n o f th e symmetry o f the c i s i so m er . The e n t h a l p y

d i f f e r e n c e may be c o r r e c t e d by th e i n c l u s i o n o f a sm a l l

o n e - f o l d component i n the term which d e s c r i b e s th e t o r s i o n2around the doub le bond , b u t th e geometry can o n ly be

improved by r e v i s i o n o f th e H . . . H p o t e n t i a l . Fo rce f i e l d

c a l c u l a t i o n s on c i s -and t r a n s - 2 - b u te n e have been perform ed

u s i n g AFF, SFF/E and WBFF and th e r e s u l t s a re t a b u l a t e d i n

T ab le 6 , which e n d o rs e s the o p in io n t h a t th e H . . .H p o t e n t i a l s

i n AFF and SFF/E a re ' h a r d 1 compared to t h e ’s o f t e r '

p o t e n t i a l s i n WBFF, which g iv e s a b e t t e r r e p r e s e n t a t i o n of

2 - b u t e n e . F u r th e rm o re , AFF c a l c u l a t e d a m o le c u la r C^-

symmetry w i th methyl groups t w i s t e d o u t o f the e c l i p s e d

- 6 0 -

T ab le 6

C a l c u l a t e d e n t h a l p i e s o f i s o m e r i s a t i o n f o r 2 -b u te n e and

C=C-CSp3 v a l e n c y a n g le s f o r c i s - 2 - b u t e n e .

* * Hc / t 9 c=c-c

E xper im ent0CMOC\J« 125.i+ , 1 2 6 .7

aAFF(2) 1 ,8k 1 2 7 .9

aSFF/E 1 .86 128 .2

WBFF (10) 1 .30 127.1

a The c o n s t r i b u t i o n due to th e o n e - f o l d b a r r i e r around

C=C has been d i s c o u n te d f o r p u rp o se s o f com par ison .

U n i t s o f e n t h a l p y d i f f e r e n c e i s k c a l /m o le

- 61 -

p o s i t i o n "by 8 . 6 ° , whereas WBFF p r e d i c t th e c o r r e c t

m o le c u l a r symmetry (C^y)* i n c o r r e c t p r e d i c t i o n o f

m o le c u la r symmetry by AFF, may be d u e , i n p a r t , to the23in c o m p le te convergence o f the m in i m i s a t i o n . The

geom etry c a l c u l a t e d by WBFF i s shown i n F ig u r e 1•

( d ) c i s . c i s - Cyclo o c t a - 1 , 5 ~ d ie n e ( 1 ,3 - COD)

C o n fo rm a t io n a l i n t e r c o n v e r s i o n s o f 1 ,5 - COD were

f i r s t s t u d i e d e x p e r i m e n t a l l y by Anet u s i n g th e dynamic2l± 25 26NMR method and t h e n t h e o r e t i c a l l y by Anet , A l l i n g e r

27and Ermer u s i n g m o le c u la r mechanics c a l c u l a t i o n s . This

t o p i c w i l l be d i s c u s s e d i n C h a p te r 3*

The minimum en erg y c o n fo r m a t io n o f 1 ,5 -COD has been2Ll 28 29shown by s p e c t r o s c o p i c and d i f f r a c t i o n 9 s t u d i e s and

by m o le c u la r mechanics c a l c u l a t i o n s ^ , ^ ^ , ^ ^ , ^ ^ , ^ < t o be

u n e q u i v o c a l l y a C2 symmetr ic t w i s t b o a t , b u t th e c a l c u l a t e d2 3 3 2d e g re e o f t w i s t ( i . e . th e Csp -Csp -Csp -Csp t o r s i o n

a n g le ) v a r i e s from 27° to 55° d ep en d ing on which f o r c e

f i e l d i s u s e d . This i s n o t a l t o g e t h e r s u r p r i s i n g as the

v a lu e o f th e d e g re e o f t w i s t depends l a r g e l y on the

h ydro gens on CU and C8 as can be s e e n from F i g . 2 . As

th e deg re e o f t w i s t i s i n c r e a s e d from 0 ° ( c o r r e s p o n d s to a

C2V b o a t c o n fo r m a t io n ) upwards , th e two h ydrogen move

c l o s e r t o g e t h e r u n t i l a l i m i t i n g v a lu e i s re a c h e d where

t h e d e c r e a s e i n t o i a o n a l s t r a i n i s o f f s e t by th e i n c r e a s e

i n s t e r i c c o m p re s s io n . The " h a r d e r " th e H . . . H p o t e n t i a l

employed, th e so o n e r t h i s l i m i t i n g v a lu e w i l l be r e a c h e d .

- 62 -

F ig u r e 1♦ The c a l c u l a t e d s t r u c t u r e o f c i s —2—b u ten e (^2y sym m etry)•

- C3 -

- 64 -

F ig u r e 2 ; The c a lc u la te d , t w i s t - b o a t c o n fo rm a t io n o f

c i s t c i s - c y c l o o c t a - l t 5~d.iene (C^ sym m etry).

- 66 -

AFP, SFF/E and WBFF c a l c u l a t e th e d e g re e o f t w i s t t o he 38° ,0 0 2 950 and 52 r e s p e c t i v e l y . X - ray c r y s t a l s t r u c t u r e a n a l y s i s

o f a dihromo d e r i v a t i v e and an e l e c t r o n d i f f r a c t i o n

e tu d y 2 ^ o f 1 ,5 - COD g iv e e x p e r i m e n t a l v a l u e s o f 65° and U5°

r e s p e c t i v e l y . Thus a g a i n c o n f i r m a t i o n i s o b t a i n e d t h a t

t h e H . . . H p o t e n t i a l s employed by A l l i n g e r a re much t o o .

' h a r d 1. The d e g re e o f t w i s t and geometry c a l c u l a t e d by

th e WBFF i s i n e x c e l l e n t agreem ent w i t h th e geometry

o b t a i n e d from th e e l e c t r o n d i f f r a c t i o n r e s u l t s ( s e e F ig u r e

2 and Table U)*

( e ) Cyclodecane

Cyclodecane and many o f i t s d e r i v a t i v e s have been31s t u d i e d e x t e n s i v e l y by X - ray and n e u t r o n d i f f r a c t i o n

9 32a n a l y s i s and by IR/Raman s p e c t r o s c o p y • A l l t h e s e

s t u d i e s p o i n t to th e f a c t t h a t th e p r e f e r r e d c o n fo rm a t io n

i n th e s o l i d , l i q u i d and gaseous s t a t e s , i s t h e b o a t -

c h a i r - b o a t (BCB) c o n fo r e l a t io n . This i s con f i rm ed by

m o le c u l a r mechanics c a l c u l a t i o n s i n most c a s e s - t h e WBFF

c a l c u l a t e s th e BCB c o n fo r m a t io n to be th e minimum en ergy

c o n f o r m a t i o n , which i s 0 .5 k c a l /m o le more s t a b l e t h a n th e

n e x t lo w e s t c o n fo r m a t io n , th e TCCC (T s t a n d s f o r " t w i s t e d " ) .

However, o n ly AFF and SFF c a l c u l a t e th e TCCC t o be the

p r e f e r r e d minimum e n e rg y c o n fo rm a t io n by 1 .7 and 0 .6

k c a l mole r e s p e c t i v e l y o v e r the BCB, which would c o n t r a

d i c t b o t h th e v a s t body o f e x p e r i m e n t a l d a t a and o t h e r

m o le c u l a r mechanics c a l c u l a t i o n s .

- 67 -

9The n e u t r o n - d i f f r a c t i o n s t u d y i n d i c a t e d t h a t th e

p r e f e r r e d c o n f o r m a t io n , the BCB, p o s s e s s e s s i x s h o r t t r a n s -

a n n u l a r H . . .H d i s t a n c e s ( < 2 . o 2 ) ( s e e Table h)> which w i l l

t h e r e f o r e be a m ajor c o n t r i b u t o r to th e s t r a i n e n e r g y .

The TCCC does have some t r a n s a n n u l a r i n t e r a c t i o n s b u t th e

H . . . H d i s t a n c e s a re l o n g e r and e n e rg y due to them l e s s

r e p u l s i v e . This im p l i e s t h a t i f ' h a r d 1 H . . .H p o t e n t i a l s ,

i . e . p o t e n t i a l s which o v e r e s t i m a t e th e r e p u l s i v e te rm , a re

u s e d , th e c o n t r i b u t i o n by th e s i x s h o r t H . . .H i n t e r a c t i o n s

t o th e s t e r i c en e rgy o f th e BCB i s o v e r e s t i m a t e d and as a

c o n seq u e n ce , th e TCCC i s p r e d i c t e d to be more s t a b l e t h a n

BCB. S in c e the l a t t e r s i x f o r c e f i e l d s i n Table 5 c o r r e c t l y

p r e d i c t t h e BCB as th e minimum energy c o n fo rm a t io n o f

c y c l o d e c a n e , th e v a l i d i t y o f th e l i m i t i n g v a lu e s f o r H . . .H

p o t e n t i a l f u n c t i o n s , d i s c u s s e d i n ( a ) , i s e n d o r s e d .

1UA r e c e n t e l e c t r o n d i f f r a c t i o n s t u d y , by Montgomery ,

r e v e a l e d t h a t gaseo u s cy c lo d ec an e a t 130°C c o n s i s t s o f a

.m ix tu re o f U9% BCB, 35% TBC, 8% TBCC and 8% BCC. Force

f i e l d s c a l c u l a t i o n s w i t h WBFF, were performed on s i x conform

a t i o n s - th e f o u r c o n fo rm a t io n ment ioned above, th e TCCC3Uand a low e n e rg y c o n fo r m a t io n , TCTC , which had no t

16a p p ea red t o have been s t u d i e d p r e v i o u s l y - H end r ick son 33and Ermer o n ly c o n s i d e r c o n fo rm a t io n s i n which th e

symmetry e le m e n ts p a s s th ro u g h a toms, th e TCTC h a s ,

however , a tw o - fo ld a x i s which p a s s e s th ro u g h th e c e n t r e o f

t h e r i n g . The s t e r i c e n e r g y , r e l a t i v e t o th e BCB, and

t o r s i o n a n g le s c a l c u l a t e d by the WBFF, f o r the s i x

- 6 8 -

05 <z <h> e a n o at *> —4-< </> ** tk -w « z o

VD a? N a or *k u ro a TOx *-*■ <s> •% « « l~ c*

m •-* 69

>1 a 0 ^ 0 m *-•—« IO «— % « « % o» oX % %c CD N O ' c r Z■< OS

30fT»

O • ►* I • ** • •ro ® t r u r o o u » c n u i o * < » c i kT S M (X a t QB (H M UI OD OB O

s • *O • * - • I t **

r o ik ^ a t N 9 » i ^ 9 N a » OIU s u u u u s u u

• •*- *- • •a u c n u i o i a t N N N N S0»O*OiaRtB«jSfB«

• •* i i ** i i ** i «o o> a * « a t » a t • a t w a i t»kIs) *- * - O N O » - o

*- • I •••* • •a o o o a i k a i o M o OMONO«»IO*«U**

o o - i-W O o

zo H (0•< O 4-»o X or* X 2o »CJ - 1 >•m M 2o o o>> Z 1“

or 2 r ro r« a o»CP

o► or- o

•X.X

- i o !►o r ~ Zo r r oo

TTCP- f

o r rTO 30Ma s oo

-4 X fWT00 « 2o m

r r joo o* •>4• f*tW CP2

-€ f*t 3Da> 3D nra o rn -< >■

-4O *-4o <Z I P-rpO - «3D O

IB Xo —€o -4 X

♦-4 r roz IB«0 o

M l 1• 1 *-•- • 1 *- *- fn » a t a t * - » « a i a i a i « - i o a ir o * - • • • • o a o o ^ o o

o-*r»

- 69 -

c o n fo rm a t io n s a r e g iv e n i n F ig u r e 3* A l l s i x conform

a t i o n s were found to co rre sp o n d to t r u e minima i n c o n t r a s t33t o E rm e r ’s f i n d i n g t h a t some were o n ly p a r t i a l minima .

The c a l c u l a t i o n s co n f i rm t h a t the BCB i s th e c o n fo rm a t io n

o f lo w e s t en e rgy o u t o f the s i x and show t h a t t h e r e i s a

c o r r e l a t i o n Between th e r e l a t i v e s t e r i c en e rg y and th e

p e r c e n t a g e o f th e f o u r c o n fo r m a t io n s , found i n th e e l e c t r o n

d i f f r a c t i o n s t u d y . I n a d d i t i o n , th e geometry c a l c u l a t e d by

th e WBFF f o r the BCB c l o s e l y m i r r o r s t h a t found i n th e

a c c u r a t e n e u t r o n d i f f r a c t i o n s tu d y o f t r a n s - 1 , 6 - 9 /c y c l o d e c a n e d i o l ( see Table 4 ) .

<r) Polyc .yc l ic Alkanes

6 35E x p e r im e n ta l work on p o l y c y c l i c a lk a n e s has

r e v e a l e d c e r t a i n d e f i c i e n c e s i n some c u r r e n t p a r a -

m e t r i z a t i o n s which i n p a r t has been a t t r i b u t e d to "an

undue emphasis on th e r e p u l s i v e n a t u r e o f H . . ,H i n t e r -5

a c t i o n s " . P r o f e s s o r P . von R. S c h le y e r h as r e p o r t e d a

l i s t o f p o l y c y c l i c hy d ro ca rbo n s whose h e a t s o f f o r m a t io n

a r e p o o r l y rep rod uced by th e AFF and SFF ( s e e Table 7)

The WBFF was s u b s e q u e n t ly a p p l i e d to the same group

o f compounds and the mean d e v i a t i o n between th e c a l c u l a t e d

and e x p e r im e n ta l h e a t s o f f o r m a t io n i s 0 ,9 8 k c a l / m o l e ,

which r e p r e s e n t s a c o n s i d e r a b l e improvement o v e r t h e

c o r r e s p o n d in g v a lu e s o f 2 .2 3 and 3*12 k c a l /m o le o b t a in e d

by th e SFF and AFF. However, th e c a l c u l a t e d h e a t o f

f o r m a t i o n f o r manxane, by the WBFF , d i f f e r s from the

r e p o r t e d e x p e r im e n ta l v a lu e by abou t 6 k c a l / m o l e , more

t h a n tw ice any o f th e o t h e r d e v i a t i o n s , w h ich , t o g e t h e r

w i t h th e f a c t t h a t SFF’s i s i n " e r r o r " by k c a l /m o l e ,

would pe rh a p s c a s t some doubt on th e a cc u ra c y o f th e

- 70 -

UJoe <o mtOOtO O O O O iO nK K

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- 71 -

e x p e r im e n ta l h e a t o f f o r m a t i o n .

S c h le y e r has a l s o r e p o r t e d t h a t AFP and SFF f o r c e

f i e l d s p r e d i c t 2 , U and 2 , 8 - e thano-n o rad am an tan e to he

i s o e n e r g e t i c , whereas i n f a c t th e fo rm er i s the s t a h io ra e r-zf.

by abou t 1 .5 k c a l /m o le ^ . Our c a l c u l a t i o n s (WBFF)

c o r r e c t l y i n d i c a t e th e 2 , 1+ - isomer as th e minimum

e n e rg y isom er b u t the e n th a lp y d i f f e r e n c e i s u n d e re s t im a te d

a t 0 .5 k c a l / m o l e .

2 .i+ Some a p p l i c a t i o n s o f th e WBFF

A p p l i c a t i o n s o f th e Y/BFF t o medium r i n g and o t h e r

c y c l i c compounds w i l l be d i s c u s s e d i n C h a p te r 3*

(a ) n -But ane

n - Butane has t h r e e co n fo rm e rs , two o f which a re

m i r r o r images o f each o t h e r and a re known as th e "gauche"

o r "skew" c o n fo rm a t io n s and one , more s t a b l e by about 0 .6

k c a l /m o le t h a n e i t h e r gauche c o n f o r m a t io n a l i so m er , which

i s known as the " t r a n s " o r " a n t i " c o n fo r m a t io n .

R e c e n t l y , t h e r e has been some c o n t r o v e r s y o v e r the

e x p l a n a t i o n f o r th e gauche d e s t a b i l i z a t i o n . The c o n v e n t io n a l 37i n t e r p r e t a t i o n i s t h a t t h e gauche i n s t a b i l i t y can be

l a r g e l y a t t r i b u t e d to 1 . . . 6 hydrogen r e p u l s i o n s be tween

gauche methyl o r methylene groups w i t h a sm a l l c o n t r i b u t i o n

f rom th e 1 . . .1+ hydrogen i n t e r a c t i o n s about the c e n t r a l

bond . A l l i n g e r ' s "gauche-hydrogen h y p o th e s i s " ^ ® , on the

- 72 -

o t h e r hand , a s s i g n s 60% o f the c a l c u l a t e d e n t h a l p y d i f f e r e n c e

be tw een gauche- and a n t i - bu tane to th e 1 • . .1+ gauche -

hydrogen i n t e r a c t i o n and c la im s t h a t t h i s i n t e r p r e t a t i o n

i s in dep e n d en t o f the e x a c t p a r a m e t r i z a t i o n o f the f o r c e

f i e l d .

T h is h y p o t h e s i s has been d i s c o u n te d on b o th p o i n t s 12 39 UOby v a r i o u s w o rke rs as a l t e r n a t i v e f o r c e f i e l d

c a l c u l a t i o n s w i t h " s o f t e r 11 H . . . H p o t e n t i a l s t h a n AFP

e s t i m a t e th e 1 • • .1+ H i n t e r a c t i o n c o n t r i b u t i o n to be r e l a t i v e l y '39 10minor a t 2k% and 19% • This h y p o t h e s i s would t h e r e f o r e

seem to depend s t r o n g l y on th e c h o ic e o f nonbonded p o t e n t i a l s ,

p a r t i c u l a r l y th e H . . .H p o t e n t i a l and the b a la n c e o f f o r c e s

i n th e d i f f e r e n t f o r c e f i e l d s , so t h a t a l t h o u g h th e o v e r a l l

r e s u l t s o f d i f f e r e n t f o r c e f i e l d s a g ree f a i r l y w e l l , the

i n d i v i d u a l components o f th e s t e r i c ene rg y to d i f f e r

s i g n i f i c a n t l y , as s e e n above . The i n t e r p r e t a t i o n o f

m o le c u la r p r o p e r t i e s , on th e b a s i s o f th e p a r t i t i o n i n g o f the

c a l c u l a t e d s t e r i c e n e rg y , r e q u i r e s extreme c a u t i o n ,

p a r t i c u l a r l y when the f o r c e f i e l d i s known to have f a u l t s

and i f o r g a n i c c h e m is t s a r e to have f a i t h i n m o le c u la r

mechanics c a l c u l a t i o n s .

Bic.yclo ( 3 . 3 . 1 ) nonane

MA r e c e n t gas phase e l e c t r o n d i f f r a c t i o n s t u d y o f

b i c y c l o (3-3*1) nonane found t h a t a t w i n - c h a i r c o n fo rm a t io n

(V) g i v e s the b e s t agreem ent w i t h th e i n t e n s i t y and r a d i a l

d i s t r i b u t i o n c u r v e s . The six-membered r i n g s show a d r a s t i c

- 73 -

f l a t t e n i n g which i s p r o b a b ly due to th e C(3) - C ( 7 )

m ethy lene nonbonded i n t e r a c t i o n s s i n c e twinned i d e a l

c y c lo h ex a n e r i n g s w i t h t e t r a h e d r a l v a l e n c y a n g le s would

have a H . . . H s e p a r a t i o n o f O.75X. X -ray s t u d i e s o f

d e r i v a t i v e s o f b i c y c l o (3*3*1) nonane r e v e a l t h a t th e

r i n g sys tem can adop t b o t h a t w i n - c h a i r (V) and a c h a i r -

b o a t (V I) c o n fo rm a t io n and t h a t the t w i n - c h a i r conform

a t i o n s show a s i m i l a r f l a t t e n i n g w i t h th e H . . . H

s e p a r a t i o n a t C(3)> C(7) m ethylene g roups b e in g

e s t i m a t e d a t be tween 1 .7X - 2.0X f o r th e v a r i o u s s t u d i e s .

A t w i n - c h a i r c o n fo rm a t io n i s u s u a l l y adop ted when t h e r e

a r e no endo s u b s t i t u e n t s on p o s i t i o n s 3 and T*2 , whereas

a c h a i r - b o a t c o n fo r m a t io n , i n which th e H3****H7 i n t e r a c t i o n

i s a b s e n t b u t th e f a m i l i a r " b o w s p r i t - f l a g p o l e i n t e r a c t i o n ”

and e c l i p s e d hydrogen i n t e r a c t i o n o f th e cyc lohexane

b o a t a r e p r e s e n t , i s u s u a l l y adopted where t h e r e a r e

b u lk y s u b s t i t u e n t s a t e i t h e r o r b o th t h e s e p o s i t i o n s .

Prom an i n s p e c t i o n o f th e t o r s i o n a n g le s i n d e r i v a t i v e s 3

which have sp - h y b r i d i s e d atoms a t p o s i t i o n s 2 , 3» 4 and

- 74 -

6 , 7 * 8 i t c an be deduced t h a t the f l a t t e n i n g i n the tw in -

c h a i r c o n fo rm a t io n s i s e f f e c t e d by d i s p l a c e m e n t s o f atoms

3 and 7 e s s e n t i a l l y p a r a l l e l to th e p la n e th ro u g h 3 , 7 , 9

so t h a t t h e r e i s no skewing o f th e r i n g s , which i s obse rved 2when sp - h y b r i d i s e d atoms a re p r e s e n t a t any o f t h e s e

p o s i t i o n s . E q u i l i b r a t i o n e x p er im en ts i n d i c a t e t h a t the

t w i n - c h a i r c o n fo rm a t io n i s more s t a b l e t h a n th e c h a i r b o a t

by abou t 3 k c a l mole~^ T h is i s su p p o r te d by low1 3t e m p e r a t u r e dynamic C NMR s t u d i e s which f u r n i s h a l i m i t

f o r th e f r e e ene rg y d i f f e r e n c e between th e two c o n fo rm a t io n sJLl5as b e in g ^ 1 .40 k c a l /m o le •

The b i c y c l o (3*3*1) nonane sys tem s has been

i n v e s t i g a t e d u s i n g m o le c u la r mechanics c a l c u l a t i o n s by17 1 10AFP , SPF , and WBFF , and from th e f o r e g o i n g d i s c u s s i o n ,

i t i s obv ious t h a t th e c h o ic e o f the H . . . H p o t e n t i a l used

i n each f o r c e f i e l d w i l l s t r o n g l y i n f l u e n c e th e r e l i a b i l i t y

o f t h e c a l c u l a t e d geometry and s t e r i c en e rgy o f th e two

■ confo rm a t ions . APP, which employs ’h a r d ’ H . . . . H p o t e n t i a l s ,

c a l c u l a t e th e H3***H7 s e p a r a t i o n to be 2 .1 5 2 and the

e n t h a l p y d i f f e r e n c e be tw een the t w i n - c h a i r and c h a i r - b o a t

c o n fo r m a t io n s to be 1 . 2 4 k c a l /m o l e , whereas th e WBFF which

u s e s ” s o f t e r ” H . . . H p o t e n t i a l s , c a l c u l a t e s th e s e p a r a t i o n to

be 1 .9 7 2 and th e e n t h a l p y d i f f e r e n c e to be 2 .8 9 k c a l /m o le

which a re i n much b e t t e r agreement w i t h th e e x p e r im e n ta l

v a l u e s ( e s t i m a t e d to be 1 . 7 2 - 2 .o 2 and 3 k c a l / m o l e ) . AFF’s

v a lu e o f 2 .1 5 2 i s much too lon g as th e c o r r e s p o n d i n g

d i s t a n c e i n 9 - t h i a b i c y c l o (3*3*1 ) - n o n a n e - 2 , 6 - d io n e (a

compound i n which th e r i n g s i n th e t w i n - c h a i r c o n fo rm a t io n

- 75 -

a r e skewed) i s 2 . 07$

The c a l c u l a t e d r i n g t o r s i o n a n g le s f o r th e t w i n -

c h a i r c o n fo rm a t io n a re compared w i th th o se from an X -ray

c r y s t a l s t r u c t u r e a n a l y s i s o f b i s - 9 - b o r a b i c y c l o ( 3 * 3 . 1 ) -

n o n a n e ^ i n F ig u r e U and th e c a l c u l a t e d r i n g t o r s i o n an g le s

f o r t h e h o a t - c h a i r c o n fo rm a t io n a re compared w i t h th o se

from an X - ra y c r y s t a l s t r u c t u r e a n a l y s i s o f 3 -b rom o-9-U 3b e n z o y l - 9 - a z a b i c y c l o (3*3*1) nonane-2 -one i n F i g u r e 5*

( c ) S t e r i c a l l . y crowded doub le bonds

When f o u r groups a t t a c h e d to an o l e f i n i c l i n k a g e

d e v i a t e s i g n i f i c a n t l y from c o p l a n a r i t y w i t h th e t r i g o n a l

c e n t r e s , th e TT-hond i s weakened due to poor o v e r l a p .

Such d i s t o r t i o n s may he induced hy c o n s t r a i n i n g th e doub le

hond i n c e r t a i n c y c l i c , h i c y c l i c o r p o l y c y c l i c sys tem s o r

i n th e p re s e n c e o f crowded h u lk y s u b s t i t u e n t s . This

weakening i n th e TT-bond can be d e t e c t e d by th e low o l e f i n i c

v i b r a t i o n a l f r e q u e n c y and long u l t r a v i o l e t a b s o r p t i o n

w a v e le n g th .

T h is seemed a good a r e a t o t e s t th e a p p l i c a b i l i t y

o f th e WBFF, as i t p roduced r e l i a b l e r e s u l t s f o r 1 - b u te n e

and 2 - b u t e n e , where th e doub le bonds a re s t e r i c a l l y

c rowded. R e p u ls iv e nonbonded i n t e r a c t i o n s which r e s u l t

from s t e r i c crowding a c r o s s a doub le bond may, i n p r i n c i p l e ,

be r e l i e v e d by bond s t r e t c h i n g , v a l e n c e a n g le d e f o r m a t i o n

and th e t w i s t o f the c e n t r a l bond.

- 76 -

F ig u r e 4 : The c a l c u l a t e d r in g t o r s i o n a n g le s (a ) o f t h e t w i n -

c h a ir c o n fo rm a tio n o f b i c y c l o ( 3 . 3 . 1 ) nonane compared

w ith t h e C^y averaged e x p e r im en ta l v a l u e s o f b i s - 9 -

b o r a b i c y c l o ( 3 • 3 . l )n o n a n e ( b ) .

114 -7 119 0

\ m y / \ _ 2 X *

-6 7 56 -6 4 56

N ^ 9 / ^ * 5 4 X

( a ) (b)

F ig u r e 5 • The c a l c u l a t e d r in g t o r s i o n a n g l e s ( a ) o f t h e b o a t -

c h a ir c o n fo rm a tio n o f b i c y c l o ( 3 - 3 « l ) n o n a n e compared

w it h t h e Cg averaged e x p e r im en ta l v a lu e s o f 3-bromo-

9 - b e n z o y l - 9 - a z a b i c y c l o ( 3 « 3 » l ) n o n a n e - 2 - o n e ( b ) •

- 77 -

T e t r a - t e r t - b u t .v le th y le n e ( V I I ) has no t y e t "been

r e p o r t e d h u t i t may he exp ec ted t h a t s t e r i c r e p u l s i o n might

a l l e v i a t e d hy a t o t a l l y u n r e a l i s t i c s t r e t c h o f th e double

hond o r hy s u b s t a n t i a l t o r s i o n . C a l c u l a t i o n s ^ s u g g e s t a

75° t w i s t which would th us g iv e t h i s compound s u b s t a n t i a l

d i r a d i c a l c h a r a c t e r .1,0

One compound which has been s t u d i e d hy s p e c t r o s c o p y

i s h i a d a m a n ty l id e n e ( V I I I ) . This compound e x h i b i t s a

p l a n a r doub le bond i n s p i t e o f th e p r e s e n c e o f s i g n i f i c a n t l y

r e p u l s i v e nonbonded hydrogen i n t e r a c t i o n s . M olecu la r

mechanics c a l c u l a t i o n s , w i t h WBFF, were i n e x c e l l e n t

agreem ent w i t h t h i s o b s e r v a t i o n - t h e c a l c u l a t e d o l e f i n i c

t o r s i o n a l a n g le was 0° - and th e hydrogens were found to

e c l i p s e th e do u b le bond . The c a l c u l a t e d s t e r i c e n e rg y ,

Vs , was o n ly 2^*00 k c a l / m o l e , which i n d i c a t e s t h a t the

compound has abou t t h e same s t r a i n as 5 - e t h y l i d e n e n o r -

b o rn en e and v/hich i s abou t tw ice th e s t e r i c e n e rg y o f

adamantane ( 1 1 .3k k c a l / m o l e ) . The c e n t r a l bond l e n g t h e n i n g

- 7 8 -

i s n o t v e r y s t r o n g - 1 .3U9& as compared to 1 .3352 i n

e t h y l e n e - and the Csp2 - Csp^ i s 1 .5232 compared 1 .5012

i n p ro p e n e . The C = C -Csp2 v a le n c y ang le i s o n ly 1 2 3 .6 °

and , as a r e s u l t , t h e H . . . . H d i s t a n c e i s o n ly 1 .8 7 2 . The

r i g i d adamantane r i n g s , i n V I I I , a re n o t s u b s t a n t i a l l y

d i f f e r e n t from an i s o l a t e d adamantane m o le cu le . These

r e s u l t s i n d i c a t e t h a t the s t e r i c crowding i n b ia d a m a n t -

y l i d e n e i s r e l i e v e d m o s t ly by bond s t r e t c h i n g a lo n e .

3Opening o f th e C = C-Csp v a le n c y a n g le to about

127°> as i n c i s - 2 - b u t e n e , would s e v e r e l y d i s t o r t the

p r e f e r r e d geometry o f the adamantane r i n g s and t w i s t i n g

abou t th e doub le bond would minimise the H . . . . H

i n t e r a c t i o n s a c r o s s th e r i n g s b u t would a g g ra v a t e o t h e r

r e p u l s i v e nonbonded i n t e r a c t i o n s and r e s u l t i n a weakening

o f th e TT-bond •A

An X -ray s t u d y o f s y n - b i s - 2 .2 - f e n c h y l i d - e n e - E (IX)U9h a s been r e p o r t e d by S im o n e t ta . There i s c o n s i d e r a b l e

s t e r i c h in d r a n c e i n t h i s m olecu le as a r e s u l t o f th e

nonbonded i n t e r a c t i o n s which a r i s e from th e p r e s e n c e of

t h e s i x m ethyl groups abou t the doub le bond. M olecu lar

m echanics c a l c u l a t i o n s have been used to i n v e s t i g a t e t h i s

- 79 -

m olecu le i n an a t t e m p t to u n d e rs t a n d how the s t e r i c

h in d r a n c e e f f e c t s th e m o le c u la r geometry and en e rg y .

The s t e r i c e n e rg y , Vs, o f t h i s molecule i s

c a l c u l a t e d t o "be 63 .75 k c a l /m o le which i n d i c a t e s t h a t

t h e m o lecu le i s h i g h l y s t r a i n e d much of which i s due to

Baeyer s t r a i n .

C a l c u l a t i o n s i n d i c a t e t h a t th e s t e r i c h in d ra n c e

c a u se s a s l i g h t d e fo r m a t io n i n the c e n t r a l hond l e n g t h

(1 . 360S) and a s l i g h t l y l a r g e r d e fo r m a t io n i n th e Csp2-

Csp^ hond (1 .5 3 US)* The v a le n c y a n g le s a re a l s o a d ju s te d

t o m in im ise th e nonhonded i n t e r a c t i o n s between th e methyl

g r o u p s . The C=C-Csp^ v a le n c y a n g le s a re opened to 1 2 6 .0 °

and 1 2 6 . 8° w i t h th e Csp^-Csp^-Csp^ ang le d i f f e r i n g

s i g n i f i c a n t l y from t h e i r e q u i l i b r i u m (1 0 9 . 5° ) v a lu e -

t h o s e i n v o lv i n g th e ca rb o n w i th a s i n g l e m ethyl group a re

o b se rv ed to be 1 2 3 «U° w h i le th e o t h e r f o u r a n g le s a s s o c i a t e d

w i t h th e c a rb on s which each b e a r two methyl g roups have

th e ave rage v a lu e o f 115*8°* The o l e f i n i c t o r s i o n a l

a n g le i s obse rved to be 1 1 . 8° i n th e c r y s t a l . This i s

s i m i l a r t o th e v a lu e o f 15*3° c a l c u l a t e d by th e WBFF, b u t

i s s i g n i f i c a n t l y d i f f e r e n t from th e v a lu e o f 2U ° c a l c u l a t e d

by AFF. T h is s u p p o r t s th e view t h a t th e AFF u s e s H . . .H

p o t e n t i a l s which a re u n a c c e p t a b l y ' h a r d * . These d e fo r m a t io n s

r e s u l t i n th e s h o r t e s t 1-6 c o n t a c t s be tween th e methyl

g roups b e in g 3 *1 oX and th e l o n g e r ones b e in g 3 *M+2 .

- 8 0 -

I t i s i n t e r e s t i n g to n o te t h a t A l l i n g e r has r e c e n t l y2 78upgraded h i s 1972 f o r c e f i e l d 9 . This was accom pl ished

by th e i n c l u s i o n o f o n e - f o ld and tw o - fo ld b a r r i e r s i n the

t o r s i o n a l p o t e n t i a l s w i t h the r e s u l t t h a t th e new H . . .H

p o t e n t i a l was made s o f t e r and s m a l l e r . As e x p e c t e d ,

t h e r e l i a b i l i t y o f th e f o r c e f i e l d i s g r e a t l y improved.

The s t a n d a r d d e v i a t i o n between th e c a l c u l a t e d and

e x p e r i m e n t a l h e a t s o f f o r m a t io n o f k2 h yd ro ca rb on s i s

0.1+2 k c a l / m o l e . The new f o r c e f i e l d , i n c o n t r a s t t o the

o ld o ne , c o r r e c t l y p r e d i c t s th e BCB as th e minimum

e n e rg y c o n fo rm a t io n o f c y c lo d e c a n e . In a d d i t i o n , he70

a l s o r e t r a c t s h i s "g auche-hydrogen h y p o t h e s i s " , b u t

a t t h e same t im e , does n o t a c c e p t th e c o n v e n t io n a l 37e x p l a n a t i o n s •

- 81 -

2 . 5 R e fe re n c e s

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J . Amer. Chem. S o c . , 2 2 , 8005 (1973)

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3 . 0 . Ermer and S. L i f s o n , J . Amer. Chem. S o c . . 31f

41 21 (19 7 3 ) .

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5* P. von R. S c h l e y e r , P r i v a t e Communication.

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J . J . Rooney, J . Amer. Chem. S o c . , 9 7 . 3835 (1975)

7 . W. P a r k e r , W.V. S t e e l e and I . W at t , su b m i t te d to

J . Chem. S o c . t F a raday

8 . R.B. T u r n e r , B . J . Mal lon , M. T ic h y , W. von E. D o e r in g ,

W.R. Roth and G. S c h ro d e r , J . Amer. Chem. S o c . ,

22 , 8605 ( 1 9 7 3 ) .

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2 2 , 272 (1976)

13* E . J . J a c o b , H.B.-Thompson and L .S . B a r t e l l , J . Chem.

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14* R .L . H i l d e r b r a n d t , J .D . W ieser and L.K. Montgomery,

J . Amer. Chem. S o c . . 9 5 . 8598 (1 9 7 3 ) .

- 82 -

S. Chang, D. McNally, S. S h a ry -T e h ran y , M.J. Hickey

and R.H. Boyd, J . Amer. Chem. S o c . . 92 . 3109 (1970)

J . B . H en d r ic k so n , J . Amer. Chem. S o c .« .82,7036, 70l+3>

70+7 (1 96 7 ) .

N.L. A l l i n g e r , M.T. T r i b b l e , M.A. M i l l e r and D.H.

W ertz , J . Amer. Chem. S o c . , 9 3 . 1637 (1971)•

S. Kondo, E. H i r o t a and Y. Morino, J . Mol. S p e c t r o s c . .

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A.A. B o thner - By, C. N a a r -C o l in and H. G un the r ,

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D.R. S t u l l , E .F . Westrum J r . , and G.C. S in k e , " The

Chemical Thermodynamics o f Organic Compounds" ,

W iley , New York, N .Y . , 1969*

S. Kondo, E. H i r o t a and Y. Morino, J . Mol. S p e c t r o s c . .

2k, 231 (1 9 7 0 ) .

A. Almenmgen, L. M. A n f in se n and A. H aa land , Acta

Chem. Sc a n d . . 21+. 1+3 (1 970)

D .N .J . White and 0 . Ermer, Chem. P h y s . L e t t . ,

2L, 111 (1 9 7 5 ) .

F .A .L . Anet and L. K o z e r s k i , J . Amer. Chem. S o c . .

21, 31+07 ( 1 9 7 3 ) .

F .A .L . Anet and R. Anet i n Dynamic N uc lea r

Magnetic Resonance S p e c t r o s c o p y . F .A. C o t to n and

L.M. J a c k s o n , E d . , Academic P r e s s , New York,

p . 571 (1 9 7 5 ) .

K.L. A l l i n g e r and J . T . Sp rag u e , T e t r a h e d r o n . 31 .

21 ( 1 9 7 5 ) .

0 . E rmer, J . Amer. Chem. S o c . . 9 8 . 3961+ (1 97 6 ) .

L. Hedberg and K. Hedberg, A bs . P a p e r s , N a t . Meeting

Amer. C r y s t . A s s . . 196U, Bozeman, Montana.

- 8 3 -

29* R.K. MacKenzie, D.D. MacNicol, H.H. M i l l s , R.A.

R a p h a e l , F .B . W ilson and J .A . Z abk iew iez , J . Chem

S o c . . P e r k in I I . 1632 (1 97 2 ) .

30 . G. F a v i n i , F . Z u c c a r e l l o and G. Buemi, J . Mol.

S t r u c t . . 2 , 385 (1 9 69 ) .

31* F o r a rev iew see J .D . D u n i t z , i n J .D . D u n i t z and

J .A . I b e r s ( E d s . ) , P e r s p e c t i v e in S t r u c t u r a l

C h e m i s t r y . No. 2 , W iley , New York, 1968, p . 7 .

32 . R. B i l l e t e r and H.H. Gunthard , H e lv . Chim. A c t a . .

l±i, 338 and 686 (1958) .

33* 0 . Ermer, S t r u c t u r e and Bonding . 2 7 . 1 (1 9 7 6 ) .

3U* D .N .J . White and M.J. B o v i l l , Acta C r y s t . . B ( i n

p r i n t •

35* T. C l a r k , T. McO. Knox, H. Mackie and M.A. McKervey,

Chem. Comm. . 666 (1975)•

3 6 . S .A . G o d le sk i and P. von R. S c h l e y e r , Chem. Comm. .

38 (1 9 7 6 ) .

-37* E .L . E l i e l , N.L. A l l i n g e r , S . J . Angyal and G.A.

M o rr i son , C o n fo rm a t io n a l A n a l y s i s . W i l e y - I n t e r s c i e n c e ,

New York, N .Y . , 1965* P*13*

3 8 . D.H. Wert?; and N.L. A l l i n g e r , T e t r a h e d r o n . 30, 1579*

(1 91k) •

39* R.H. Boyd, J . Amer. Chem. S o c . . 97 . 5353 (1975)

(no te r e f . 19)

J+0. S . F i t z w a t e r and S. B a r t e l l , J . Amer. Chem. S o c . .

2 8 , 5107 (1976 ) .

41• E .L . Osma, V.S . Mastryukov, L.V. V i lkov and N.A.

B e l ik o v a , J . Chem. Soc . . Chem Comm.. 13 (1976)

- 8 4 -

4 2 . W.A.C. Brown, G. E g l i n t o n , J . M a r t in , W. P a r k e r and

G.A. Sim, P r o c . Chem. S o c . . 57 (1964)

43* P.D. Cradwick and G.A. Sim, J . Chem. S o c . ( B ) . 2213(1971 ) .

44 • E.N. M arvel l and R .S . Knutson, J . Org. Chem. . 3 5 .

388 (1970) .

45* H . J . S c h n e id e r , Org. Mag. R e s . . 8 , 363 (1976)

4 6 . M.J. B o v i l l , P . J . Cox, H.P. P l i t m a n , M.H.P. Guy,

A.D.U. Hardy, G.A. Sim, D .N .J . W hite , A c ta C r y s t ( B ) .

i n p r e p a r a t i o n .

4 7 . D . J . B rauer and C. K ruger , Acta C r y s t . B29. 1 6 8 4 (1 9 7 3 ) .

4 8 . J .H . W ie r in g a , J . S t r a t i n g , H. Wynberg and W. Adam,

T e t r a h e d r o n . 28, 169 (1 9 72 ) .

49* M. S im o n e t t a , p r i v a t e communicat ion .

5 0 . J .D . Cox and G. P i l c h e r , " Thermochemis try o f Organic

and O rg a n o m e ta l l ic Compounds'1. Academic P r e s s ,

New York, N .Y., (1970)

51 • S.W. Benson, P .R . C ru ic k s h a n k , D.M. Golden, G.R.

Haugen, H.E. O 'N ea l , A.S . R odgers , R. Shaw and

R. Walsh, Chem. Rev . . 6 9 . 279 (1 9 6 9 ) .

5 2 . R.H. Boyd, S.N. Sanwai, S . S ha ry -T ehrany and D. McNall ly ,

J . Phys . Chem. . 21$ 1264 (1971 ) .

53* R. Walsh and J.M. W e l l s , J . Chem. Therm. . 1 4 9 (1 9 7 5 ) .

54* M.P. K oz ina , L .P . T im ofeeva , th e l a t e S.M. S k u ra to v ,

N.A. B e l ik o v a , E.M. M i l v i t s k a y a and A.P . P l a t e ,

J . Chem. Therm. . 563 (1971 ) .

95* K. K u c h i t s u , J . Chem. P h y s . . 4 4 . 906 (19 6 6 ) .

5 6 . D.R. L ide and D. C h r i s t e n s e n , J . Chem. P h y s . . 35 .

1374 (1561 ) .

- 8 5 -

5 7 * L.H. Scharpen and V.W. L a u r i e , J . Chem. P h y s . , 3 9 ,

1 7 3 2 ( 1 9 6 3 ) .

5 8 . T. Shimanouchi , Y. Abe and K. K u c h i t s u , J . Mol. S t r u c t . .

2 , 82 (1 968 ) .

5 9 * I* Tokue, T. Fukuyama and K. K u c h i t s u , J . Mol. S t r u c t . .

2 5 , 3 3 ( 1 9 7 4 ) .

6 0 . J . Laane and F .C . Lord , J . Chem. P h y s . , 47 . 4941 (1967)

61 . J . F . Chiang and S.H. Bauer , J . Amer. Chem. S o c . , 91 .

1898 (1969) .

6 2 . A. Almenningen, G.G. J a co b sen and H.M. S e i p , Acta

Chem. Sc a n d . , 2 5 , 1 49 5 ,(1969)

6 3 . A. Yokozeki and K. K o c h i t s u , B u l l .C h em .S o c . . J a p a n ,

2356 (1 97 1 ) .

64. A. Yokozeki and K. Kochitsu, Bull. Chem. Soc., Japan,y t , 1783 (1971 ) .

6 5 . G. D a l l i n g a and L.H. Toneman, J . Mol. S t r u c t . , 1_,

117 (19 67 ) .

6 6 . B.A. Arbuzov and V.A. Naumov, Doklady Akad Nauk S . S . S . R . ,

1 5 8 , 376 (1 96 4 ) .

67* H . J . G e i s e , H.R. Buys and F .C . M i j l h o f f , J . Mol. S t r u c t . ,

2, 447 (1971 ) .

6 8 . M. Davis and 0 . H a s s e l , Acta Chern. Sc a n d . , 1 7 . 1181 (1970)

- 86 -

CHAPTER THREE

A p p l i c a t io n o f t h e W h i te - B o v i l l f o r c e f i e l d (WBFF)

t o t h e c o n fo r m a t io n a l a n a l y s i s o f

c y c l i c h y d rocarb on s ,

- 87 -

3 .1 . I n t r o d u c t i o n

C o n fo rm a t io n a l a n a l y s i s c o u ld p r o f i t a b l y u t i l i z e more

d e t a i l e d knowledge of th e r e l a t i o n s h i p between conforma

t i o n a l s t r u c t u r e and energy . M olecu lar mechanics (MM)

c a l c u l a t i o n s supp ly t h i s i n f o r m a t io n and, in a d d i t i o n ,

p r e d i c t p r o p e r t i e s o f u n o b se rv ab le c o n fo rm a t io n , e . g . t r a n s i

t i o n s t a t e s .

I t i s u s u a l t o c l a s s i f y c a r b o c y c l i c r i n g s as f o l lo w s :

sma11 3 ,4"no rm al” 5 , 6 , 7medium 8 , 9 , 1 0 , 1 1l a r g e 11

The s t r a i n e n e r g i e s and g e o m e t r i e s o f c y c l e n e s , w i th

one double bond in t h e r i n g , r a n g in g from a n d w i th

two double bonds in th e r i n g , r a n g in g from C g - C ^ have been

c a l c u l a t e d u s in g t h e W h i t e - B o v i l l Force F i e l d (WBFF), which

was d e s c r i b e d in C hapte r 2. In t h e p a r a m e t r i z a t i o n o f th ej)e

WBFF , use was made o f what e x p e r im e n ta l d a ta was a v a i l a b l e

f o r medium r i n g compounds, which most of th e s tu d y w i l l be

conce rn ed w i th and which had been l a r g e l y n e g l e c t e d in t h e

p a r a m e t r i z a t i o n of o t h e r f o r c e f i e l d s . I t was t h e r e f o r e

p o s s i b l e t o p l a c e a c e r t a i n deg ree of c o n f id e n c e in our

r e s u l t s from th e i n v e s t i g a t i o n of th e p l e t h o r a of conforma

t i o n s and t r a n s a n n u l a r i n t e r a c t i o n s e x h i b i t e d by medium

r i n g s .

*The WBFF produced e x t r e m e ly r e l i a b l e r e s u l t s f o r

g e o m e t r i e s , h e a t s o f fo r m a t io n and h e a t s o f hydrogenation o f a number of medium r i n g compounds.

- 88 -

Combustion measurements a l lo w an e s t i m a t e t o be made

o f t h e t o t a l s t r a i n in c y c l o a l k a n e s r e l a t i v e t o a c y c l i c

a l k a n e s which a r e assumed t o be s t r a i n - f r e e . ' * ' A l l r i n g s ,

e x c e p t c y c lo h ex an e , have h ig h e r h e a t s of combust ion p e r

m ethy lene group, and th e e s t i m a t e d t o t a l s t r a i n p e r mole

i s g iven below.

RING SIZE (n) 5 6 7 8 9 10 11 12 13 14

ESTIMATED TOTALSTRAIN ( k c a l .

1 mole) 7 0 6 10 13 12 12 4 5 0

The medium r i n g s th u s p o s s e s s a s p e c i a l c o n f o r m a t i o n a l

s i t u a t i o n in t h a t they have more s t r a i n t h a n th e "no rm al”

and l a r g e r i n g s . On t h e b a s i s of i n f o r m a t i o n from s p e c t r o

s c o p i c and X-ray d i f f r a c t i o n and from i n s p e c t i o n of m o le cu la r

model , we can a n t i c i p a t e 3 t y p e s o f s t r a i n in medium r i n g s .

1. T r a n s a n n u la r S t r a i n , which i s due t o crowding of a toms,

u s u a l l y hydrogens , a c r o s s t h e r i n g . In c y c lo d e c a n e , th e

major c o n t r i b u t i o n t o t h e s t r a i n energy of t h e BCB conforma

t i o n a r i s e s from s i x ve ry s h o r t H . . . . H c o n t a c t s which

l i e on t h e r e p u l s i v e p o r t i o n o f t h e Van der Waals cu rve .

2. P i t z e r S t r a i n , i s due t o t h e e x i s t e n c e o f e c l i p s e d con

f o r m a t io n s , e . g . in c y c lo d e c a n e , t h e r e a r e 2 a n t i - and

8 gauche - bu tan e i n t e r a c t i o n s .

33. Baeyer or Angle S t r a i n , e . g . i n c y c lo d e c a n e , th e CSp -

CSp - CSp° a n g le s a r e i n c r e a s e d t o a mean v a lu e o f 117

t o m in im ise P i t z e r and t r a n s a n n u l a r s t r a i n s i n c e v a le n c e

a n g le d e fo rm a t io n i s e n e r g e t i c a l l y "cheap" .

3We a l s o might a n t i c i p a t e t h a t t h e c o n v e r s io n o f spo

t o sp^ h y b r i d i z a t i o n a t one o r more ca rbon atom i s f a v o u re d

- 89 -

2i n some of t h e s e sys tem s because th e sp c o n f i g u r a t i o n has3

a s m a l l e r number of C-H bonds th an th e sp c o n f i g u r a t i o n

and th u s l e a d s t o a r e d u c t i o n in s t r a i n , due in p a r t t o

t h e p r o x im i ty o f s u b s t i t u e n t s on o p p o s i t e s i d e s o f t h e

r i n g s and t o bond o p p o s i t i o n s . However, changes o f bond

h y b r i d i z a t i o n may p roduce co nco m itan t changes in a n g le

s t r a i n a n d /o r t r a n a n n u l a r s t r a i n . These changes may be

e i t h e r f a v o u r a b l e o f u n fa v o u r a b le .

T his s u p p o s i t i o n i s su p p o r t e d by a number o f r e a c t i o n s

which show t h e e f f e c t s o f I - s t r a i n , which i s d e f i n e d a s th e

"change in i n t e r n a l s t r a i n which r e s u l t s from change in

c o o r d i n a t i o n number of a r i n g atom in v o lv e d in chem ica l

r e a c t i o n " . ^

1. R e a c t i o n s of Cycloalkanones w i th Hydrogen Cyanide t o3

g iv e Cyanohydrins

Ring 5 6 7 8 9 10 11 12 13 14S ize

K 3 .33 70 0 .5 4 0 .0 8 1 0 .0 41 sm a l l 0 .0 63 0 .2 2 6 0 .2 6 9 1 .17

- 90 -

2. A c e t o l y s i s o f C y c lo a lk y l T o s y l a t e s 4

GHOTs > (C

RingS iz e 5 6 7 8 9 10 11 12 13 14

R e l a t i v ek a t 70 10 .5 0 .7 5 1 9 .0 144 129 286 30 .8 2 .44 2 .6 3 0 .9 9

In r e a c t i o n 1, t h e d i s s o c i a t i o n o f th e c y an o h y dr in r e s u l t s

bond a n g le s ( d i s t r i b u t e d over t h e whole r i n g ) , bu t much

more im p o r t a n t , t h e r e i s a r e d u c t i o n of t r a n s a n n u l a r s t r a i n ,

so t h a t , in t h e c a se of medium r i n g s , t h e e q u i l i b r i u m l i e s

t o t h e l e f t . In r e a c t i o n 2, t h e r e i s a r e l i e f o f t r a n s -, 2a n n u la r s t r a i n in t h e t r a n s i t i o n s t a t e (sp h y b r i d i s e d ) .

The a c t i v a t i o n energy i s lo w e s t , hence t h e r a t e i s h i g h e r ,

when t h e ground s t a t e com press ion i s g r e a t e s t , a s i t i s in

t h e medium r i n g s . The i n c r e a s e i n a n g u la r s t r a i n on 3 2going from sp t o sp a g a i n i s l e s s im p o r t a n t . G e n e r a l l y ,

i n t h e r e g i o n o f medium r i n g s , r e a c t i o n s which in v o lv e an

3in an i n c r e a s e o f t h e a l r e a d y s t r a i n e d sp - h y b r i d i z e d

i n c r e a s e in I - s t r a i n a r e s low and r e a c t i o n s

which in v o lv e a d e c r e a s e in I - s t r a i n a r e

f a s t .

3 .2 . The E f f e c t o f i n t r o d u c i n g a doub le bond i n t o

C y c lo a lk a n e s , C7-C^q

Columns (1) and (2) in Table 1 m i r r o r t h e same t r e n d

0 0 0 0« t u « •

«• - v« v*W

K CM CM K.0 0 ««• K«k • •t •

0 CM 0 K.z CM «*o

0t - o•uX ►»ac *■% 0-+ ««o 0 0 0 0 0U. A • u u u u XZ «•« «v*o ou 0 to •u CM 0 z

0 0 0 0 Ul ««>> • • • m Z 0C3 0 0 0 0 Ul Ul za. to V* «*M? o0 Ul 0 Ul Mz 2 < « ►>Ul WMO •<

*-t 3 zX 0)0< t 03 *■% W < 0 3 €3X 0 0 0 0 « 2 t J< o*-# u u 0 Ul 3 0 O Xz * • •>• «« Z t <>- 3 oM w ^ 0 «_# w 0 3 0 0 0 >-X 0 0 CM 0 0 X < 3 1 »- X

0 CM ■ 'M 0 0 3 0 0 0 0u. • • • m Z •< 3 >- Z • 0o m 0 ■M < o o o < « o

«-• «■* t 3 v ■ ae z0 3 0 0 0 1- <Ul • <>-•»-» »(K *->W 0) O O 0 O 0 *- •<3 O 3 • Z «Z % 0at z 0 0 K O 0 < 0 < 0 XUl 3 (O 0 0 fO > m or m it mz o • • • • o o o *~ o Xui a. 0 0 w* o

X «« «-» w 0 0 0 0 0 0 ctu o o o o o o o 0M O •ac >-»->->->->- O 0Ul <3 00(9 0 0 0 0 zH Z acacfleoritQc *- 0n 0 0 K 0 0 0 0 0 0 0 < X

cr CM 9 0 M" 9 z z z z z z X 3 0a m • • • 0 0 0 0 0 0 M < 3Ul X m IS. 0 0 ►“ • O►- 3 o o o o o o 0 0 X< H 0 •-* V.3 O SKiraffK o 33 ul 0 0 0 0 0 0 >- •<u x 1- 13 U o3 « « 0 0 0 0 0 0 or o< U. to ■ ■! 0 9 0o a «-• to 0 0 •»-» z z z

■W m • • • /■% »> 0 o M0 ro M *4(MOMID«0 M

M v« v« »-# W WWW w o ►- 0«4 M < 0

z z z z z z a x MUl (3 Ul X X X X X X 0 X C33 2 NIK 0 9 9 3 3 3 3 3 3 ►> o Xao M •-» 3 3 3 3 3 3 0 0 0-< a: 0 o o o o o o z»— o o o o o o * 0

- 92 -

i n s t r a i n a s t h a t d e r i v e d from t h e h e a t o f combus t ion

measurements and co n f i rm t h a t th e i n t r o d u c t i o n o f a c i s

doub le bond i n t o t h e r i n g r e s u l t s in a r e d u c t i o n in s t r a i n ,

a s p r e d i c t e d above. Column 3, however , does n o t show t h i s

t r e n d . M olecu lar mechanics c a l c u l a t i o n s i n d i c a t e t h a t th e

i n t r o d u c t i o n of a t r a n s r a t h e r th an a c i s double bond l e a d s

t o u n f a v o u r a b l e changes in t o r s i o n a l s t r a i n , and t o a

s m a l l e r bu t s i g n i f i c a n t change, in a n g le s t r a i n and t r a n s

a n n u la r s t r a i n . These s t r a i n components a r e l a r g e s t in

Cg compound and d e c r e a s e a s r i n g s i z e i n c r e a s e s s i n c e t h e

s t r a i n a s s o c i a t e d w i th th e i n t r o d u c t i o n o f a t r a n s double

bond can be d i s t r i b u t e d more e f f i c i e n t l y in t h e l a r g e r

r i n g s . F u r th e rm o re , th e poor TT o v e r l a p , which a r i s e s a s

a r e s u l t of t h e t w i s t i n g of t h e doub le bonds in t r a n s -

c y c l o a l k e n e s , t h e s t r a i n e d O bonds and nonbonded r e p u l s i o n s

make some of t h e s e compounds h i g h ly r e a c t i v e and d i f f i c u l t

t o i s o l a t e e . g . t r a n s - c y c l o h e p t e n e .

Heats o f h y d r o g e n a t io n f o r c y c l o a l k e n e s (c i s

and t r a n s ) a g re e f a v o u r a b ly w i th t h e o b se rv ed v a lu e s and

e n a b l e s some c o n f id e n c e t o be p l a c e d i n t h e above o b s e r v a

t i o n s ( see Table 2 ) .

3 . 3 . The E f f e c t o f i n t r o d u c i n g a second double bond i n t o

C y c lo a lk e n e s , Cg-C1Q

The i n t r o d u c t i o n of a second c i s doub le bond i n t o c i s -

c y c l o o c t e n e a t ca rbon 5 r e s u l t s in an i n c r e a s e in s t r a i n of

2 .1 7 k c a l . / mole. The minimum energy c o n fo rm a t io n of

c i s , c i s - 1 , 5 - c y c l o o c t a d i e n e has been shown by s p e c t r o s c o p i c

and d i f f r a c t i o n s t u d i e s t o be a t w i s t - b o a t (F ig u re 1, s e e

0» XI »•M H C3

O M to QD IS4 Z r~> Z m o mr~n >■ X IOa o n» Mr~ i t f « 1 >>*» -» PO iu IO -t—« M (52 Ui ro o -4 Xm o • a a *-* o x> mo O' o> VO 09 T ► >•

> IO OB Z -1CE O X o s o s-< M -<

o c o o-1 XI -< nX 1 a • o om w IO Ui -1 <0 f~ X

o to x rn o -<X • a • ► z o oOD CO *> IO z ► r~ xT *>• *9 CA -1 r*i oT M t o

o m mz z z

CA ►m w - c

ao ►CO O z

• • • 04 ou i IO «o m >a a a * X XIu OB CO c a © IT

>4 o n» x (To o ►

»■ -«r~ M

n * <► ’V nf ” X

a o o c e« a *» c r* —*

w -* t s f “ in >•a a • ► V4k. O >a H•— ** M i*i r*

o *-4-4

> o«**n*►

• • r~ » -• a* a* n Z• • a a o« ''O * . a*» *> * o

V« •

- 94 -

F ig u r e 1 : The c a l c u l a t e d t w i s t - h o a t con form ation o f

c i s , c i s - c y c l o o c t a - l , 5 “^ i ene (Cg symmetry)#

- 96 -

a l s o C hap te r 2 . 3 ( d ) ) . In F ig u re 1, The Cl . . . C6 and

C4 . . . C7 nonbonded d i s t a n c e s a r e found e x p e r i m e n t a l l y 6 ° °t o be 3 .0 5 A and 3 .1 9 A r e s p e c t i v e l y . The c o r r e s p o n d in g

o ov a l u e s , c a l c u l a t e d by th e WBFF a r e 3 .08 A and 3 .19 A

r e s p e c t i v e l y , which a r e in good agreement w i th t h e e x p e r im e n ta l

v a lu e s . The H4 . . . H8 d i s t a n c e i s c a l c u l a t e d to be 1 .94 A.

A l l t h e s e nonbonded i n t e r a c t i o n s l i e on t h e r e p u l s i v e

p o r t i o n o f t h e Van der Waals cu rv e s and th u s g ive r i s e t o

t r a n s a n n u l a r s t r a i n . The more im p o r tan t f a c t o r h e re i s

t h a t th e C = C - C 3 bond a n g le s a r e i n c r e a s e d t o a meanspv a lu e o f 1 2 7 .8 ° and t h e C 2 - C 3 - C 3 a n g le s t o asp sp spmean v a lu e o f 1 1 5 .8 ° in o r d e r t o accommodate t h e second

c i s double bond i n t o t h e e i g h t membered r i n g . This Baeyer

s t r a i n and t r a n s a n n u l a r s t r a i n a r e m a n i f e s t e d i n t h e s t r a i n

energy components .

The i n t r o d u c t i o n o f a t r a n s double bond i n t o c i s -

c y c l o o c t e n e , which y i e l d s 1 , 5 - c i s , t r a n s - c y c l o o c t a d i e n e

l e a d s t o an i n c r e a s e of 16.79 k c a l . / m o l e in t h e o v e r a l l

s t e r i c ene rg y . S i m i l a r l y , when a t r a n s coub le bond i s

i n t r o d u c e d i n t o t r a n s - c y c l o o c t e n e to g ive 1 , 5 - t r a n s , t r a n s -

c y c l o o c t a d i e n e , t h e s t e r i c energy i n c r e a s e s by 17.26 k c a l . /

mole. As i n t h e c a se of t h e i n t r o d u c t i o n of th e f i r s t

t r a n s doub le bond i n t o an e ight-membered c y c l i c compound,

t h e i n t r o d u c t i o n o f t h e t r a n s double bonds in t h e l a t t e r

two c a s e s r e s u l t s i n l a r g e and u n fa v o u ra b le changes in

t o r s i o n a l s t r a i n and t r a n s a n n u l a r s t r a i n a s w e l l a s s m a l l e r

i n c r e a s e s in Baeyer s t r a i n .

The s t e r i c energy o f t h e minimum energy c o n fo rm a t io n of

c i s , c i s - 1 , 5 - c y c l o n o n a d i e n e , th e c h a i r (F ig u re 2) i s 3 .2 1 k . c a l

/mole l e s s t h a n t h a t o f c i s - c y c lo n o n e n e . This d e c r e a s e i s

- 97 -

F ig u r e 2 : The minimum energy con form ation o f c i s , c i s - 1 . 5 -

c y c lo n o n a d ie n e .

F igure The minimum energy c on form ation o f c i s , c i s

1 16- c y c l o d e c a d ie n e .

- 98 -due t o t h e f a c t t h a t t h e r e i s a d e c r e a s e in t h e crowding

o f atoms a c r o s s t h e r i n g because t h e r e a r e fewer hydrogens

in t h e d i e n e and a l s o because t h e minimum energy conforma

t i o n o f t h e d ie n e i s a c h a i r , in which Cl . . . C6 nonbondedo

d i s t a n c e i s 3 .34 A and which i s r e l a t i v e l y s t r a i n - f r e e .

S i m i l a r l y , t h e s t e r i c energy o f c i s , c i s - l , 6 - c y c l o d e c a d i e n e

i s 4 .3 1 k c a l . / mole lower th an c i s - c y c l o d e c e n e . The

minimum energy co n fo rm a t io n i s a g a in a c h a i r (F igure 3) ,

which i s r e l a t i v e l y s t r a i n - f r e e and C 2 . . .C 6 nonbonded i s o

3 .65 A. T h is d e c r e a s e i s mainly due to a d e c r e a s e in t r a n s

a n n u la r s t r a i n because t h e r e a r e fewer C-H bonds and t o a

d e c r e a s e in a n g le s t r a i n because t h e i n t e r n a l r i n g a n g le s do

n o t have t o i n c r e a s e as much t o minimise t h e t r a n s a n n u l a r

s t r a i n .

The minimum energy co n fo rm a t io n of c i s , t r a n s - 1 , 6 -

c y c lo d e c a d ie n e (F ig u re 4) i s only 1 .9 k c a l . / m o l e lower

th a n c i s - c y c lo d e c e n e . In F ig u re 4, t h e Cl . . . C7 nonbondedo

d i s t a n c e i s 2 .99 A ( th e a s s o c i a t e d non bonded energy i s

0 . 7 k c a l . / m o l e in WBFF), so t h a t t h e t r a n s a n n u l a r s t r a i n

w i l l n o t be re d u c e d . The major r e d u c t i o n in energy i s

due to a r e d u c t i o n in Baeyer s t r a i n (which i s a r e s u l t o f

th e d e c r e a s e in t h e number o f C-H bonds) . However, i t i s

i n t e r e s t i n g t o n o te t h a t th e t o r s i o n a l energy i s h ig h e r (by

0 .3 4 k c a l / m o l e ) in th e c i s , t r a n s - d i e n e th a n in t h e c i s ene

which i n d i c a t e s t h a t th e i n t r o d u c t i o n of t h e t r a n s double

bond i n t o c i s - c y c l o d e c e n e s t i l l p roduces u n f a v o u r a b l e changes

in P i t z e r s t r a i n .

The minimum energy co n fo rm a t io n of t r a n s , t r a n s - 1 , 6 -

- 99-F ig u re 4 : -he minimum ©".er£y c o n fo im a iio n o f c i s t t r a n s

i t 6 -o y c lo d e c a d :.cn e .

f i g u r e rj ; ih e minLmum c n o - jy confor m:ica o f t ran s , t r a n s - - > 6 -

c y c lo d c c a d ie n e .

- 100 -

c y c lo d e c a d ie n e has been shown t o be t h e " c h a i r - c h a i r " con

fo r m a t io n (F ig u re 5 ) . This co n fo rm a t io n i s computed t o be

4 .5 5 k c a l . / m o l e lower th an t h a t o f t r a n s -c y c lo d e c e n e .

The change in h y b r i d i s a t i o n in t h i s c a s e , p ro d u ce s a

r e d u c t i o n i n t o r s i o n a l s t r a i n and a n g le s t r a i n . I t a l s o

p ro d u ce s a r e d u c t i o n in th e t r a n s a n n u l a r i n t e r a c t i o n s i n v o l v

in g t h e hydro gen s , b u t , s i n c e th e Cl . . . C7 and C2 . . . C6o

nonbonded d i s t a n c e s a r e bo th only 2 .84 A, t h e Van der Waals

p r o f i l e s o f t h e two double bonds a r e f o r c e d t o i n t e r p e n e t r a t e

and r e s u l t i n a s t r a i n energy component of 2 .58 k c a l . / mole.

Thus t h e t r a n s a n n u l a r s t r a i n i s 0 . 2 k c a l . / m o l e h ig h e r in

t h e d ie n e .

On t h e b a s i s o f t h e r e s u l t s in Table 1, t h e f o l lo w in g

p o i n t s may be deduced:

(a) The l e a s t s t r a i n e d Cg compound i s c i s - c y c lo o c t e n e a n d

t h e most s t r a i n e d i s t r a n s , t r a n s - 1 , 5 - c y c l o o c t a d i e n e .

(b) t h e l e a s t s t r a i n e d C^ compound i s c i s , c i s - 1 , 5 -c y c lo n o n a -

d ie n e and t h e most s t r a i n e d i s t r a n s , t r a n s - 1 , 5 - c y c l o n o n a d i e n e .

(c) t h e l e a s t s t r a i n e d C10 compound i s c i s , c i s - 1 , 6 - c y c l o

d e c a d ie n e and th e most s t r a i n e d i s cy c lo d ec an e .

(d) f o r C0-C, , c i s - c y c l o a l k e n e s a r e l e s s s t r a i n e d th ang J_Q ----

t h e c o r r e s p o n d i n g t r a n s - c y c l o a l k e n e s .

(e) f o r Cg and CQ r i n g s , t h e c i s , c i s - c y c l o a l k a d i e n e s

a r e l e s s s t r a i n e d than th e c o r r e s p o n d in g c i s , t r a n s - i s o m e r s

which, in t u r n , a r e l e s s s t r a i n e d th an th e t r a n s , t r a n s -

i s o m e r s .

( f ) t h e s t r a i n , a s s o c i a t e d w i th th e i n t r o d u c t i o n o f a t r a n s

double bond, i s s i g n i f i c a n t l y l e s s in th e ten-membered r i n g s

- 101 -

t h a n i n t h e e i g h t - o r - n i n e membered r i n g , w i th t h e r e s u l t t h a t

no g e n e r a l i z a t i o n can be made r e g a r d i n g th e s t a b i l i t y o f t h e

v a r i o u s t y p e s o f d i e n e s t h a t occur in t e n - ( a n d e l e v e n - )

membered r i n g s . The c o n t r o l l i n g f a c t o r h e re i s th e

p a r t i c u l a r minimum energy co n fo rm a t io n t h a t each type of

d i e n e a d o p t s .

3 .4 . Conform at ions o f th e i n d i v i d u a l Cyclenes

(a) Cyclohexene

The h a l f - c h a i r co n fo rm a t io n (I) w i th Cg symmetry i s

t h e most s t a b l e co n fo rm a t io n . The d i h e d r a l

Observed (7)

V = 2 . 7 8 k c a l . / mole s

GO 1234 GO 2345 G 03456

- 1 5 .2 - 1 5 .3

4 4 .9 4 5 .4

- 6 0 . 2 - 6 2 .3

a n g l e s , c a l c u l a t e d by a m o d i f ied Karplus e q u a t io n , from

NMR c o u p l i n g c o n s t a n t s J 2 3 fs ^ 3 ° anc* a r e S°°d

agreement w i th t h e t h e o r e t i c a l l y o b t a i n e d (by WBFF) v a lu e s

o f 44° and 74°.

(b) c i s - C y c l o h e p t e n e

The problem i s s im p le r th an fo r c y c lo h e p ta n e , because

t h e i n t r o d u c t i o n o f t h e double bond i n t o t h e r i n g sys tem

a f f o r d s a r i g i d i t y which p r o h i b i t s t h e p s e u d o r o t a t i o n .

WBFF, AFF9 and CFF10 a l l c a l c u l a t e t h e C c h a i r a s t h e

- 102 -

F ig u r e 6 ; The c a l c u l a t e d minimum energy c o n fo rm a tio n 1 o f

c y c lo h e p t e n e (C sym m etry), s

- 103 -

enro00

enroCD

- 104 -

most s t a b l e form of c y c lo h e p te n e , be ing 1 .5 k c a l . / mole,

(WBFF) and abou t 0 .5 k c a l . / mole (AFF and CFF) lower in

energy th a n th e C2 t w i s t con fo rm a t ion .

CHAIR(Q TWIST- CHAIR(C ) TWIST-BOAT B0AT(C_)

y 5 .9 8 7 . 51 8 . 37 ^ . 64( k c a l . / m o l e )

The geometry c a l c u l a t e d f o r th e C c h a i r i s shown insF ig u r e 6. D ih e d ra l a n g l e s , c a l c u l a t e d from NMR c o u p l in g

c o n s t a n t s ^ S ' s anc* 109° ) a g re e w i th th e v a lu e s

c a l c u l a t e d by t h e WBFF f o r th e C c h a i r (3° and 114°)sc o n fo rm a t io n . The obse rved h e a t o f h y d ro g e n a t io n of

c y c lo h e p te n e i s 25 .85 k c a l . / mole** and t h i s a g r e e s w i th

t h e c a l c u l a t e d v a lu e of 25 .15 k c a l . / mole. S ince d e r i v a

t i v e s o f c y c l o a l k e n e s a r e o f t e n low m e l t in g and d i f f i c u l t

t o c r y s t a l l i s e , f o r c e f i e l d c a l c u l a t i o n s p r o v id e a u s e f u l ,

and sometimes o n ly , method f o r i n v e s t i g a t i n g conforma

t i o n s of c y c l i c compounds. However, t h e X-ray c r y s t a l12s t r u c t u r e a n a l y s i s of £ - c a p r o l a c ta m has been pe rform ed

and was found t o have a n e a r l y symmetric c h a i r co n fo rm a t io n

w i th t o r s i o n a n g le s s i m i l a r t o th o se c a l c u l a t e d by th e

WBFF f o r t h e C symmetric c h a i r c y c lo h e p te n e co n fo rm a t io n , sa s shown ove r .

- 105 -

- 7 6 1

II. (a) E-CAPROLACTAM-TORSION ANGLES OBTAINED PROM

CRYSTAL STRUCTURE ANALYSIS.

(t>) CHAIR CYCLOHEPTENE- TORSION ANGLES CALCULATED BY WBFF.

The d i s c r e p a n c y between th e obse rved and c a l c u l a t e d v a lu e s

o f t h e t o r s i o n a n g le s i s , i n p a r t , due t o t h e f a c t t h a t

t h e amide group has a f a r lower r o t a t i o n b a r r i e r than th e

double bond and a l s o has a much lower r e s i s t a n c e t o o u t - o f

p l a n e bend ing a t th e N-H group.

In c o n t r a s t t o th e C F F ^ th e WBFF c a l c u l a t e s th e

C b oa t t o be an e x t rem e ly sh a l lo w minimum c l o s e l y f l a n k e d sby a p a i r o f maxima about 0 .04 k c a l . / mole above th e

minimum ( i . e . a s a d d le p o i n t ) (see F ig u re 7 ) .

TWIST-BOAT

COF i g u r e 7

- 106 -

t r a n s - c y c l o h e p t e n e has been g e n e r a t e d and t r a p p e d , but

no t y e t o b se rv ed s p e c t r o p h o t o m e t r i c a l l y . 14

(c) C yc lo o c te n e

The c i s and t r a n s i som ers of c y c lo o c te n e a r e bo th known

and a r e o f c o n fo r m a t io n a l i n t e r e s t . There i s good e x p e r i

m en ta l e v id e n c e a s t o t h e ty pe o f c o n fo rm a t ion o f c i s - 14c y c l o o c t e n e though i t s d e t a i l e d s t r u c t u r e has n o t y e t been

d e te rm in e d ( i l l ) .

V = 7 . 8 8 k c a l . / mole s '

The t o r s i o n a l a n g le s around th e bonds o f t h e r i n g

c o n f i rm t h a t t h e fo u r atoms of t h i s c i s -d o u b le bond a r e

e s s e n t i a l l y p l a n a r . The r em a in in g atoms o f t h e r i n g th en

a r r a n g e th e m se lv e s t o m inimise t r a n s a n n u l a r s t e r i c i n t e r

a c t i o n s and e c l i p s i n g of th e s u b s t i t u e n t s abou t each bond

o f th e r i n g . The d i h e d r a l a n g le s f o r c i s - c y c l o o c t e n e from

NMR c o u p l i n g c o n s t a n t s J 2 3 ’s anc* 1^5° ) a g re e w i th th e

v a lu e s o b t a i n e d by MM c a l c u l a t i o n s u s in g WBFF (23° and 140°) .

Good agreem ent i s a l s o o b t a i n e d between t h e ob se rv ed t o r s i o n

- 107 -

a n g le s (from X-ray) f o r en an th o la c ta m h y d r o c h l o r i d e 15 and

t h e c a l c u l a t e d t o r s i o n a n g le s f o r c i s - c y c l o o c t e n e , ( IV ) .

HO, -54

-68.-85

“ 47

-73-82

(IV) (a) T o rs io n a n g le s from (b) T o rs io n a n g le s c a l -X-ray s tu d y of Enantho lac tam c u l a t e d f o r c i s - c y c l o o c t e n e H y d r o c h lo r id e by WBFF

The s m a l l e s t s t a b l e t r a n s - c y c l o a l k e n e t o be i s o l a t e d i s 1 — —

t r a n s - c y c l o o c t e n e , which u n l i k e t h e c i s isom er , has an

e x c e p t i o n a l l y h ig h h e a t o f h y d r o g e n e r a t io n . Model c o n s i d e r a

t i o n s show t h a t t h e double bond and two a t t a c h e d m ethy lenes

in t h e t r a n s isomer forms a t r a n s - b u te n e sys tem and w i th

on ly fo u r r e m a in in g ca rb o ns t o b r id g e t h e ends o f t h e

b u te n e sys tem , h ig h d i s t o r t i o n of t h e m olecu le i s r e q u i r e d .

I t has been shown t h a t t h e m olecu le p o s s e s s e s a d i p o l e

moment which i s e x t r a o r d i n a r i l y l a r g e . f o r an o l e f i n

(0.82D compared w i th 0 . 15D f o r t r a n s - c y c l o d e c e n e ) and t h i s

l a r g e moment has been i n t e r p r e t e d in te rms o f a un ique

h y b r i d i s a t i o n a t t h e o l e f i n i c ca rbons which p u t s c o n s i d e r a b l e

s c h a r a c t e r i n t o t h e TT-bond. The t i g h t b e l t o f s a t u r a t e d

c a rb o n s j o i n i n g th e ends o f th e o l e f i n l e a d s t o m o lecu la r

asymmetry which canno t be d e s t r o y e d by r o t a t i o n o f th e b e l t

- 108 -

around t h e o l e f i n and t r a n s - c y c l o o c t e n e has been o p t i c a l l y

r e s o l v e d . The h ig h b a r r i e r t o r a c e m i z a t io n r e s u l t s from

s t e r i c d e s t a b i l i z a t i o n of th e t r a n s i t i o n s t a t e caused by

hydrogens f o r c e d i n t o th e i n t e r i o r o f th e r i n g en r o u t e to

a 180° r o t a t i o n a round th e double bond. I n c r e a s e d r i n g

s i z e a l l o w s more f a c i l e p a ssa g e of t h e v i n y l i c hydrogens

th ro u gh th e c e n t r e o f a r i n g , t h u s , a t room t e m p e r a t u r e , t r a n s

cyc lononene ra c e m iz e s a s i t i s formed.

In r e c e n t y e a r s , t h e r e has been some c o n t r o v e r s y as t o

w he ther th e c r o s s (V) ( a l s o c a l l e d th e crown) or c h a i r (VI)

c o n fo rm a t io n i s t h e minimum energy c o n fo r m a t io n ,b o th on th e

e x p e r i m e n t a l and t h e o r e t i c a l f r o n t s .

Vg= l 8 . 6 0 k c a l . / m o l e

16On t h e e x p e r i m e n t a l s i d e , t h e r e s u l t s o f X-ray s t u d i e s

o f a d d u c t s o f t r a n s - c y c l o o c t e n e w i th complexing a g e n t s ,

such as s i l v e r n i t r a t e , a r e t o be t r e a t e d w i th c a u t i o n as

t h e p r e s e n c e o f heavy m e ta l atoms i n t r o d u c e u n d e s i r e d

p e r t u r b a t i o n s o f t h e double bond sys tem a n d /o r s e v e r e l y l i m i t

- 109 -

t h e a t t a i n a b l e a ccu racy o f t h e s t u d i e s . While t h e X-ray

s t u d i e s i n d i c a t e t h a t t h e c r o s s co n fo rm a t io n i s t h e minimum

energy confo rm er , gas phase e l e c t r o n d i f f r a c t i o n s t u d i e s by 17Gavin and Wang i n d i c a t e a d i s t o r t e d c h a i r (V I ) . How

e v e r , r e c e n t X-ray r e s u l t s on t r a n s - 2 - c y c l o o c t e n y l 3 ^ ,5 ^ - 18d i n i t r o b e n z o a t e a s w e l l a s more r e c e n t e l e c t r o n d i f f r a c t i o n

19d a ta on th e p a r e n t compound by T r a e t t e b e r g fav o u r t h e c r o s s

c o n fo rm a t io n (V).

MM c a l c u l a t i o n s w i th WBFF, AFF and CFF a l l c a l c u l a t e

t h e c r o s s c o n fo rm a t io n to be lower in energy by 1 .6 7 , 2 .43

and 3 .14 k c a l . / mole r e s p e c t i v e l y .

I t would now seem t h a t t h e c r o s s c o n fo rm a t ion i s ,

w i th o u t d o u b t , t h e minimum energy conformer and t h a t th e

X. t r a n s - c y c l o o c t e n e sample s t u d i e d by Gavin and Wang had been

p r e p a r e d under n o n - e q u i l i b r i u m c o n d i t i o n s and had c o n s i s t e d

p r i m a r i l y o f t h e c h a i r c o n fo rm a t io n , which i s p r e v e n te d from

r a p i d l y c o n v e r t i n g t o th e c r o s s co n fo rm a t io n by a h igh

i n t e r c o n v e r s i o n b a r r i e r .

The t o r s i o n a n g l e s , o b t a i n e d from an X-ray c r y s t a l 20s t r u c t u r e a n a l y s i s of a non-complexed i o d in e c o n t a i n i n g

d e r i v a t i v e of t r a n s - c y c l o o c t e n e (V I I (a ) ) i s compared w i th

t h e t o r s i o n a n g le s of t h e c r o s s (V II (b ) ) and c h a i r con

f o r m a t io n s ( V I I ( c ) ) , c a l c u l a t e d w i th WBFF. VII (d ) and (e)

show t o r s i o n a n g le s o b t a in e d from th e e l e c t r o n d i f f r a c t i o n

s t u d i e s .

- 110 -

V I I . ( a ) t r a n s - C y c lo o c t e n e a s o b s e r v e d i n I o d i n e d e r i v a t i v e (CQ a v e r a g e d )

(b) t r a n s - C y c lo o c te n e C r o s s - C a l c u l a t e d T o r s i o n A ngles (C2 }

(c) t r a n s - C y c l o o c t e n < C h a i r - C a l c u l a t e d t o r s i o n a n g l e (C2 >

Thus, t h e c r o s s c o n f o r m a t i o n i s i n good a g re e m e n t w i t h t h e

c r y s t a l s t r u c t u r e a n a l y s i s .

- 9 s-83

136 112

-121157

VII. (d) T o r s i o n a n g l e s from T r a e t t e b e r g e l e c t r o n d i f f r a c t i o n

(e) T o r s i o n a n g l e f romGavin and Wang e l e c t r o nd i f f r a c t i o n (C ) 17 s

- Ill -

(d) C yc lo n o n e n es

No d e t a i l e d c o n f o r m a t i o n a l p r o p e r t i e s o f c y c l o n o n e n e s

a r e known. The c i s i som er i s c a l c u l a t e d t o be lo w er i n

e n e rg y t h a n t h e t r a n s , i n a g re em e n t w i t h t h e o b s e r v e d h e a t

o f h y d r o g e n a t i o n v a l u e s . C o n f o r m a t io n a l m odels f o r c i s

and t r a n s i s o m e r s were d e r i v e d from two r e c e n t c r y s t a l

s t r u c t u r e a n a l y s e s o f c a p r y l o l a c t a m and i t s h y d r o c h l o r i d e .

The c i s i so m er i s a sy m m e tr ic w h i l e t h e t r a n s i so m er h a s

symmetry ( V I I I ( a ) and (b) r e s p e c t i v e l y ) .

V I I I ( a ) V = 1 0 .4 7 k c a l . / mole (b) V = 15 .08 k c a l . / m o l e s s

The c a l c u l a t e d t o r s i o n a n g l e s f o r c i s and t r a n s c y c lo n o n e n e

a r e compared w i t h t h e e x p e r i m e n t a l ones f o r c a p r y l o l a c t a m

and i t s h y d r o c h l o r i d e i n ( I X ( a ) - (d)) .

- 112 -

-86 104

IX(a) O b se rv e d t o r s i o n a n g l e s . o f c a p r y l o l a c t a m

h y d r o c h l o r i d e

(c) O bse rv e d t o r s i o n a n g l e s o f c a p r y l o l a c t a m

-8 9105

(b) C a l c u l a t e d t o r s i o n a n g l e s o f c i s - c y c l o n o n e n e .

(d) C a l c u l a t e d t o r s i o n a n g l e s o f t r a n s - c y c lo n o n e n e

- 113 -

(e) C yc lo d e ce n e

The c i s i so m er i s c a l c u l a t e d t o be low er i n e n e rg y t h a n

t h e t r a n s i so m e r . C o n fo rm a t io n models f o r c i s and t r a n s

i s o m e r s were d e r i v e d from X -ray c r y s t a l s t r u c t u r e a n a l y s e s21o f s i l v e r n i t r a t e a d d u c t s and t h e c a l c u l a t e d t o r s i o n a n g l e s

f o r c i s and t r a n s c y c l o d e c e n e compare f a v o u r a b l y w i t h t h e

X-ray r e s u l t s X(a) - (e) .

-107119-4 5

-7 7-150

63Vg=8.96 kcal ../mole

116 -1 0 9-5 5

X(a) O b se rv e d t o r s i o n a n g l e s (b) C a l c u l a t e d t o r s i o no f AgNOg complex o f c i s - a n g l e s f o r c i s - c y c l o d e c e n ec y c l o d e c e n e

(c) The c o n f o r m a t i o n o f t r a n s i som er (C2 symmetry) - T w is t

- 114 -

V = 1 1 . 3 7 k c a l . / m o l e s

(d) O b se rv e d t o r s i o n a n g l e s (e) C a l c u l a t e d t o r s i o n i n AgNOg a d d u c t o f t r a n s - a n g l e s i n t r a n s - c y c l o d e c e n ec y c l o d e c e n e

The r e a s o n f o r t h e l a r g e d i s c r e p a n c i e s i n (d) and (e) may,

i n p a r t , be due t o p e r t u r b a t i o n s o f t h e d o u b le bond sy s te m

by t h e s i l v e r a tom and t h e l i m i t e d a c c u r a c y o f t h e e x p e r i m e n t a l

r e s u l t s .

( f ) C y c l o o c t a - 1 , 5 - d i e n e (1,5-COD)

The minimum e n e rg y c o n f o r m a t i o n o f c i s , c i s - c y c l o o c t a -

1 , 5 - d i e n e , t h e Cg sy m m etr ic t w i s t - b o a t c o n f o r m a t i o n was

d i s c u s s e d f u l l y i n C h a p te r 2. The v a r i o u s t w i s t - b o a t

i n t e r c o n v e r s i o n p a th w ay s w i l l be d i s c u s s e d i n t h i s s e c t i o n .

The dynam ics o f c i s , c i s -1,5-COD s y s te m was f i r s t22s t u d i e d e x p e r i m e n t a l l y u s i n g l o w - t e m p e r a t u r e NMR m etho d s .

These m ea su re m e n ts show two d i s t i n c t NMR p r o c e s s e s , w here

t h e two b a r r i e r s a r e c a l c u l a t e d t o be 4 . 4 and 4 . 9 k c a l . / m o l e .

MM c a l c u l a t i o n s 2 3 ’ 2^ ’ 2 5 »26 have u s e d i n a n a t t e m p t t o

a s s i g n t h e s e b a r r i e r h e i g h t s u n am b ig u o u s ly t o t h e a p p r o p r i a t e

- 115 -

23 25c o n f o r m a t i o n a l i n t e r c o n v e r s i o n . Anet and Ermer c a l

c u l a t e t h a t t h e r o u t e t h r o u g h t h e Dg skew c o n f o r m a t i o n i s

t h e l o w e s t e n e rg y p r o c e s s f o l l o w e d by t h o s e t h r o u g h t h e

b o a t and C^ c h a i r w i t h a p p r o x i m a t e l y e q u a l b a r r i e r 24h e i g h t s . A l l i n g e r on t h e o t h e r hand , c a l c u l a t e s t h a t t h e

r o u t e t h r o u g h t h e b o a t i s t h e minimum e n e rg y pa thway

f o l lo w e d by t h a t t h r o u g h t h e c h a i r and f i n a l l y t h e r o u t e

t h r o u g h t h e skew a s t h e maximum e n e rg y i n t e r c o n v e r s i o n

r o u t e .

B ecause o f t h e marked d i f f e r e n c e be tw een t h e s e r e s u l t s ,

we d e c i d e d t o i n v e s t i g a t e t h i s s y s te m r a t h e r c l o s e l y . I t

seemed u n l i k e l y t h a t su c h a d icho tom y a r o s e from d i f f e r e n c e s

be tween t h e v a r i o u s f o r c e f i e l d s , b e c a u s e o f t h e u s u a l l y

s i m i l a r r e s u l t s o b t a i n e d f o r o t h e r c a l c u l a t i o n s . I n s t e a d

t h e d i f f e r e n c e s i n t h e methods i n g e n e r a t i n g t h e t r a n s i t i o n

s t a t e s were t h o u g h t t o h o l d t h e key t o t h e p ro b lem .

In t h e f i r s t i n s t a n c e , w e u se d t h e method o f Wiberg and 27Boyd i n o r d e r t o map t h e e n e rg y c h a n g e s f rom t h e t w i s t

b o a t t o t h e b o a t and skew c o n f o r m a t i o n s and g e n e r a t e d t h e

t r a n s i t i o n s t a t e be tw een t w i s t b o a t and c h a i r c o n f o r m a t i o n s

w i th a m o le c u le b u i l d i n g p rogram . In a l l t h r e e c a s e s , we

used a l a r g e r number o f c o n s t r a i n t s on t h e s y s te m t h a n was

a c t u a l l y n e c e s s a r y . For ex am p le , i n mapping from t h e t w i s t

b oa t t o t h e skew a l l n i n e t o r s i o n a n g l e s a r o u n d e ach o f t h e

C 3 - C 3 bonds w ere d r i v e n i n s t e a d o f o n ly C 2 - C 3 - sp sp sp spC 3 - C 2 t o r s i o n a n g l e s . In t h i s c a s e , we o b t a i n e d t h e sp spsame o r d e r o f p r e f e r e n c e f o r t h e v a r i o u s i n t e r c o n v e r s i o n

pathways a s A l l i n g e r and s i m i l a r v a l u e s f o r t h e b a r r i e r h e i g h t s .

- 116 -

In t h e n e x t s e r i e s o f c a l c u l a t i o n s , we u se d t h e W iberg-

Boyd a l g o r i t h m , b u t w i t h t h e minimum number o f c o n s t r a i n t s ,

and o b t a i n e d t h e same o r d e r o f p r e f e r e n c e a s Anet and Ermer.

I t t h e r e f o r e seemed a s th o u g h A l l i n g e r had imposed t o o many

c o n s t r a i n t s . In o r d e r t o c h eck t h i s c o n c l u s i o n we r e p e a t e d

t h e s e c a l c u l a t i o n s u s i n g AFF whereupon t h e r o u t e t h r o u g hj|c

t h e skew emerged a s t h e minimum e n e rg y pa thw ay .

F i n a l l y , we r e p e a t e d t h e c a l c u l a t i o n s y e t a g a i n u s i n g

t h e Newton-Raphson m a x i m is a t i o n p r o c e d u r e t o d e f i n e t h e

t h r e e t r a n s i t i o n s t a t e s . The r e s u l t s were v e r y s i m i l a r t o

t h o s e o b t a i n e d u s i n g t h e Wiberg-Boyd a l g o r i t h m w i t h m in im al

c o n s t r a i n t s e x c e p t t h a t t h e e n e r g i e s o f t h e t r a n s i t i o n

s t a t e s were some 0 . 0 2 k c a l . / mole lo w e r , p r o b a b l y a s a

c onsequence o f c o m p le te m o l e c u l a r r e l a x a t i o n ( i . e . no

a r t i f i c i a l c o n s t r a i n t s ) . T h is l e n d s a d d i t i o n a l s u p p o r t t o

th e c o n c l u s i o n t h a t a s e c o n d - d e r i v a t i v e m i n i m i s a t i o n /

m a x im is a t i o n p r o c e d u r e , su c h a s t h e Newton-Raphson, i s t h e28only s a f e o p t i m i s a t i o n a l g o r i t h m f o r MM c a l c u l a t i o n .

The symmetry and th e s t e r i c energy c a l c u l a t e d

by t h e WBFF f o r e a c h o f t h e f i v e c o n f o r m a t i o n s c o n s i d e r e d

in t h i s s t u d y a r e shown i n F i g u r e 8 w h i l e t h e c a l c u l a t e d

(WBFF) b a r r i e r h e i g h t s a r e compared w i t h E rm e rTs and A n e t ' s

^ 2* A l l i n g e r ' s c a l c u l a t i o n s were p e r f o r m e d w i t h AFF-73

9w h i l s t we u s e d AFF-72 . A l tho u gh f u l l d e t a i l s o f AFF-73 a r e n o t a v a i l a b l e i t a p p e a r s t o be a s l i g h t l y im proved v e r s i o n o f AFF-72. These do n o t a f f e c t t h e a rg u m e n t s ab ov e .

Boat C~—<cVVg = 14*60 kca l . /m a le

SkewV = I 2.32 kcal . /mole s

Twist-boat C- 2V = 10.05 kcal . /mole s

T ran s i t io n s t a t e C V = 14.69 kca l . /mole V

Chair -2hs = 10.82 kca l . /mole

Figure 82 Major conformations of c i s j c i s - c y c l o o c t a - l , 5 -d iene .

- 118 -

i n T a b le 3 a l o n g w i t h t h e e x p e r i m e n t a l v a l u e s .

29 3n 31c i s , t r a n s i , 5 - C O D ’ and t r a n s , t r a n s - 1 , 5-COD

have been i s o l a t e d b u t no e x p e r i m e n t a l d a t a r e g a r d i n g

c o n f o r m a t i o n a l i n f o r m a t i o n i s a v a i l a b l e . c i s , t r a n s - 1 , 5-COD32i s o p t i c a l l y a c t i v e which i m p l i e s t h a t i t i s a h i g h l y

s t r a i n e d and r i g i d m o le c u l e . From an i n s p e c t i o n o f

m o le c u l a r m o d e ls , t h e minimum e n e rg y c o n f o r m a t i o n i s v e ry

s i m i l a r t o t h a t o f c i s - c y c l o o c t e n e ( I I I ) . The t o r s i o n

a n g l e s and s t e r i c e n e rg y c a l c u l a t e d by t h e WBFF a r e shown

below ( XI)1

-86-6 3

>aV = 2 4 .6 7 k c a l / mole s

The NMR d a t a on t r a n s , t r a n s - 1 ,5 - C O D do n o t a l l o w a s s ig n m e n t31o f s t r u c t u r e X I I ( a ) o r X I I ( b ) t o i t . MM c a l c u l a t i o n s

u s in g t h e WBFF, h ave been a p p l i e d t o t h i s p ro b le m and i t

i s found t h a t t h e (a) i s more s t a b l e t h a n (b) by 5 .1 4 k c a l . /

mole, s i n c e (b) p o s s e s s e s u n f a v o u r a b l e e c l i p s e d t o r s i o n

a n g le s a ro u n d t h e two C 3-C 3 bonds w h i l e i n ( a ) , t h esp spc o r r e s p o n d i n g t o r s i o n a n g l e s a r e s t a g g e r e d .

- 1 1 9 -

c>■r~c:rnCO

p*p* >c < c *—»(A m o ^ o x m ► >

f><n0 O N m m mMOW

*> a i m

MNtO * * *

M 4 A • • •ft# aim

* to » *

mJO:xmxl\3cn

M T»n Z O *►h x r n» oX H Co x r~ o m > Z H c c m m ► o x xCO M >»-• o z o c oZ COco m • o x

w X co m• xO *-iw X co re « z

o —i ■< >■ n r c~o a> o xo x-4 X > *-*• m♦* x %at x « mo*-»

6) m i Z -4 m co

o x z o

30 X . X Xo o-4 0m ntOwX

- 120 -

-1 3 8-8 0

-139 -139 -41-41

V - 3 5 .8 6 k c a l . / mole V = 4 1 . 0 0 k c a l . / moleo S

(g) C y c l o n o n a - 1 , 5 - d i e n e s (1,5-CND)

The s t r u c t u r e o f two c i s , c i s , two c i s , t r a n s and t h r e e

t r a n s , t r a n s c o n fo rm e r o f 1,5-CND have been c a l c u l a t e d and

t h e r e s u l t s a r e shown i n F i g u r e 9. The minimum e n e rg y

c o n f o r m a t i o n i s t h e c i s , c i s - i s o m e r o f F i g u r e 9 ( a ) , and3 3 34e q u i l i b r a t i o n t o g e t h e r w i t h NMR e x p e r i m e n t s a r e i n com

p l e t e a g re e m e n t w i t h t h i s c o n c l u s i o n a s t o t h e f a v o u r e d

isom er b u t g i v e no i n d i c a t i o n a s t o i t s c o n f o r m a t i o n .35However, F a v i n i a l s o c a l c u l a t e s t h e c i s , c i s - i s o m e r o f

F i g u r e 9 ( a ) t o be t h e g l o b a l minimum and h i s c a l c u l a t e d

geometry i s v e ry s i m i l a r t o o u r s . I t may a l s o be p e r t i n e n t

t h a t t h i s c o n f o r m a t i o n b e a r s a s t r o n g r e s e m b l a n c e t o t h e known

g l o b a l minimum e n e rg y o f c y c l o d e c a - 1 , 6 - d i e n e ( F i g u r e 1 5 ( a ) ) .

There i s v e r y l i t t l e e x p e r i m e n t a l s t r u c t u r a l d a t a a v a i l a b l e

f o r t h e 1,5-CND’ s b u t a r e c e n t X -ray c r y s t a l s t r u c t u r e36a n a l y s i s o f b y s s o c h l a m i c a c i d h a s shown t h a t t h e c i s , c i s -

1,5-CND r i n g h a s a c o n f o r m a t i o n v e ry s i m i l a r t o t h a t o f

F ig u re 9 (b ) and t h e two c o n f o r m a t i o n s a r e compared i n F i g u r e

- 121 -

F i g u r e 9 : C y c l o n o n a - 1 , 5 - d i e n e c o n f o r m a t i o n s ; p e r i p h e r a l v a l u e s

a r e t o r s i o n a n g l e s and t h e i n n e r v a l u e i s t h e s t e r i c

e n e r g y i n k c a l . / m o l e above t h e minimum. Symmetry

i s e x c e p t a s n o t e d ( a ) C 2 » ( c ) C g , ( e ) C g .

- 122 -

- 123 -

F i g u r e 1 0 : The c a l c u l a t e d ( a ) and o b s e r v e d (b) s t r u c t u r e s o f

t h e c i s , c i s - c y c l o n o n a - 1 , 5 - d i e n e r i n g a s found

i n b y s s o c h la r a i c a c i d . Bond l e n g t h s and a n g l e s

i n n e r and t o r s i o n a n g l e s p e r i p h e r a l v a l u e s .

- 124 -

1.339r36

115.7i—86 113.6

- 125 -

The minimum e n e rg y c i s , c i s c o n f o r m a t i o n i s c a l c u l a t e d

t o be 5 . 6 k c a l . / mole more s t a b l e t h a n t h e l o w e s t e n e rg y

c i s , t r a n s c o n f o r m a t i o n compared w i t h a v a l u e o f 4 . 3 k c a l . / mole

d e r i v e d from r e c e n t m easu rem en ts o f h e a t s o f h y d r o g e n a t i o n .

Some c a l c u l a t e d and o b s e r v e d h e a t s o f h y d r o g e n a t i o n a r e

shown i n T a b le 3 i n C h a p te r 2.

(h) C y c lo d e c a d i e n e s

The c o n f o r m a t i o n s o f c y c l o d e c a - 1 , 5- and - 1 , 6 - d i e n e s

have n o t been p r e v i o u s l y s t u d i e d i n any g r e a t d e t a i l a l t h o u g h

t h e r e s u l t s o f q u a l i t a t i v e m o l e c u l a r m ec h an ic s c a l c u l a t i o n s37have been p u b l i s h e d , and c i s , c i s - c y d o d e c a - 1 , 6 - d i e n e s have

38 10been s t u d i e d by A l l i n g e r and Ermer.

( i ) C y c l o d e c a - 1 , 5 - d i e n e (1,5-CDD)

The i n t e r e s t i n t h i s s y s te m s t e m s from t h e f a c t t h a t

t h e 1,5-CDD r i n g i s f a i r l y w i d e s p r e a d amongst n a t u r a l l y39o c c u r r i n g g e r m a c r a n o l i d e s , w i t h one c i s , t r a n s and two

t r a n s , t r a n s c o n f o r m a t i o n s o b s e r v e d v i a X - ray c r y s t a l s t r u c t u r e

a n a l y s e s . The geom etry and r e l a t i v e e n t h a l p i e s o f one

c i s , t r a n s - , two c i s , c i s - and f i v e t r a n s , t r a n s - c o n f o r m e r s o f

1,5-CDD have been c a l c u l a t e d u s i n g t h e WBFF. The r e s u l t s

a r e shown i n F i g u r e 11. The minimum e n e rg y c o n f o r m a t i o n

i s t h e c i s , t r a n s - i s o m e r shown i n F i g u r e 11(h) and i t s

geometry i s compared w i t h t h a t o b t a i n e d from an X - ray c r y s t a l40s t r u c t u r e a n a l y s i s o f ©upaformonin i n F i g u r e 12. T here

a p p e a r s t o be no e x p e r i m e n t a l e v id e n c e r e g a r d i n g t h e

minimum e n e r g y c o n f o r m a t i o n o f 1,5-CDD b u t t h e a g re em e n t o f

t h e c a l c u l a t e d g e o m e t r i c a l p a r a m e t e r s f o r t h e c i s , t r a n s - i s o m e r

- 126 -

F i g u r e 1 1 ; C y c lo d .e c a -1 , 5 “d i e n e c o n f o r m a t i o n s ; s ym m e tr ie s a r e

( a ) C 2 , ( e ) C 2 .

- 127 -

5.281.68

’-71

168'-121

106-6 8

107 3.6211.45

103106.

-632.22

r91116,-11r 89

0.001.00

F ig u r e 1 2 : The c a l c u l a t e d minimum e n e rg y c o n f o r m a t i o n o f

c y c l o d e c a - 1 , 5 -d . iene (a) compared w i t h t h e ge o m e t ry

o f t h e 1 0 - r i n g o f eu p a fo rm o n in ( h ) •

- 129 -

.341-91126.5267

-13 113.7'1112.3

110.114.2122.98511.533

r-173113.5h1.532^1?'8 u 0 4

# V J1332\ J 124/^ 128.7

J112.2 112‘5( ^-135

108.'\\§ 2

125.818011.5361.33

L1.533 1151-16811912

- 130 -

w i t h t h e X -ray r e s u l t s i s e x c e l l e n t , d e s p i t e f a i r l y heavy

s u b s t i t u t i o n o f t h e 1,5-CDD r i n g i n t h e l a t t e r i n s t a n c e .

T here a r e t h r e e o t h e r c o n f o r m a t i o n s w i t h i n 2 k c a l . / m o l e

o f t h e c a l c u l a t e d g l o b a l minimum; t h e two a p p r o x i m a t e l y

i s o n e r g e t i c c i s , c i s i s o m e r s and t h e t r a n s , t r a n s - i s o m e r shown

i n F i g u r e 1 1 ( a ) . A c o n f o r m a t i o n v e ry s i m i l a r t o t h a t o f

t h e l o w e s t e n e rg y t r a n s , t r a n s - i s o m e r h a s been o b s e r v e d i n41a s e r i e s o f g e r m a c r a n o l i d e s o f which c o s t u n o l i d e i s a

good r e p r e s e n t a t i v e . The co n fo rm e r i n F i g u r e 1 1 (a ) h a s

Cg symmetry w h i l s t t h e m a c r o c y c le i n c o s t u n o l i d e h a s o n ly

a p p r o x i m a t e C2 symmetry b e c a u s e o f i t s v a r i o u s s u b s t i t u e n t s .

N e v e r t h e l e s s , t h e r e i s good a g re em e n t be tw een t h e c a l c u l a t e d

geometry and t h e C g - a v e r a g e d r e s u l t from t h e X - ray c r y s t a l41s t r u c t u r e a n a l y s i s , which a r e shown i n F i g u r e 13. T here

a r e a l s o some e x p e r i m e n t a l d a t a r e g a r d i n g t h e c o n f o r m a t i o n

o f F i g u r e 1 1 (e ) and t h e c a l c u l a t e d r i n g t o r s i o n a n g l e s a r e

compared w i t h t h o s e from an X -ray c r y s t a l s t r u c t u r e a n a l y s i s 42of S h i r o m o d io l i n F i g u r e 14. A d e t a i l e d c o m p a r i s o n c a n

no t be made b e c a u s e one o f t h e d o u b le bonds i s r e p l a c e d by

a t r a n s - f u s e d e p o x id e i n t h e n a t u r a l p r o d u c t ; b u t t h e two

c o n f o r m a t i o n s a r e q u a l i t a t i v e l y s i m i l a r .

( i i ) C y c l o d e c a - 1 , 6 - d i e n e (1,6-CDD)

The 1,6-CDD s y s te m i s b e t t e r d e f i n e d e x p e r i m e n t a l l y

t h a n t h e 1 , 5 - i s o m e r and a number o f u s e f u l s t r u c t u r a l and

thermodynamic m easu rem en ts a r e a v a i l a b l e . Nine c o n fo rm a

t i o n s o f 1,6-CDD w ere s t u d i e d by a d e ve lop m en t v e r s i o n o f43t h e WBFF and t h e r e s u l t s were p u b l i s h e d . The g e o m e t r i e s

and r e l a t i v e e n t h a l p i e s o f e leven , c o n f o r m a t i o n s o f 1,6-CDD

- 1 3 1 -

F i g u r e 1 3 : The g e o m e t ry o f t h e c a l c u l a t e d ( a ) minimum e n e rg y

c o n f o r m a t i o n o f t r a n s t t r a n s - c y c l o d e c a - 1 , 5 ~ d i e n e

compared w i t h t h e a v e r a g e d g e o m e t ry o f t h e m a c ro

c y c l e i n c o s t u n o l i d e ( b ) .

- 1.32 -

1.537% "87

121.1 124,

1.492-8 41.536

av.1.499

114.:122.8 123.9

- 1 3 3 -

F i g u r e 14 : C a l c u l a t e d ( a ) and o b s e r v e d (b) g e o m e t r i e s o f t h e

s h i r o m o d i o l - t y p e c y c l o d e c a d i e n e r i n g *

- 134 -

115.11.511 1.53- 10«

^.338 124.4 112.1 1-535

- 135 -

have been c a l c u l a t e d w i t h t h e p r e s e n t WBFF f o r c e f i e l d and

r e s u l t s a r e shown i n F i g u r e 15. The g l o b a l minimum i s

c a l c u l a t e d t o be t h e sym m etr ic c i s , c i s - c h a i r co n fo rm a

t i o n , i n e x c e l l e n t a g re e m e n t w i t h t h e r m o c h e m ic a l m e a s u re - 11 44m en ts , ' and t h i s h a s a m o l e c u l a r geom etry a lm o s t

e x a c t l y i d e n t i c a l t o t h a t o b s e r v e d by gas p h a s e e l e c t r o n 45d i f f r a c t i o n ( s e e T a b le 4 i n C h a p te r 2 ) . The Cgy c i s ,

c i s - b o a t form (shown i n F i g u r e 1 5 (b ) ) i s , a t b e s t , b a r e l yo 45p r e s e n t i n t h e gas p h a s e a t 35 C an o b s e r v a t i o n which

a c c o r d s w e l l w i t h ou r c a l c u l a t e d e n t h a l p y d i f f e r e n c e o f

1 .2 k c a l . / mole be tw een t h e two c o n fo r m e rs which c o r r e s

ponds t o 88% c h a i r : 1 2 % b o a t ( c . f . 0 . 1 6 k c a l . / mole w i t h10 9CFF and 0 . 3 0 k c a l . / mole w i t h AFF .

44E q u i l i b r a t i o n e x p e r i m e n t s i n d i c a t e t h a t a l t h o u g h

t h e c i s , c i s - i s o m e r i s c e r t a i n l y t h e p r e d o m in a n t c o n fo rm a

t i o n t h e r e were d e t e c t a b l e amounts o f a c i s , t r a n s - i s o m e r i n

t h e e q u i l i b r i u m m i x t u r e a t 25°C and t h i s would seem t o

c o r r e s p o n d w i t h t h e c o n f o r m a t i o n o f F i g u r e 15 ( i ) which h a s

a c a l c u l a t e d e n t h a l p y 3 .1 2 k c a l . mole above t h a t o f t h e

c i s , c i s - c h a i r . No t r a n s , t r a n s - i s o m e r was o b s e r v e d and

t h e r e f o r e t h e c a l c u l a t e d minimum e n e r g i e s f o r t h e c i s , c i s -

c h a i r and c i s , t r a n s - c h a i r a r e p r o b a b l y 1 -2 k c a l . / mole t o o

h ig h w i t h r e s p e c t t o t h e t r a n s , t r a n s - i s o m e r o f F i g u r e 1 5 ( d ) .

T h e re i s r e a s o n a b l e , i f n o t c o n c l u s i v e e v i d e n c e a s t o

t h e minimum e n e r g y c o n f o r m a t i o n o f t r a n s , t r a n s - 1 , 6-CDD.

An X -ray c r y s t a l s t r u c t u r e a n a l y s i s o f 2 , 7 , - d i b r o m o - 3 , 8 -46dimethoxy d e r i v a t i v e h a s shown t h a t t h e ten -m em b ered

r i n g a d o p t s a crown c o n f o r m a t i o n w i t h symmetry . F u r t h e r -

- 136 -

F i g u r e 1 5 : C a l c u l a t e d c o n f o r m a t i o n s o f c y c l o d e c a - 1 , 6 - d i e n e

w i t h t h e f o l l o w i n g s y m m e tr i e s ( a ) ^ ^ ! (b )C2y»

( c ) C s , ( ^ ^ h * ^ ^ 2 h f ^ ^ 2 * ^ ^ 2 * ^ ^ i *

(o)d2, (k)c1.

-137 ~

- 1 1 6 -11- 6 7 .0.00 1.17 5 .0 5 1 - 5 6

1-170, -11 -1 7 0-57<r 6 2

2 .1 74 .3 8 6.71

1731 1 9

-7 6 ,

5 .4 4 5 .1 3 3 .1 2'- 7 2

-114 '

- 1 6 7

r3l- 3 5 ' 7 .1 3

-3 5 j" 4 3

F i g u r e 1 6 : The c a l c u l a t e d g e o m e tr y ( a ) o f t h e minimum e n e r g y

t r a n s , t r a n s - c y c l o d e c a - 1 16 -d . i e n e c o n f o r m a t i o n compared

w i t h t h e Cgk a v e r a g e d e x p e r i m e n t a l v a l u e s from X - r a y

c r y s t a l s t r u c t u r e a n a l y s e s o f a s u b s t i t u t e d

h y d r o c a r b o n (b) and 1 , 5 - d i a z a - 6 , 1 0 - c y c l o d e c a d i o n e ( c ) .

- 139 -

115.2.— 170

111.8 115.,123.2

J.338 -621.50

112.4 r l62

113.4123.7

1.327 -68

115.5 ,-•63

116112.2119.9

1.333 -67

11.47!

- 140 -

47more, 1 , 5 - d i a z a - 6 , 1 0 - c y c l o d e c a d i o n e e x h i b i t s t h i s same

crown c o n f o r m a t i o n w i t h v e ry s i m i l a r r i n g t o r s i o n a n g l e s

t o t h e 1,6-CDD d e r i v a t i v e . The s i m i l a r i t i e s be tw een t h e

minimum e n e rg y c o n f o r m a t i o n s o f medium r i n g a l k e n e s and

am ides have been p r e v i o u s l y n o t e d , 10 ,48 and t h i s , t a k e n

t o g e t h e r w i t h t h e f a c t t h a t t h e same c o n f o r m a t i o n o c c u r s

i n two e n t i r e l y d i f f e r e n t c r y s t a l s t r u c t u r e s , l e n d s s u p p o r t

t o t h e c a l c u l a t i o n o f t h e crown c o n f o r m a t i o n o f F i g u r e 1 5 (a )

a s t h e minimum e n e rg y t r a n s , t r a n s - v a r i a n t . Our c a l c u l a t e d

c o n f o r m a t i o n h as symmetry w h i l s t t h e s u b s t i t u e n t s

p r e v e n t t h e d ib rom o, d im ethony d e r i v a t i v e from a d o p t i n g t h i s

form a l t h o u g h t h e d e p a r t u r e from a symmetry i s n o t v e ry

g r e a t . The c y c l i c d iam id e h a s no symmetry and w h i l e t h e

d e p a r t u r e from C^^ i s l a r g e r t h a n f o r t h e d ib r o m o ,d im e th o o y -

1,6-CDD, i t i s s t i l l a r e a s o n a b l e a p p r o x i m a t i o n t o t h e same.

The t h r e e c o n f o r m a t i o n s a r e shown i n F i g u r e 16 w i t h t h e

r e s u l t s o f t h e two c r y s t a l s t r u c t u r e a n a l y s e s a v e r a g e d t o

g iv e a Cgk sy m m et r ic r i n g .

( i ) The C o n f o r m a t i o n a l A ss ignm en t o f c i s , c i s , c i s - 1 , 5 , 9 -

c y c l o - d o d e c a t r a e n e (CDDT)

One o f t h e most p o p u l a r e x p e r i m e n t a l t e c h n i q u e s f o r

i n v e s t i g a t i n g t h e c o n f o r m a t i o n s o f m o le c u l e s and t h e i r

i n t e r c o n v e r s i o n s i s n u c l e a r m a g n e t i c r e s o n a n c e (NMR)»

a n a l y s i s . The NMR s p e c t r u m o f c o n f o r m a t i o n s w h ich i n t e r

c o n v e r t r a p i d l y on t h e s o - c a l l e d NMR t im e s c a l e w i l l show

a v e ra g e d c h e m ic a l s h i f t s and c o u p l i n g c o n s t a n t s . When t h e

i n t e r c o n v e r s i o n i s s lo w , e ac h c o n f o r m a t i o n w i l l g i v e p i s et

to i t s own c h a r a c t e r i s t i c s p e c t r u m . In t h e i n t e r m e d i a t e

- 141 -

r e g i o n , t h e s p e c t r u m i s b r o a d e n e d , and s u i t a b l e a n a l y s i s

can g i v e t h e r a t e c o n s t a n t s and f r e e e n e r g i e s o f4:

a c t i v a t i o n ( AG ) f o r t h e i n t e r c o n v e r s i o n .

When an o r g a n i c c h e m is t i s i n t e r e s t e d i n d e t e r m i n i n g

t h e minimum e n e rg y c o n f o r m a t i o n o f a p a r t i c u l a r m o le c u l e ,

he f o r m u l a t e s a l l t h e c o n c e i v a b l e c o n t e n d e r s , and t h e n , on

t h e b a s i s o f t h e a n a l y s i s o f t h e NMR s p e c t r u m , e l i m i n a t e s

t h o s e i n which t h e r e i s no c o r r e l a t i o n be tw een t h e o b s e r v e d

sp e c t r u m and t h e e x p e c t e d g e o m e try , w i t h t h e hope t h a t t h e

i n f o r m a t i o n from t h e s p e c t r u m w i l l a l l o w an unambiguous

a s s ig n m e n t o f one o f t h e p o s t u l a t e d c o n f o r m a t i o n s a s b e i n g

t h e one o f minimum e n e r g y . In p r a c t i c e , t h i s i s n o t u s u a l l y

t h e c a s e a s two o r more o f t h e p r o p o s e d c o n f o r m a t i o n s a r e

c o n s i s t e n t w i t h t h e o b s e r v e d s p e c t r u m .

T h is i s t h e r e f o r e an a r e a o f a p p l i c a t i o n t o which MM

c a l c u l a t i o n s can be a p p l i e d a s t h e y c a l c u l a t e t h e s t e r i c

e n e r g i e s and d e t a i l e d g e o m e t r i e s o f a l l t h e p r o p o s e d c o n

f o r m a t i o n s and hen ce n o t o n ly can t h e y u n i q u e l y d e t e r m i n e

th e minimum e n e rg y c o n f o r m a t i o n b u t a l s o v e r i f y t h e e l i m i n a

t i o n o f t h e o t h e r p r o p o s e d c o n f o r m a t i o n s i n a q u a n t i t a t i v e

m anner .

One i l l u s t r a t i v e exam ple o f t h e above i s t h e a t t e m p t e d

a s s ig n m e n t o f t h e minimum e n e r g y c o n f o r m a t i o n o f c i s , c i s , c i s -491 , 5 , 9 - c y c l o d o d e c a t r i e n e (CDDT) r i n g (X I I I ) by NMR a n a l y s i s .

- 142 -

XI I I

From an e x a m i n a t i o n o f m o l e c u l a r m o d e ls , t h e r e seems

t o be f o u r c h o i c e s f o r t h e c o n fo rm e r o f t h e CDDT r i n g - t h e

crown ( X I V ( a ) ) , t h e s a d d l e (X IV (b ) ) , t h e s y m m e t r i c a l s - t r a n s

(XIV(c)) and t h e u n s y m m e t r i c a l s - t r a n s (X IV (d ) ) . The

crown (XIV(a)) and t h e s a d d l e (XIV(b)) p o s s e s s u n f a v o u r a b l e

nonbonded i n t e r a c t i o n s due t o t h e e c l i p s e d h y d ro g e n s w h i l e

t h e two s - t r a n s c o n f o r m a t i o n s have r e p u l s i v e t r a n s a n n u l a r

hydrogen i n t e r a c t i o n s .

An NMR a n a l y s i s o f 1 , 5 , 9 - t r i b r o m o - c i s , c i s , c i s - 1 , 5 , 9 -49c y c l o d o d e c a t r i e n e h a s been p e r f o r m e d w i t h t h e a im o f

d e t e r m i n i n g i t s minimum e n e rg y c o n f o r m a t i o n . S in c e

m o le c u l a r m odels i n d i c a t e t h a t t h e b rom ine a tom s c a u s e no

s e r i o u s s t e r i c i n t e r a c t i o n s i n t h e s e f o u r c o n f o r m a t i o n s ,

we can assume t h a t t h e c o n f o r m a t i o n o f t h e r i n g i n t h e

t r i b r o m o t r i e n e i s v e r y s i m i l a r t o t h a t fo u n d i n t h e

u n s u b s t i t u t e d compound ( X I I I ) . T h ere i s ample e v id e n c e

t h a t su c h an a s s u m p t io n i s v a l i d , e . g . t h e c o n f o r m a t i o n o f

t h e c i s , c i s - c y c l o o c t a - 1 , 5 - d i e n e r i n g d e r i v e d from an X -ray50c r y s t a l s t r u c t u r e a n a l y s i s o f 3 , 7 , - d i b r o m o d e r i v a t i v e i s

ve ry s i m i l a r t o t h a t fo u nd by t h e e l e c t r o n d i f f r a c t i o n6 23 -2 6s tu d y and MM c a l c u l a t i o n s o f t h e h y d r o c a r b o n i t s e l f .

From t h e m a g n i tu d e s o f t h e v i c i n a l c o u p l i n g c o n s t a n t s

- 143 -

XIV ( a ) Crown (ta) S a d d le

( c ) u n s y m m e t r i c a l e - t r a n s

(d ) s y m m e t r i c a l s - t r a n s

- 144 -

o f t h e e t h a n o h y d ro g e n s d e r i v e d from t h e h i g h - r e s o l u t i o n49p r o t o n s p e c t r u m o f t h e t r i b r o m o t r i e n e , i t c an be deduced

t h a t p a i r s o f h y d ro g e n s a r e t r a n s and p a i r s o f h y d ro g e n s

a r e g au ch e a s shown below.

Group 2Group 3

The o n ly c o n f o r m a t i o n s o f t h e p o s t u l a t e d f o u r which s a t i s f y

t h e s e c o n d i t i o n s a r e t h e two s - t r a n s c o n f o r m a t i o n s (XIV(c))

and (X IV (d ) ) . A n o th e r f a c t o r from t h e NMR a n a l y s i s which

must be t a k e n i n t o a c c o u n t , i s t h a t t h e m o le c u l e i s r a p i d l y

i n t e r c o n v e r t i n g be tw een e q u i v a l e n t c o n f o r m a t i o n s which

i m p l i e s t h a t d u r i n g t h i s i n t e r c o n v e r s i o n , t h e t r a n s hy d ro g en

p a i r s r e m a in t r a n s and t h e gauche p a i r s r e m a in gauche - a

c o n d i t i o n t h a t i s s a t i s f i e d by i n t e r c o n v e r s i o n be tw een

e q u i v a l e n t s - t r a n s c o n f o r m a t i o n s . In t h e crown con fo rm a

t i o n , how ever , p a i r s o f h y d ro g e n a r e c i s and p a i r s a r e

g a u c h e , and t h e r e l a t i v e o r i e n t a t i o n i s p r e s e r v e d i n p a i r s

d u r in g t h e r a p i d i n t e r c o n v e r s i o n o f e q u i v a l e n t crown c o n

f o r m a t i o n s . D ur ing t h e i n t e r c o n v e r s i o n among t h e s i x

e q u i v a l e n t c o n f o r m a t i o n s o f t h e s a d d l e , t h e g e m in a l

hydrogens t o t h e b rom ine assume a l l t h r e e p o s s i b l e

o r i e n t a t i o n s w i t h r e s p e c t t o t h e ones , i . e . c i s e c l i p s e d ,

gauche (60°) and gau ch e ( 1 2 0 ° ) .

T h e r e f o r e , on t h e b a s i s o f t h e d a t a p r o v i d e d by t h e

a n a l y s i s o f t h e nmr s p e c t r u m , t h e crown and s a d d l e can be

- 145 -

r i g o r o u s l y e x c l u d e d from b e i n g p r e s e n t t o any a p p r e c i a b l e

e x t e n t , and hence one o f t h e two s - t r a n s c o n f o r m a t i o n s must

be t h e minimum e n e rg y c o n fo r m e r . However, s i n c e t h e two

s—t r a n s c o n f o r m a t i o n s have i d e n t i c a l s p a t i a l o r i e n t a t i o n s o f

t h e e t h a n o h y d ro g e n s and t h u s t h e same p r o t o n NMR s p e c t r u m ,

i t i s i m p o s s i b l e t o d i s t i n g u i s h be tw een them.

MM c a l c u l a t i o n s , u s i n g WBFF, have been p e r f o r m e d on t h e

f o u r p o s s i b l e c o n f o r m a t i o n s ( X l V ( a ) - ( d ) ) and t h e s t e r i c

e n e r g i e s a r e 1 1 .6 8 , 1 1 .4 8 , 15 .2 1 and 9 .9 5 k c a l . / mole

r e s p e c t i v e l y which c o r r e s p o n d s t o a p e r c e n t a g e c o m p o s i t i o n

o f 6 : 7 : 0 : 8 7 a t room t e m p e r a t u r e . These c a l c u l a t i o n s t h u s

i n d i c a t e t h a t , i n f a c t , i t i s t h e u n s y m m e t r i c a l s - t r a n s

form which i s t h e minimum e n e rg y c o n f o r m a t i o n o f t h e

CDDT r i n g .

M o le c u la r m odels i n d i c a t e t h a t r e p u l s i v e i n t e r a c t i o n s

between t r a n s a n n u l a r h y d ro g e n s a t p o s i t i o n s 4 , 8 , 1 2 and

a t p o s i t i o n s 3 , 7 , 1 1 i n t h e s y m m e t r i c a l c o n f o r m a t i o n (XIV(c))

a r e more s e v e r e t h a n t h e c o r r e s p o n d i n g i n t e r a c t i o n s a t

p o s i t i o n s 3 , 8 , 1 2 and a t p o s i t i o n s 4 , 7 , 1 1 i n t h e u n s y m m e t r i c a l

c o n f o r m a t i o n (X IV (d ) ) . MM c a l c u l a t i o n s c o n f i r m t h i s and

r e v e a l t h a t , i n o r d e r t o m in im is e t h e t r a n s a n n u l a r s t r a i n ,

t h e i n t e r n a l bond a n g l e s i n XIV(c) a r e i n c r e a s e d w i t h r e s p e c t

t o t h o s e i n XIV (d) ( t h e a v e r a g e C 2 = C 2 - Cgp3 a n g l e i s

1 .4 and t h e a v e r a g e C 2 - C 3 - C 3 i s 1 . 8 ° g r e a t e r i nsp sp spXIV(c) t h a n i n XIV(d)) and XIV(c) h a s c o n s i d e r a b l y more P i t z e r

s t r a i n t h a n XIV (d) . Even w i t h t h e a n g u l a r and t o r s i o n a l

d i s t o r t i o n s , t h e i n t r a - a n n u l a r H . . . H d i s t a n c e i s s t i l lo o

only 2 .0 7 A i n XIV(c) compared t o 2 .1 5 A i n X I V (d ) . Thus,

- 146 -

on a c c o u n t o f t h i s u n f a v o u r a b l e n a t u r e o f a n g u l a r , t o r s i o n a l

and nonbonded c o n t r i b u t i o n s t o t h e s t e r i c e n e r g y , XIV(d)

i s found t o have a low er s t e r i c e n e rg y by 5 .2 6 k c a l . / mole

t h a n X I V ( c ) .✓

F u r t h e r m o r e , t h e c a l c u l a t i o n s i n d i c a t e t h a t t h e crown

(XIV(a)) and t h e s a d d l e ( X I V ( b ) ) , n o t u n e x p e c t e d l y , s u f f e r

a p p r e c i a b l y from t h e u n f a v o u r a b l e nonbonded i n t e r a c t i o n s o f

t h e e c l i p s e d h y d ro g e n s i n t h e e th a n o g ro u p s and have h i g h e r

s t e r i c e n e r g i e s t h a n t h e u n s y m m e t r i c a l s - t r a n s (X IV (d ) ) .

Moreover, f rom t h e d e t a i l e d geom etry and r e l a t i v e

s t e r i c e n e r g y t h a t MM c a l c u l a t i o n s p r o v i d e f o r e ach c o n fo rm a

t i o n , i t i s o f t e n p o s s i b l e t o i n t e r p r e t e x p e r i m e n t a l o b s e r v a

t i o n s which i s o t h e r w i s e n o t f e a s i b l e . To i l l u s t r a t e t h i s ,

one f e a t u r e o f t h e o b s e r v e d v i c i n a l c o u p l i n g c o n s t a n t s

(10 .57 and 5 .4 9 ) o f t h e e th a n o h y d ro g e n s i n t h e t r i b r o m o -

t r i e n e i s t h a t t h e y a r e a t t h e low er and uppe r ends o f t h e

r a n g e s f o r t r a n s ( 1 0 . 5 - 1 2 . 4 c ps ) and gauche ( 2 . 7 - 5 . 4 cps)

v i c i n a l c o u p l i n g c o n s t a n t s f o r s i x - o r l a r g e r membered r i n g s .

This can be i n t e r p r e t e d a s b e i n g a r e s u l t o f one o f two

e f f e c t s :

( i ) Small p r o p o r t i o n s o f t h e crown a n d / o r s a d d l e c o n fo r m e rs

a r e p r e s e n t i n e q u i l i b r i u m w i t h t h e u n s y m m e t r i c a l s - t r a n s

c o n f o r m a t i o n , and

( i i ) t h e u n s y m m e t r i c a l s - t r a n s co n fo rm e r (XIV(d)) i s skewed

away from a p u r e s - t r a n s a r r a n g e m e n t o f t h e i r e t h a n o

hydrogens i n o r d e r t o r e l i e v e p a r t o f t h e s t r a i n e n e r g y due

t o t r a n s a n n u l a r hy d ro g en i n t e r a c t i o n s .

R e s u l t s f rom t h e f o r c e f i e l d c a l c u l a t i o n s imply t h a t t h e

- 147 -

crown and s a d d l e c o n f o r m a t i o n s a r e o n ly p r e s e n t t o a v e ry

s m a l l e x t e n t (6 and 7 p e r c e n t r e s p e c t i v e l y ) and t h a t t h e

s - t r a n s a r r a n g e m e n t , i n t h e u n s y m m e t r i c a l c o n f o r m a t i o n (X IV (d ) ) ,

which i s c a l c u l a t e d t o be t h e minimum e n e rg y c o n f o r m a t i o n ,

i s "found t o be skewed away from t h e p u r e s - t r a n s form by,

on a v e r a g e , 14° . C o n s i d e r i n g t h e m a g n i tu d e s o f t h e s e

two e f f e c t s , MM c a l c u l a t i o n f a v o u r t h e l a t t e r o f the two

e x p l a n a t i o n s .

- 148 -

3 .5 . R e f e r e n c e s

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M cGraw-Hil l , New York, N . Y . , p 189, (1962) .

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O rg a n ic C h e m i s t r y ” , John Wiley 8s Sons, I n c . , New York,

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5. E .L . ELIEL. ’’S t e r e o c h e m i s t r y o f Carbon Compounds” ,

M cG raw -H il l , New York, N . Y . , p . 192 (1962) .

6. L. HEDBERG and K. HEDBERG. A b s . P a p e r s , N a t . M ee t ing

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W.R. ROTH and G.SCHRODER. J .A m er .C hem .S oc . ,

95, 8605 (1973) .

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(1973) .

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13. E . J . COREY, F . A. CAREY and R.A.E. WINTER. J.Amer.

Chem.Soc. , 87 , 934 (1965) .

14. A .F . CAMERON, K.K. CHEUNG and J.M. ROBERTSON.

J . C h e m . S o c . ( B ) , 559 (1969)✓

15. F .K. WINKLER and J .D . DUNITZ, J .M o le c . B i o . , 59, 169

(1 9 7 3 ) .

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20. G. FERGUSON and D. HAWLEY, U n p u b l i sh e d r e s u l t s ,

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54 , 2469 (1 9 7 1 ) ;

(b) P.GANIS and J .D . DUNITZ. H e l v .C h im .A c ta . , 50,

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R eso n an ce S p e c t r o s c o p y . F.A. C o t to n and L.M. J a c k s o n ,

E d . , Academic P r e s s , New York, p 571 (1 9 7 5 ) .

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(1 9 7 5 ) .

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25. 0 . ERMER. J .A m e r . Chem. S o c . , 98, 3964 (1976) .

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(1 9 7 2 ) .✓

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(1 9 7 5 ) .

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84 , 3190 (19 6 2 ) .

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G.M. WHITESIDES, J .A m er .C hem .S oc . , 8 9 , 7136 (1967) .

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H . J . S . WINKLER, J .Amer. Chem.Soc. , 88 , 761 (196 6 ) .

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J .A m e r . Chem. S o c . , 85 , 1553 (1963) .

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35. F. ZUCCARELLO, G. BUEMI and G. FAVINI. J . M o l . S t r u c t . ,

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37, 2423 (1 9 7 2 ) .

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39. G.A. SIM i n M o le c u la r S t r u c t u r e by D i f f r a c t i o n M e th o d s ,

The C hem ica l S o c i e t y , London, Vol 2 , p 131 and Vol 3

p 163 (19 7 4 ) .

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578 (19 7 6 ) .

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G.A. SIM and D .N .J . WHITE. Acta G ry s t . , B32,

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Chem.Commun., 128 (1970) .

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2239 (1 9 7 5 ) .

44. J . DALE, Angew C h e m . ( I n t . E d . ) , 5 , 1000 (19 6 6 ) .

45. A. ALMENNINGEN, G.G. JACOBSEN and H.M. SEIP. A c t a .

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47. T . SRIKRISHNAN and J .D . DUNITz. Ac ta C r y s t , B31, 1372

(1975) .

48. D .N .J . WHITE and M.H. GUY. J.C h e m .S o c .P e rk in I I , 43

(19 7 5 ) .

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4238 (1 9 6 6 ) .

50. R.K. MACKENZIE, D.D. MacNICOL, H.H. MILLS, R . A.

RAPHAEL, F .B . WILSON and J .A . ZABKIEWIEZ, J .C h e m .S o c .

P e r k i n I I , 1632 (1972) .

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CHAPTER four

M o le c u l a r m e c h a n ic s c a l c u l a t i o n s on t h e

s t a b i l i t y o f b r i d g e h e a d o l e f i n s i n b i c y c l o -

( n u n » l ) a l k - l - e n e s y s t e m s .

- 153 -

U*1 I n t r o d u c t i o n

On t h e b a s i s o f e x p e r i m e n t a l d a t a r e g a r d i n g a n o m a l i e s

a s s o c i a t e d w i t h t h e b r i d g e h e a d p o s i t i o n o f b r i d g e d b y c y c l i c

WBFF) c o u ld s a t i s f a c t o r i l y r e p r o d u c e t h e a v a i l a b l e e x p e r

i m e n t a l d a t a on b r i d g e h e a d o l e f i n s . On a c c o u n t o f t h e f a c t

t h a t a l l t h e r e l e v a n t e x p e r i m e n t a l d a t a was o f a q u a l i t a t i v e

n a t u r e , i t was i m p o s s i b l e t o i n c l u d e any su c h d a t a i n t h e

p a r a m e t r i z a t i o n o f t h e WBFF. However o t h e r h i g h l y s t r a i n e d

b u t i s o l a b l e b y c y c l i c o l e f i n s e . g . 5 - e t h y l id enenor .bo rnene

( I ) , n o r b o r n a d i e n e ( I I ) and o C - p in e n e ( i l l ) and s t r a i n e d

t r a n s - c .v c l o a l k e n e s were i n c l u d e d i n t h e p a r a m e t r i z a t i o n o f

th e WBFF, w h ich a c c u r a t e l y p r e d i c t e d t h e g e o m e t r i c and

therm odynam ic p r o p e r t i e s o f t h e s e compounds ( s e e T a b l e s 3

and 2+ i n C h a p t e r 2 ) .

1 2 3compounds, B r e d t , F a w c e t t and Wiseman p ro p o s e d r u l e s

r e g a r d i n g t h e s t a b i l i t y o f b r i d g e h e a d o l e f i n s

The f i r s t aim o f t h i s s t u d y was t o d e t e r m i n e i f t h e

W h i t e - B o v i l l a l k a n e / a l k e n e f o r c e f i e l d ( r e f e r r e d t o as

I I I I I I

V 25.22 3 1 . 3 2 3 8 . 2 3(iccal./mole)

The d e v e lo p m e n t and r e s u l t s o f t h e WBFF a r e d i s c u s s e d

f u l l y i n C h a p t e r 2 . '

- 154 -

The seco n d aim o f t h i s s t u d y i s t o a s s e s s t h e l i m i t s

o f a p p l i c a t i o n o f t h e p ro p o se d r u l e s and where p o s s i b l e ,

p r o v i d e g u i d e l i n e s o r r u l e s f o r s i t u a t i o n s , n o t c o v e r e d by

t h e p r e v i o u s r u l e s .

k*2 Review

D u r in g B r e d t ’ s i n v e s t i g a t i o n s o f camphane (IV) and

p in a n e (V) d e r i v a t i v e s be tw ee n 1900 and 1 9 2 he r e c o g n i s e d

t h e r e l u c t a n c e o f b r i d g e d b i c y c l i c sy s te m s t o a l l o w th e

p la c e m e n t o f d o u b le bonds a t t h e i r b r i d g e h e a d s . H is o r i g i n a l

f o r m u l a t i o n o f t h e r u l e p r e s e n t l y b e a r i n g h i s name s u g g e s t s

t h a t !d o u b le bonds a t t h e b r i d g e h e a d atoms o f cam phenes ,

p i n e n e s and s i m i l a r l y c o n s t i t u t e d b i c y c l i c compounds

impose an u n n a t u r a l s p a t i a l a r r a n g e m e n t upon t h e i n v o lv e d

atoms and t h e s e compounds would t h e r e f o r e s u f f e r p r o h i b i t i v e

8 t r a i n * o r , more p r e c i s e l y , when a d o u b le bond i s c o n s t r a i n e d

a t t h e b r i d g e h e a d p o s i t i o n o f a b i c y c l i c compound, t h e

f o u r g ro u p s a t t a c h e d t o t h e o l e f i n i c l i n k a g e d e v i a t e

s i g n i f i c a n t l y f rom c o p l a n a r i t y w i t h t h e t r i g o n a l c e n t r e s ,

as a r e s u l t o f t h e t o r s i o n a l s t r a i n and t h e TT-bond i s

t h e r e f o r e weakened due t o p o o r o v e r l a p .

- 155 -

c o 2h

VI V II V I I I

C h em ica l e v id e n c e s u p p o r t i n g B r e d t ’ s r u l e i n c l u d e s

t h e f a i l u r e o f hromocamphor ( V I ) t o e l i m i n a t e h y d r o g e n

b rom ide i n th e p r e s e n c e o f a b a s e and t h e f a i l u r e o f t h e

u n s u b s t i t u t e d d i a c i d ( V I I ) t o c y c l i s e t o i t s a n h y d r i d e ( V I I I ) .

S y s t e m a t i c i n v e s t i g a t i o n s o f t h e l i m i t s o f B r e d t ’s

r u l e were u n d e r t a k e n d u r i n g t h e l a t e 1 9 4 0 ’s by P r e l o g ^ .

R ing c l o s u r e o f t h e d i k e t o n e (A) i n F i g u r e 1 may g iv e r i s e

t o e i t h e r t h e f u s e d - r i n g sy s te m (B ) o r th e b r i d g e d - r i n g

8 y s te m ( C ) . P r e l o g c o n c lu d e d f rom t h e s e r e s u l t s t h a t

-CH, COCH. CH

!02CH3•CH,

ACID or,

\ ~ \+ (CH2 ) n CO C

•CH.

CH. I I

•CH OIU

n=4n=5n=6

36 4 32£ none

none 14i

F i g u r e 1 . L i m i t a t i o n s o f B r e d t ’s Rule

l a r g e r b i c y c l i c r i n g s y s t e m s c a n , i n f a c t , accommodate

b r i d g e h e a d d o u b l e bonds and t h a t b i c y c l i c r i n g s y s te m s

- 156 -

i n t h e (n .3*1 ) s e r i e s w i t h n = 5 c a n have a "br idgehead

d o u b le b o n d , w h e reas t h e b i c y c l o d e c y l and s m a l l e r•Z £

sy s te m s c a n n o t , ( I t has b e e n n o te d t h a t a l l t h e s e

e x p e r i m e n t s were p e r fo rm ed u n d e r e q u i l i b r a t i n g c o n d i t i o n s

and as a r e s u l t , would g i v e t h e t h e r m o d y n a m ic a l ly p r e f e r r e d

p r o d u c t . )

2I n F a w c e t t f s r e v i e w , a t t e m p t s were made t o d e f i n e

t h e l i m i t s o f B r e d t ' s r u l e more p r e c i s e l y and a s t a b i l i t y

( o r s t r a i n ) p a r a m e t e r S was i n t r o d u c e d . I n b i c y c l o

(x , y , z ) a l k - l - e n e s , S i s t h e sum o f t h e number o f atoms

i n t h e b r i d g e , i . e . S = x + y + z and t h e s m a l l e s t

o b s e r v e d v a l u e a t t h e t im e was 9* F a w c e t t t h e r e f o r e

s u g g e s t e d t h a t b r i d g e d b i c y c l i c sy s te m s w i t h S ^ 9 a r e

l a r g e enough t o p e r m i t i s o l a t i o n o f b r i d g e h e a d a l k e n e ,

w h e rea s t h o s e s y s t e m s , w i t h S = 6 o r 7 , would e x i s t s o l e l y

as t r a n s i e n t s p e c i e s . However, t h i s S c r i t e r i o n f o r

s t a b i l i t y d id n o t e x p l a i n why p - k e t o a c i d (IX) r e s i s t s

d e c a rb o x y la t i o n " ^ w h i l e p - k e t o a c i d (X) d e c a r b o x y l a t e so

r e a d i l y - i n (IX) and (X ) , S = 7 .

N e i t h e r does i t e x p l a i n t h e i n s t a b i l i t y o f t h e enone

(X I)^ and t h e s t a b i l i t y o f enone ( X I I ) ^ a s S = 9 i n b o t h

e n o n e s . D e s p i t e t h e f a c t t h a t F a w c e t t ' s p r o p o s a l d i d n o t

- 157 -

XI XII

t a k e i n t o a c c o u n t t h e f a c t t h a t t h e s t a b i l i t y o f a

b r i d g e h e a d d o u b le bond d epends on which b r a n c h o f t h e

b i c y c l i c s y s te m c o n t a i n s i t , i t was 17 y e a r s b e f o r e i t

was s u p e r c e d e d .

•zI n 1 967, r e c o g n i t i o n by Wiseman^ t h a t t h e d e t e r

m in in g f a c t o r was t h e s i z e o f t h e s m a l l e s t r i n g c o n t a i n i n g

a t r a n s l i n k a g e r e p l a c e d t h e S c r i t e r i o n f o r s t a b i l i t y .

S t r u c t u r e X I I I r e p r e s e n t s a b i c y c l i c a lk e n e w i t h a

b r i d g e h e a d d o u b l e b o n d . Wiseman n o te d t h a t t h e d o u b le

X I I I

bond i n X I I I i s e x o c y c l i c t o r i n g a b , b u t e n d o c y c l i c i n

r i n g s ac and b e . S i n c e t h e d o u b le bond i s a t t h e b r i d g e

head o f r i n g s ac and b e , i t f o l l o w s t h a t i t must be c i s

i n one r i n g ( i n t h i s c a s e , b e ) and t r a n s i n t h e o t h e r ( i n

t h i s c a s e , a c ) . He t h e n p o s t u l a t e d t h a t ' t h e s t r a i n i n

b r i d g e h e a d a l k e n e s i s c l o s e l y r e l a t e d t o t h e s t r a i n o f

- 158 -

t r a n s - c y c l o a l k e n e s . O r d i n a r i l y , a b r i d g e h e a d d o u b le bond

w i l l be more s t a b l e when i t i s t r a n s i n t h e l a r g e r o f t h e

two r i n g s , i n w h ich i t i s e x o c y c l i c .

The s t r a i n o f t r a n s - c y c l o a l k e n e s was d i s c u s s e d i n

C h a p t e r 3- t r a n s -C.yclohexene h a s n e v e r b e e n i s o l a t e d ,

b u t h a s b e e n invoked as a t r a n s i e n t i n t e r m e d i a t e i n many

r e a c t i o n s . B r id g e h e a d a l k e n e s c o n t a i n i n g a t r a n s -

c y c lo h e x e n e r i n g m igh t be e x p e c t e d t o be t o t a l l y

i n a c c e s s i b l e . t r a n s - C y c l o h e p t e n e h a s b e e n g e n e r a t e d and

t r a p p e d b u t n o t y e t o b s e r v e d s p e c t r o p h o t o m e t r i c a l l y ,

t h e r e f o r e a b i c y c l i c b r i d g e h e a d o l e f i n i n c o r p o r a t i n g a

t r a n s - c y c l o h e p t e n e f r a g m e n t may be i s o l a b l e . t r a n s -

C y c lo o c t e n e and h i g h e r t r a n s - c y c l o a l k e n e s have b e e n

i s o l a t e d , so t h a t a b r i d g e h e a d a lk e n e s h o u ld be i s o l a b l e

when t h e l a r g e r o f t h e two r i n g s c o n t a i n i n g t h e d o u b le

bond i s a t e ig h t - m e m b e r e d •

T h i s h y p o t h e s i s i s q u a l i t a t i v e l y s u p p o r t e d by

d e c a r b o x y l a t i o n s t u d i e s o f b i c y c l o p - k e t o a c i d s ^ and1 0e n o l i s a t i o n o f k e t o n e s • I t e x p l a i n s why t h e d e c a r b o

x y l a t i o n o f IX i s l e s s f a c i l e t h a n X - IX i n v o l v e s a

t r a n s - c v c l o h e x e n e i n t e r m e d i a t e w h i l e X i n v o l v e s a t r a n s -

c y c l o o c t e n e i n t e r m e d i a t e . S i m i l a r l y , XI c o n t a i n s a t r a n s -

c y c l o o c t e n e r i n g as opposed t o t h e more s t a b l e t r a n s -

c y c lo d e c e n e r i n g i n X I I .

However , i n a r e c e n t r e v i e w , i t h a s b e e n n o t e d t h a t

t h i s c r i t e r i o n i s q u a n t i t a t i v e l y i n a d e q u a t e i n t h e r e s p e c t

- 159 -

t h a t i t d oes n o t d i f f e r e n t i a t e be tw ee n b i c y c l o (4 .3*1 )

dec-1 (2 ) ene (XIV) and b i c y c l o (1+ • 3• 1 ) dec-1 ( 9 ) - e n e (XV),

e a c h o f w h ich c o n t a i n a t r a n s - c y c lo n o n e n e r i n g and an S

v a l u e o f 8 .

XIV XV

4*3 M o l e c u l a r Mechanics (MM) C a l c u l a t i o n s and R e s u l t s

MM c a l c u l a t i o n s , u s i n g th e WBFF, were p e r fo rm e d on

a c a r e f u l l y s e l e c t e d g rou p o f s e v e n t e e n b r i d g e d b i c y c l i c

o l e f i n s (A-Q), s i x t e e n o f w hich a r e b r i d g e h e a d o l e f i n s .

A l l s e v e n t e e n compounds a r e shown i n F i g u r e 2 w i t h t h e i r

c o r r e s p o n d i n g s t e r i c e n e r g y , Vs ( k c a l / m o l e ) . A l l compounds

were m in im ised u n t i l a l l t h e f i r s t d e r v i a t i v e s o f th e

p o t e n t i a l e n e r g y w i t h r e s p e c t t o t h e a to m ic c a r t e s i a n

c o - o r d i n a t e s were l e s s t h a n 10 k c a l / m o l e A • A l l

compounds, e x c e p t G, r e p r e s e n t e n e r g y minim a. The f a i l u r e

o f G t o e x h i b i t t h i s f e a t u r e i s p r o b a b l y due t o t h e i n s t a b

i l i t y o f t h e c a l c u l a t i o n s a t s u c h a h i g h s t e r i c e n e r g y

v a l u e ( 5 9 .4 6 k c a l / m o l e ) . The t o r s i o n a n g l e s f o r e a c h

" b ic y c l i c compound i s g i v e n i n T ab le 1 •

T a b le 2 shows - t h e b r i d g e h e a d o l e f i n s l i s t e d i n

- 160 -

( a ) B i c y c l o ( 3 « 2 . l ) o c t e n e s y s t e m s .

y p 4 0 .5 3( K c a l . / m o l e )

(k) B i c y c l o ( 3 . 3 > l ) n o n e n e s y s t e m s .

4 0 . 1 5 4 0 . 9 9

Vs 51.93 (k ;c a l . /m o le )

7 . 0 32 6 . 5 2

(c ) B i c y c l o ( 4 . 2 . 1 ) n o n e n e s y s t e m s .

5 9 . 4 6 4 9 . 9 9

2 6 . 2 5

£3 1 . 1 4

( k c a l . / mole)

Figure 2: The b i c y c l i c o l e f i n s u s e d i n t h e s t u d y .

5 8 . 5 1

- 161 -

(d.) B i c y c l o ( 4 . 3 * l ) d e c e n e s y s t e m s .

V„ 3 5 f 8 4 55 .9 8

( k c a l . / m o l e )

(e) B i c y c l o ( 4 . 4 * l ) u n d e c e n e s y s t e m .i

5 1 '3

Vs 1 2 .4 1

(k’c a l . / m o l e )

( f ) B i c y c l o ( 5 . 3 ‘ l)''-indecene Cyst em.9

vs 12.82

( k c a l . / m o l e )

£i£H£e_2: ( c o n t d . )

- 1 6 2 -

n r> ’t i o n i O K ’tcaaiO 'OiOQTrKio U ^Wr)*^(MO©-^TTlD-*CMrjr^I I t B i l l

Sf acN G 'TOinQ'r ' tCHOQC3'0cc rocMevio<OMD^«^vin*-Ttctf>K.^l i t l i l t I

COIUZLa»~uo

CM<OIOIi*<rt»IO»»TKK IOTMOO© k o i k k ’c a —• ca —♦ m

I t I I t i l l

CJ>~oMlfiQ

ia_ i15

rr r* T n r y r fx a o ^ K W N ^ tw o c o io oa h fovo «rin»n<o>o<r-*<r-.co-»c\iir><MhvCL U )r cc cyiKiosr ^ i o i o o o i i k *«i o ^<^*O OL) I— ^ ^ (M n rt^ ’ IOlO'OOKNCOO

ll TOR

ANGLES

DEGREE

BJCYCL

IC BRE

DT CON

FOUNDS

- 163 -

OCO’CNf|OCD«’TO»KNIO^«NfO X < V i O i D K K > I O I D n a « O i « l D R r

I I I I I I I I

« «s® Q « ® n K O l O I * 4 CM

I I • I I I

n n io«4K«4K>ostnM iaok® it. K « H o i M « r a D « ^ N ® e « r > i oi t i i i i l l

m fv®(MNQ<OIORrQ®fOOKMQ Q» Ixl R r« V ^^K iO r)< » N »K K w O !® F jI I I I I I I I

mh i2TbJ I D ^ S VO»|»Ok«Tf>KKl*IN«4CI2T e » > K M K M ® B n K n ® n ® K ® «c | | | I I I I I

nw tuo _i-I C5U 2V * <o C« 2 2 'T AO D«OkN*4®fl-»Ciair»»fHNtCD D O

o hCL ®

« z ar Nan'iRrnff ®oiK««<roi*«dO O t t t t t t t B t l t l t t t i io i - > « 4 * 4 f i n n M « i i « i o i « i « ® ® a i o i

11 TOR

ANGLES

DEGREE

BICYCL

IC BRE

DT COM

POUNDS

- 164 -

m nt ©<on^«o>4 K K S H n i o o ^ c o nt NP)I t t I • ■ t

cm mQO «M W O*^»W (M I!3t0^lOtaQ KiocM«io*««>cyia«4io»«<c*«*4 t I t f i t l i t

m1aZ *«• Ovhi O I K O B N K } t « « « C « t B N O O B2 H r ) M K « « B K K C M « * * 4 * * O i n « D B to I I t t l l t l2:

w uO _l_l uU 2v- -*cu om z 2 MKDiOK ai«<>««4nMainto roaa0 3 o « » » « « » * % » « % « « * « «

O M nC»Mia«OK(tO<4#l«4(t(»MK«L « « « » « « * « % « % » « » « % »« r <e N » n M i o i D < O 0 K » « « « « « « « ^ t0 o o % * % % * * * % • * % * * • •-%^ U H C m ^M ’O tO O tO K ^ O * OkOl

- 165 -

mOklOKn<0«»Qr«N{Sl(0<OnOt *4 « iO K n K in c o c o 'V O in < o K * 4 N N ^ • I ■ « I • I I

I d "9 AOOlN NO TfFO^T^*4»4K'0 IS KN»4CVIIO OCKKr)'-*K'U^M —* *T *0 »-*I I I I I I I I I

^ Gi^ ( M S H O N O n W O N O jN ^ O -T? fvsnfoso^oD — r^ w ^ c v ^ r j fv c cc cc r t i l i t f f t

COhi2 ts. <tftxl N N T K N OkOlvHMlftCIKOSS ^u —i n i t N « » * K n K i ) * * n « « N « n K i r )UI t i l l I f I I Ic

v» IjJO _l s iro z5~ * • « B « % % % S N K

o w n <k^O «0 OK <4<D »o««««Q| w * « flL CO * s ^ « » » % * % • % % % % *W n^ zz cr Nwn^BiB««Kw«»o»a,«w « %O o C .4b *k Jb. 4b. . * > » % * * % . »«B cao •— w w w r> 4»srf> o«O K «e»® »o»w w

.)- 166 —

. •Ui2:«<ru CM CM CMhi o>k ® i > o o n r > « n ^ n v N O iO tL ^ M ^ t O Q ^ O ^ K X O N t O O l K K ^z l i l t I V « • t

w UIo _»—I ou z>- < to 01o c o 0 «-» * 4 B « p n %H Z Z 'V % »DON,tt> «*OA «• % **4 « sIB Z O *>(B «• % » « • * 4 %*4 4 19 CM *4 CM *4

o h n * 4 * 4 7 n o K 4 i 0 « 4 ( i « 4 % % « «OL SO « « 4 . « « * 4 » < 4 * * 4 » »»4«4«4«4XT OC CM —+ ^ O O O K C I B O 4 4 4 4

Ui O O 4 4 4 4 4 4 4 4 4 4 4 4 s (fi *4 «4vp O f - ^ M N d O M O O M K N O p t f t t

- 167 -

COc.3OCLXoo

c.USctauMc_>

oMecu.o

COUJmcceLiC l

•*~t LJ»— 2

LiCO U CVLi laJ tv- »*•-J C C5 ■•-» K «0O 1X 13<

—*•

C_J> <c

w> u C a rv■»-* »-f

rr —\ o * C5 »-*L> r> M ro ••* *■*__* a. tccr- X cr CM »• ^<r L. c a ^i ~ *-* o *~ - * € ¥ CM

(V a c nc k c M o n o i T f O K N C O w h h V N TT i OCK f ■ I I I IV

fs. O*»♦ 5 *■* fO % O » Ovto o k o o i * *-« «* ^ -*-• r i <*

« % • « > % •>* % I* C\i <rt (V «-* COt f tO >0 N CO *-i Ofc •>< % % » % %

lO’VLOONKtOKC« * • % % » * % %(> 5 <H w~* «4w n ^ i n o o K O » ^ w ^ ^ H

- 1 6 8 -

»-3 IU

2 0 3O CO ODM o cvr)o 0 0 0 0<o o a ® 0- a ® *>SUIO z0 - 1 oa2 H

< U*- O

2 3 2o o o*■“* SO 20 0 0 S <«0 0 « 0 M03 <« A0 *v 00 40 00 0 0 « «ac ui •4 «4»* «4OU« J*-32®

o o2 a o41-0

UI2 2•« O3 H4a *-• < N0O t e cm cm ®a x > ^ N(M S K (vok aOKO • • • • • • • • •• o ac ■3 if) AO *v ® 0M0MHIl U3 bi 2OOUI

ao« » *v ® « 0 0 0 C

UI (9M 03 2H t-»M0UK

UI 2 <3 0 K 6 O 0 KNKNN < 2M 2 H« k a

9 0 S K ^

tn> k »Nl V NT n aoNN K K

n*ooiKOCW

N O CB fO • •»V flftm m

oo 0 CO® S IOk Ok

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• • • • •0 0 0 ^ 0 O O I O 0 V

Ok to to <* o n « 4 0

« 0 ^ n

n « « n w • • • • •n ^ ^ io foW WA W W WUI UI UI UIO IC Z O X

M c v n n • • • •« « n ^

W V_# W VA« UI U < 0 J

V N 0 S K CM *-»* H 0 N 0 0 0 AT

• m m • • • ••40 0 SB *v CM CM0 ( V N CM •-* —4

4*4 4*4T —* ^ —4 «M —4• m m • • • •

CM IO CM io n n a»• m m • • • •

A»rtAi 'M >04-* W S-» WA W v*» W

« « ♦ «n U J w a 2 o a UI *

- 169 -

o r d e r o f d e c r e a s i n g s t e r i c e n e r g y (Vs)(Colum n 2 ) .

Columns 3 and 2j. g iv e i n f o r m a t i o n on t h e s i z e s o f t h e

t r a n s - c y c l o a l k e n e and c i s - c .y c lo a lk e n e i n c o r p o r a t e d i n t o

t h e h i c y c l i c s k e l e t o n . Column 5 shows th e e n e r g y due t o

o u t - o f - p l a n e d e f o r m a t i o n s c a l c u l a t e d by t h e WBFF f o r e a c h

compound. Columns 6 and 7 g i v e t h e t o r s i o n a n g l e s a round

th e t r a n s and c i s d o u b le bonds r e s p e c t i v e l y . Compound F

h a s b e e n e x c lu d e d s i n c e i t i s n o t a b r i d g e h e a d o l e f i n .

D i s c u s s i o n

B i c y c l o (ii . l+.l ) undec-1 ( 2 ) - e n e ( P ) , w h ich c o n t a i n s1 1a t r a n s - e y e l o d e c e n e r i n g , and b i c y c l o (U-3-1 ) dec-1

(3)-ene (N) and b i c y c l o (4 -3-1 )dec-1 ( 2 ) - e n e ( 0 ) ^ , w h ich

c o n t a i n a t r a n s - c y c l o n o n e n e r i n g , h a v e a l l b e e n i s o l a t e d -

t h e s m a l l e s t i s o l a b l e members o f t h e b i c y c l o ( x , y , l )

a l k - l - e n e sy s te m a r e b i c y c l o ( 3 - 3 - 1 ) non-1 ( 2 ) - e n e ( E ) ^ 3

b i c y c l o (4 -2 .1 )non-1 ( 9 ) - e n e ( i ) ^ * ^ ^ and b i c y c l o ( 4 - 2 .1 )

.■ non-1 (2 ) - e n e (J ) ^ > , e a c h o f w h ich c o n t a i n a t r a n s -

c y c l o o c t e n e r i n g . Compound E e x h i b i t s no rm al s p e c t r a l

p r o p e r t i e s b u t shows a h i g h d e g r e e o f r e a c t i v i t y i n

e l e c t r o p h i l i c and n u c l e o p h i l i c a d d i t i o n r e a c t i o n s ^

However, f rom a c o m p a r i s o n o f s p e c t r a l p r o p e r t i e s and o f1 5th e r a t e s o f e l e c t r o p h i l i c a d d i t i o n r e a c t i o n s o f

compounds E and I , i t c a n be c o n c lu d e d t h a t t h e d o u b le

bond i s s l i g h t l y l e s s s t r a i n e d i n t h e l a t t e r .

The r e s u l t s f rom t h e MM c a l c u l a t i o n s s u p p o r t

t h e s e e x p e r i m e n t a l o b s e r v a t i o n s . The s t e r i c e n e r g i e s

- 170 -

c a l c u l a t e d f o r a l l t h e s e i s o l a b l e b r i d g e h e a d o l e f i n s ( J ,

E, I , N, 0 and P) a r e n o t e x c e s s i v e l y h i g h and a l l a r e

i n d e e d , l e s s t h a t t h e s t e r i c e n e r g y , Vs , o f 31*32 k c a l / m o l e

which was c a l c u l a t e d f o r n o r b o r n a d i e n e ( I I ) . T h e r e f o r e ,

on t h e b a s i s o f MM c a l c u l a t i o n s , t h e s e b r i d g e h e a d o l e f i n s

( J , E , I , N , 0 and P) would be e x p e c te d t o be i s o l a b l e .

F u r t h e r m o r e , t h e c a l c u l a t e d s t e r i c e n e r g y , V s , o f I i s

0 . 3 k c a l / m o l e l e s s t h a n t h a t o f E and th e c a l c u l a t e d

t o r s i o n a n g l e a b o u t t h e d o u b le bond i s 12+9° i n I compared

w i t h 12+ 7° i n E - b o t h t h e s e r e s u l t s , t o g e t h e r w i t h t h e

r e l a t i v e m a g n i tu d e s o f t h e o u t - o f - p l a n e b e n d in g components

o f t h e s t e r i c e n e r g y o f I and E ( s e e column 5 i n T ab le 2 ) ,

p o i n t t o t h e f a c t t h a t t h e d o u b le bond i s l e s s s t r a i n e d

i n I and t h a t E s h o u ld be more r e a c t i v e .

B i c y c l o ( 3 * 2 . 1 ) o c t - 1 ( 2 ) - e n e ( A ) and b i c y c l o ( 3 * 2 .1 )

oc t -1 ( 7 ) - e n e ( B ) , e a c h o f w hich c o n t a i n s a t r a n s -c .y c lo -

h e p te n e r i n g , h av e b e e n p r e p a r e d b u t p ro ved t o be u n s t a b l e

.and h e n c e , a f t e r t h e i r g e n e r a t i o n , c o u ld o n l y be t r a p p e d16w i th d i p h e n y l i s o b e n z o f u r a n b u t n o t o b s e r v e d • A t t e m p t s

to p r e p a r e b i c y c l o ( 2 . 2 . 1 ) h e p t - l - e n e (XVI) , w hich

i n c o r p o r a t e s a t r a n s - c y c l o h e x e n e f r a g m e n t i n t o i t , haveA 7

been u n s u c c e s s f u l . These o b s e r v a t i o n s a r e i n a c c o rd

w i th r e s u l t s f rom MM c a l c u l a t i o n s . The s t e r i c e n e r g i e s

o f t h e b i c y c l o ( 3 . 2 . 1 ) sy s te m s and s i m i l a r sy s te m s

- 171 -

c o n t a i n i n g a t r a n s -c .yc lohexene r i n g , a r e a l l i n e x c e s s o f

1+0 k c a l / m o l e ( s e e T a b le 2 ) , w h ich i m p l i e s t h a t t h e s e

m o le c u l e s a r e h i g h l y s t r a i n e d and h e n ce d i f f i c u l t t o

i s o l a t e . The f a c t t h a t t h e c a l c u l a t e d s t e r i c e n e r g y

o f t h e compounds A and B a r e a b o u t 9 k c a l / m o l e h i g h e r

t h a n t h a t o f n o r b o r n a d i e n e ( I I ) r e i n f o r c e s t h i s o p i n i o n

as n o r b o r n a d i e n e i s i t s e l f a s t r a i n e d b i c y c l i c d i e n e , as1 8e v id e n c e d by i t s h i g h h e a t o f h y d r o g e n a t i o n , w h ich

a v e r a g e s 3k k c a l / m o l e p e r d o u b le bond v s , a norm al v a l u e

o f a b o u t 26 t o 28 k c a l / m o l e and by i t s r e a r r a n g e m e n t on

h e a t i n g , t o t r o p y l i d e n e (X V II ) , a m o n o cy c l ic t r i e n e ^ .

The o n l y e x p e r i m e n t a l l y d e r i v e d p h y s i c a l d e s

c r i p t i o n o f a b r i d g e h e a d a l k e n e comes f rom an X - r a y20 21c r y s t a l s t r u c t u r e a n a l y s i s o f compound XV III 9 . T h is

i s a r e l a t i v e l y u n s t r a i n e d example o f an 11 a n t i -B red t M

CO.NH.C^KLCl

compound. The s t r a i n , a p p e a r s t o m a n i f e s t i t s e l f b o t h i n

th e w a r p in g o f t h e d o u b le bond (by 8 , 6 ° ) and bond a n g le

d e f o r m a t i o n , p a r t i c u l a r l y a round the "br idgehead p o s i t i o n .

M oreover , t h e d o u b le bond i s i n a p o t e n t i a l l y c o n j u g a t i n g

p o s i t i o n w i t h t h e c a r b o n y l p o s i t i o n , t o g i v e an enone

s y s t e m . However, e nones have c h a r a c t e r i s t i c c h e m ic a l and

s p e c t r o s c o p i c p r o p e r t i e s and t h i s example e x h i b i t s b e h a v i o u r

w hich i s i n t e r m e d i a t e b e tw ee n t h e t r u e enone and i s o l a t e d

d o u b le bond and c a r b o n y l s y s t e m s , i . e . t h e s t r a i n imposed

by t h e b r i d g e h e a d p o s i t i o n o f t h e d o u b le bond r e s u l t s i n a

d i s t o r t i o n f rom i d e a l ( p l a n a r ) enone g e o m e t r y . E m p i r i c a l

e x a m i n a t i o n o f t h e u . v . s p e c t r u m i n d i c a t e d an a n g le o f

t w i s t o f a b o u t i |0° b e tw e e n th e d o u b le bond and c a r b o n y l

p l a n e . X - r a y a n a l y s i s r e v e a l e d an a n g le o f t w i s t o f 3 2 ° .

MM c a l c u l a t i o n s on t h e c o r r e s p o n d i n g u n s u b s t i t u t e d

e q u i v a l e n t o f XV III i . e . XIX, a r e i n e x c e l l e n t a g re em e n t

w i t h t h e X - r a y r e s u l t s . F i g u r e 3 shows a c o m p a r i s o n o f

th e c a l c u l a t e d g e o m e t ry o f XIX and t h e o b s e r v e d geo m e try

o f X V I I I . The f o r c e f i e l d u sed i n t h e MM c a l c u l a t i o n s was

an e x te n d e d v e r s i o n o f t h e WBFF, w hich i s p a r a m e t r i s e d22f o r t h e c a r b o n y l f u n c t i o n .

From t h e f o r e g o i n g d i s c u s s i o n , i t i s c l e a r t h a t t h e

r e s u l t s f rom t h e MM c a l c u l a t i o n s , u s i n g t h e WBFF, a r e i n

- 173 -

1.56 (1.53)

125.4(123.2) 112.8

(113.2)

1.29(1.34) 1.56 (1.53)

106.2(107.8).

120.1125.8 ( 1 2 3 . 4 | u o .o)

X i 3 V v/(1 1 6 -5 ) \ i 4g (1.47)

110.1 (113.8)

(104.7)1 1 2 .7(115-1)

1.56 (1-54)12 2.7(1 2 3 .6 )

1.53 (1.50)

113.0(115.6)

117.1(117.8)

1.56 (1.54) 1.56 (1.54)

/1.51114.5 / ( 1 . 5 4 ) [115.5 /

Hiftnre 3 ( a 3 ' Com parison o f t h e e x p e r i m e n t a l l y o b s e r v e d and c a lc u l a t e d , ( i n p a r e n t h e s e s ) "bond, l e n g t h s and a n g l e s f o r t h e b i c y c l o ( 5 * 3 # l ) u n d e c - l ( l O ) - e n e - 1 1 -o n e sy stem #

- 174 -

25(34 (-1)

-170 (-176) 0 (-1} 62 (61)

C35 (-28) 59(55K \

-5 9 (-67) _ 42 ^ _ 3 i \ _ i 5 7 (_148)137(1 47)

121 (121) /- 5 0 (-54)

94 (88).-44 (-38)

90(93) -9 4 (-98)

ffifture ■ Com parison o f t h e e x p e r i m e n t a l l y observed , andc a l c u l a t e d ( i n p a r e n t h e s e s ) t o r s i o n a n g l e s f o r t h e " b ic y c lo ( 5 . 3 « l ) u n d e c - l ( l 0 ) - e n e - l l - o n e system #

- 175 -

s u f f i c i e n t a g re em e n t w i t h t h e e x p e r i m e n t a l o b s e r v a t i o n s

a t o u r d i s p o s a l , t o e n a b l e us t o p l a c e a c e r t a i n d e g r e e o f

c o n f i d e n c e i n t h e p r e d i c t i o n s and c o m p a r i s o n s o b t a i n e d

f rom t h e u s e o f t h e WBFF,

e n e r g i e s o f E and F , t h a t p l a c i n g a d o u b le bond i n a

b r i d g e h e a d p o s i t i o n as opposed t o a n o n - b r i d g e h e a d p o s i t i o n

i n t h e b i c y c l o (3*3*1) nonene s y s te m r e s u l t s i n an

i n c r e a s e o f t h e s t e r i c e n e r g y o f a b o u t 19 k c a l / m o l e . T h is

i n c r e a s e i s due t o t h e f a c t t h a t m o le c u le s p o s s e s s i n g

b r i d g e h e a d d o u b le bonds a r e s t r a i n e d as a r e s u l t o f

f o r c i n g t h e n - b o n d i n g sy s te m t o assume an u n n a t u r a l

g e o m e t r y and n o t as a r e s u l t o f m o l e c u l a r o v e r c r o w d i n g .

T h is i s b o rn e o u t by t h e e x p e r i m e n t a l o b s e r v a t i o n t h a t

e l i m i n a t i o n o f HY f rom b i c y c l o (3*3*1) nonane compound

(XX) l e a d s p r e d o m i n a n t l y t o t h e 2 - e n e ( F ) r a t h e r t h a n t h e

I t c a n be deduced from a c o m p a r i s o n o f t h e s t e r i c

1 - e n e (E )1 ^ .

- 1 7 6 -

The v a l i d i t y o f y / i s em an 's t r a n s - c y c l o a l k e n e a n a lo g y

i s v i n d i c a t e d hy th e MM c a l c u l a t i o n s as sy s te m s i n c o r p o r

a t i n g t r a n s -c .y c lo d ec en e r i n g a r e c a l c u l a t e d t o he l e s s

s t r a i n e d t h a n t h o s e w i t h a t r a n s -c .yc lononene and so on

( s e e column 3 o f T a b le 2 ) . I n a d d i t i o n , t h e t o r s i o n

a n g le a b o u t t h e t r a n s d o u b le bond i n th e b i c y c l o ( x . y . 1 )

a l k - l - e n e sy s te m s i s i n t h e same o r d e r o f m ag n i tu d e as i n

t h e t r a n s - c y c l o a l k e n e a n a l o g u e . I t i s n o t e w o r t h y , b u t n o t

u n e x p e c t e d , t h a t t h e r e i s a c o r r e l a t i o n b e tw e e n th e s t e r i c

e n e r g y , Vs (column 2 ) , t h e o u t - o f - p l a n e d e f o r m a t i o n

e n e r g y (co lum n 5) and t h e t o r s i o n a n g le a b o u t t h e t r a n s

d o u b le bond (column 6 ) . The d o m in an t f a c t o r c o n t r o l l i n g

t h e i n h e r e n t d e g r e e o f s t r a i n o f a b i c y c l o ( x , y , 1 ) a l k - l - e n e

compound i s t h e r e f o r e t h e s i z e o f t h e t r a n s - c y c l o a l k e n e

f r a g m e n t •

B r id g e h e a d o l e f i n s have b e e n d i v i d e d i n t o two c l a s s e s 2

/by F a w c e t t - t h o s e w h ich a r e i s o l a b l e and t h o s e w h ich a r e

t r a n s i e n t i n t e r m e d i a t e s . The s t e r i c e n e r g i e s o f t h e

f o r m e r a r e a l l c a l c u l a t e d t o be l e s s t h a n o r e q u a l t o 31 *14

k c a l / m o l e , w h i l e t h o s e o f t h e l a t t e r c l a s s a r e g r e a t e r

t h a n o r e q u a l t o 35*84 k c a l / m o l e . I t would a p p e a r t h a t i f

t h e s t e r i c e n e r g y , V s , o f a b i c y c l i c b r i d g e h e a d o l e f i n i s

l e s s t h a n a b o u t 33 k c a l / m o l e w i t h r e s p e c t t o t h e WBFF, i t

sh o u ld be i s o l a b l e . Whereas i f t h e c a l c u l a t e d s t e r i c

e n e r g y e x c e e d s t h i s v a l u e , th e b r i d g e h e a d o l e f i n would

- 177 -

be e x p e c t e d t o be h i g h l y s t r a i n e d and e x i s t a s a t r a n s i e n t

i n t e r m e d i a t e . F u r t h e r m o r e , t h e l a r g e d i s t o r t i o n f rom

c o p l a n a r i t y o f t h e f o u r g ro u p s a t t a c h e d t o t h e o l e f i n i c

l i n k a g e i n b i c y c l i c sy s te m s c o n t a i n i n g t r a n s - c y c l o h e x e n e

r i n g s ( s e e column 6 i n t a b l e 2) s u g g e s t t h a t s u c h compounds

must have s u b s t a n t i a l d i r a d i c a l c h a r a c t e r .

As p r e v i o u s l y m e n t i o n e d , W isem an 's h y p o t h e s i s

t e l l s us n o t h i n g a b o u t t h e r e l a t i v e s t a b i l i t i e s w i t h i n a

g i v e n r i n g s y s te m i . e . f o r b i c y c l o ( x . y . l ) a l k - l - e n e

s y s te m s where x / y , w i t h a d o u b le bond a t , b u t n o t o n , t h e

b r i d g e h e a d , i t i s n o t p o s s i b l e t o p r e d i c t w h e t h e r i t i s

e n e r g e t i c a l l y more e x p e n s i v e t o p l a c e t h e d o u b le bond i n

t h e s m a l l e r r i n g o r i n t h e l a r g e r r i n g .

On t h e b a s i s o f W isem an 's p o s t u l a t e , no d i s t i n c t i o n

c a n be made b e tw e e n i so m e rs A and B, I and J and K and 0 .

MM c a l c u l a t i o n s u s i n g th e WBFF, i n d i c a t e t h a t i t i s more

f a v o u r a b l e t o p l a c e t h e d o u b le bond i n t h e second l a r g e s t

b r i d g e so t h a t B i s l e s s s t r a i n e d t h a n A, I i s l e s s

s t r a i n e d t h a n J and N i s l e s s s t r a i n e d t h a n 0 ( s e e F i g u r e

2 ) . A s i m i l a r c o n c l u s i o n h a s b e e n drawn f rom MM c a l c u l a t -

23io n s p e r f o r m e d by B u r k e r t u s i n g A l l i n g e r ' s f o r c e f i e l d .

E x a m in a t io n o f b i c y c l o ( 3 * 2 . 1 ) o c t - l - e n e s y s t e m s ,

A and B r e v e a l s t h a t i n c o r p o r a t i o n o f t h e d o u b le bond i n t o

l a r g e s t b r i d g e o f t h i s t r a n s - c y c l o h e p t e n e a n a l o g u e , as i n

A r e s u l t s i n t h e f o r m a t i o n o f a h i g h e n e r g y b o a t c o n fo r m

a t i o n o f c i s - c y c l o h e x e n e w hich i s c h a r a c t e r i s e d by

- 178 -

u n f a v o u r a b l e t o r s i o n a l and nonbonded i n t e r a c t i o n s . I f , on

t h e o t h e r h a n d , t h e d o u b le bond i s p l a c e d i n t h e second

l a r g e s t b r i d g e ( a s i n B ) , t h i s e n a b l e s t h e s ix -m em bered

r i n g t o assume an e n e r g e t i c a l l y p r e f e r r e d c h a i r c o n f o r m a t i o n .

S i m i l a r l y , compound B i s more s t a b l e t h a n compound C, s i n c e

t h e f o r m e r p o s s e s s a c h a i r c y c lo h e x a n e r i n g and t h e l a t t e r

a b o a t c y c l o h e x a n e r i n g .

M o l e c u l a r models o f b i c y c l o ( 4 * 2 . 1 ) non-1 ( 8 ) - e n e ( I )

and b i c y c l o ( 4 * 2 . 1 ) non-1 (2 ) - e n e ( J ) and o f b i c y c lo ( 4 * 3 * 1 )

dec-1 ( 9 ) - e n e (N) and b i c y c l o (4*3*1 ) dec-1 ( 2 ) - e n e ( 0 )

i n d i c a t e t h a t t h e d o u b le bond i s d i s t o r t e d more when i t i s

p l a c e d i n t h e l a r g e s t b r i d g e ( a s i n J and 0) as compared

t o when i t i s p l a c e d i n t h e second l a r g e s t b r i d g e ( a s i n

I and N) w i t h i n a g i v e n s k e l e t o n . T h i s i s due t o t h e

' f a c t t h a t when a d o u b le bond i s i n t r o d u c e d i n t o a r i n g

s y s t e m , t h e sy s te m becomes l e s s f l e x i b l e . T hus , when a

c i s d o u b l e bond i s p l a c e d i n t h e seco n d l a r g e s t b r i d g e

so as t o fo rm a r i g i d c i s - c y c l o p e n t e n e , as i n I , o r a

c i s - c y c l o h e x e n e . as i n N, t h e o t h e r s a t u r a t e d s e v e n

membered r i n g i n ,1 and N h a s more d e g r e e s o f f r e e d o m , by

which i t c a n a c t t o m in im is e t h e d i s t o r t i o n o f t h e d o u b le

bond and i t s s u b s t i t u e n t s f rom t h e p r e f e r r e d p l a n a r

g e o m e try and t h e s t r a i n s u f f e r e d by t h e compound, t h a n when

t h e d o u b le bond i s p l a c e d i n t h e l a r g e s t b r i d g e t o form

a c i s - c .y c lo h e n te n e r i n g ( a s i n J and 0) and t h e u n f a v o u r

a b l e s t r a i n components m in im ised by o n l y f i v e - and s i x -

membered r i n g s , a s i n J and 0 r e s p e c t i v e l y . T hu s , f rom

m o d e l s , one would e x p e c t I t o be l e s s s t r a i n e d t h a n 0 .

MM c a l c u l a t i o n s c o n f i r m t h e s e p r o p o s a l s - t h e s t e r i c

e n e r g y o f I i s c a l c u l a t e d t o be 4*89 k c a l / m o l e l e s s t h a n

J and the steric energy of N is 2.73 kcal/mole less than

0 . The s u b s t i t u e n t s on t h e d o u b le bond d e v i a t e f rom

p l a n a r i t y , on a v e r a g e by 1 7 ° i n I and by 21° i n J . The

torsion angle about the trans double bond is 149° in I

as opposed t o 143° i n J . The b r i d g e bond a n g le i s 9 1 .4°

in I compared to 88.5° in J. Similarly, the deviation of

t h e s u b s t i t u e n t s f rom p l a n a r i t y i n N i s 1 0 ° a s opposed t o

,16° i n 0 . The t o r s i o n a n g le a b o u t t h e t r a n s d o u b le bond

is 164° in N and 153° in 0, the bridge bond angle is

1 0 1 .9 ° i n N and 1 0 1 . 6 ° i n 0 .

I t i s a l s o i n t e r e s t i n g t o n o t e t h a t t h e c a l c u l a t e d

s t e r i c e n e r g y f o r compound I i s l e s s t h a n t h a t o f

compound E, w h ic h , i n t u r n , i s l e s s t h a n t h a t o f compound

J ( s e e T a b le 2 ) . Compounds I , E and J a l l i n c o r p o r a t e a

t r a n s - e y e l o o c t e n e r i n g i n t o t h e i r s k e l e t o n . Compound I

- 1 8 0 -

h a s a c i s - c y c l o p e n t e n e and c y c l o h e p t a n e r i n g , compound E

h a s a c i s - c y c l o h e x e n e and c y c lo h e x a n e r i n g , w h i l e J h a s a

c i s - c y c l o h e p t e n e and c y c l o p e n t a n e r i n g . The d e v i a t i o n o f

d o u b le bond s u b s t i t u e n t s from p l a n a r i t y i s 17° i n I , 20°

i n E and 21° i n J . The t o r s i o n a n g le a b o u t t h e t r a n s

d o u b le bond i s 1 i+9° i n I , i 1+7° i n E and 143° i n J .

These r e s u l t s , t o g e t h e r w i t h t h e r e s u l t s f o r t h e b i c y c l o

( ^ • 2 . 1 ) - n o n e n e s I and J and b i c y c l o (14-.3.1 •) d e c e n e s N and

0 , s u p p o r t t h e t h e o r y t h a t , w i t h i n a g i v e n s k e l e t o n , which

h a s a d o u b le bond a t , b u t n o t o n , t h e b r i d g e , t h e d o u b le

bond i s more f a v o u r a b l e when i t i s p l a c e d i n t h e second

l a r g e s t b r i d g e o r a l t e r n a t i v e l y , t h e sy s te m w i t h a c i s -

c y c l o p e n t e n e r i n g i s more s t a b l e t h a n one w i t h a c i s -

c y c lo h e x e n e r i n g w h ich i n t u r n i s more s t a b l e t h a n one

•with a c i s - c y c l o h e p t e n e r i n g . S i m i l a r d e d u c t i o n c a n be

drawn f rom t h e r e s u l t s o f P and Q.

U n f o r t u n a t e l y , t h e o n l y e x p e r i m e n t a l c o n f i r m a t i o n

o f t h i s t h e o r y i s t h e a f o r e m e n t io n e d d a t a t h a t t h e d o u b le

15bond i s more s t r a i n e d i n E t h a n i t i s i n I . To o b t a i n

c o n c l u s i v e e x p e r i m e n t a l p r o o f , i t would be n e c e s s a r y t o

d e t e r m i n e t h e h e a t s o f h y d r o g e n a t i o n a n d / o r h e a t s o f

f o r m a t i o n o f t h e a p p r o p r i a t e b r i d g e h e a d o l e f i n s . Many

- 1 8 1 -

r e a c t i o n s w h ich y i e l d t h e s e o l e f i n s o c c u r u n d e r e q u i l

i b r iu m c o n d i t i o n s and t h u s y i e l d t h e r m o d y n a m i c a l l y p r e f e r r e d

p r o d u c t s , o r a l t e r n a t i v e l y , t h e r e l a t i v e p e r c e n t a g e o f

p r o d u c t s f rom a r e a c t i o n may n o t r e f l e c t t h e i r r e l a t i v e

s t a b i l i t i e s , b u t r a t h e r t h e s t a b i l i t i e s o f t h e t r a n s i t i o n

s t a t e s , whose c o n f o r m a t i o n s do n o t r e s e m b le t h o s e o f t h e

p r o d u c t s •

When t h e d o u b le bond i s p l a c e d i n t h e s m a l l e s t

b r i d g e ( u s u a l l y r e f e r r e d t o ' t h e b r i d g e h e a d ' ) , t h e t r a n s

d o u b le bond as a c o n seq u e n ce i s l o c a t e d i n a r e l a t i v e l y

s m a l l t r a n s - c y c l o a l k e n e r i n g . MM c a l c u l a t i o n s i n d i c a t e

t h a t on a c c o u n t o f t h e f a c t o f t h e l a r g e d i s t o r t i o n s o f

t h e t r a n s t o r s i o n a n g l e f rom 180° and o f t h e c i s t o r s i o n

a n g le f rom 0 ° , e . g . t h e c o r r e s p o n d i n g v a l u e s i n H a r e 86°

and 59°> t h e s e compounds a r e u s u a l l y h i g h l y s t r a i n e d and i n

some c a s e s , i t becomes d i f f i c u l t t o d i f f e r e n t i a t e b e tw e e n

s i t u a t i o n s i n w h ich t h e d o u b le bond i s t r a n s and t h o s e i n

w h ich i t i s c i s .

I n g e n e r a l , w i t h i n a g i v e n s k e l e t o n , s y s te m s w i t h a

d o u b le bond p l a c e d i n t h e second l a r g e s t b r i d g e w i l l be

l e s s s t r a i n e d t h a n t h o s e w i t h a dou b le bond l o c a t e d i n t h e

- 182 -

l a r g e s t b r i d g e , which i n t u r n i s l e s s s t r a i n e d t h a n

t h o s e w i t h a d o u b le bond s i t u a t e d on th e s m a l l e s t

b r i d g e •

4*5 R e f e r e n c e s

1 . J . B r e d t , H. Thouet and J . S c h m i tz , A n n a le n , 4 3 7 «

1 ( 1 9 2 4 ) .

2 . P . S . F a w c e t t , Chem. R e v . . 4 7 , 2 1 9 ( 1 9 5 0 ) .

3 ( a ) . J . R . Wiseman, J . Amer. Chem. S o c . . 8 9 . 5966 (1 96 7 )

(*.) • J . R . Wiseman and W.A. P l e t c h e r , J . Amer, Chem. S o c . ,

2 2 , 956 ( 1 9 7 0 ) .

4* J . B r e d t , J . Houben and P . Levy , B e r . , 3 5 . 1286(1 902)

5* V. P r e l o g , J . Chem. S o c . , 420 (1950) and r e f e r e n c e s

c i t e d •

6 . G.L. Buchanan , Chem. S o c . R e v . , jj , 41 (1974)

7* A.C. Cope and M.E. S y n e rh o lm , J . Amer. Chem. S o c . ,

2 2 , 5228 (1950)

8 . H. Meerwein, P . K i e l , G. K lo sg e n and E. Schoch ,

J . P r a k t . Chem. . 1 0 4 . 1 6 3 , 1 6 6 (1 9 2 2 )

9* G.L. Buchanan and G. J a m ie s o n , T e t r a h e d r o n , 2 8 ,

1129 (1972)

1 0 . K.W. T u r n b u l l , S . J . Gould and D. A r i g o n i , J . C . S .

Chem. Comm. , 597 ( 1 9 7 2 ) .

1 1 . T. Westman, Ph .D . D i s s e r t a t i o n , U n i v e r s i t y o f

C a l i f o r n i a , 1962•

1 2 . P . T . Bond, Ph .D . D i s s e r t a t i o n , U n i v e r s i t y o f

C a l i f o r n i a , 1962 .

1 3 . J . A . M a r s h a l l and H. P a u b l , J . Amer. Chem. S o c . .

82, 5965 (1 9 6 7 ).14. J . R . Wiseman, H.‘ Chan and C . J . A h o la , J . Amer. Chem.

s o c . . 2L» 2812 ( 1 5 6 9 ) .

1 5 . K.B. B e c k e r , T e t r a h e d r o n L e t t . , 2207 (1975)

- 184 -

16. J.A. Chong and J.R. Wiseman, J. Amer. Chem. Soc., 94.8627 (1972).

17. W.G. Dauben and J.D. Robbins, Tetrahedron Lett.,

151 (1975).18. R.B. Turner, W.R. Meador and R.E. Winkler, J. Amer.

Chem. Soc., 79. 4116 (1957)19. Shell Chemical Corporation, New York, private

communication (circular), June 1956.20. A.P. Cameron and G. Jamieson, J. Chem. Soc.(B),

1581 (1971 ).21 . G.L. Buchanan and G. Jamieson, Tetrahedron, 28 ,

1123 (1972).22. D.N.J. 'White and H.P. Flitman, private communication.

23* U. Burkert, Chem. Ber.. 110, 773 (1977)*

- 185 -

CHAPTER FIVE

P r e d i c t i o n o f t h e s t e r e o c e l e c t i v i t y o f h i n d e r e d s u b s t r a t e s

- 1 8 6 -

5.1 I n t r o d u c t i o n

S t e r i c and e l e c t r o n i c e f f e c t s s t r o n g l y i n f l u e n c e

t h e r a t e s and e q u i l i b r i a o f many r e a c t i o n s i n o r g a n i c and

i n o r g a n i c c h e m i s t r y . I t i s t h e r e f o r e n e c e s s a r y t o examine

c l o s e l y t h e s t e r i c and e l e c t r o n i c p r o p e r t i e s o f t h e

r e a c t i n g s p e c i e s , b o t h i n t h e i r ground and e x c i t e d s t a t e s ,

i f t h e n a t u r e o f t h e p r o d u c t s and r a t e o f a p a r t i c u l a r

r e a c t i o n a r e t o be p r e d i c t e d .

S t e r e o s e l e c t i v i t y i s o f g r e a t im p o r t a n c e i n t h e

d e s i g n o f o r g a n i c r e a c t i o n s , p a r t i c u l a r l y i n t h e s y n t h e s e s

o f n a t u r a l p r o d u c t s . A S t e r e o s e l e c t i v e 1 r e a c t i o n i s one

i n w h ich o f two ( o r more) p o s s i b l e s t e r e o i s o m e r i c p r o d u c t s ,

one i s p ro d u ce d i n ( g r e a t ) p red om in an c e o v e r t h e o t h e r ( s ) .

A l th o u g h i t h a s l o n g b e e n r e c o g n i s e d t h a t s t e r i c

h i n d r a n c e i s an i m p o r t a n t f a c t o r i n s t e r e o - s e l e c t i v e .■\

t r a n s f o r m a t i o n s , few a t t e m p t s have b e e n made t o d e a l w i t h

t h i s c o n c e p t i n a q u a n t i t a t i v e m anner .

Most o r g a n i c c h e m i s t s t r y t o e s t i m a t e t h e d e g r e e o f

s t e r i c c o n g e s t i o n a t s i t e s o f c h e m i c a l a t t a c k f rom a

v i s u a l i n s p e c t i o n o f a m o l e c u l a r model o f t h e compound o f

i n t e r e s t . However, m o l e c u l a r models c a n be m i s l e a d i n g and

t h i s a p p r o a c h becomes i n c r e a s i n g l y complex p a r t i c u l a r l y

when t h e r e i s v e r y l i t t l e s t e r i c h i n d r a n c e f rom t h e

im m edia te n e i g h b o u r s and t h e medium-and l o n g - r a n g e

s t e r i c e f f e c t s become dom inan t f a c t o r s i n c o n t r o l l i n g t h e2

s t e r e o s e l e c t i v i t y o f a r e a c t i o n and when more t h a n one

- 187 -

c o n f o r m a t i o n o f t h e m o le c u le may r e a c t .

3Y/ipke and Gund have d e v i s e d an a l g o r i t h m f o r

c a l c u l a t i n g s e m i - q u a n t i t a t i v e e s t i m a t e s o f t h e r e l a t i v e

s t e r i c c o n g e s t i o n a t p o s s i b l e r e a c t i o n s i t e s . T h is

t e c h n i q u e i s e x t r e m e l y u s e f u l f o r p r e d i c t i n g w h ich o f th e

p o s s i b l e p r o d u c t s w i l l d o m in a te i n r e a c t i o n s , w h ich a r e

c o n t r o l l e d by s t e r i c i n f l u e n c e o f n e i g h b o u r i n g atoms i n

t h e m o l e c u l e . A c e r t a i n d e g r e e o f s u c c e s s h a s b e e n

a c h i e v e d when t h i s t y p e o f method h a s b e e n a p p l i e d t o t h e

p r e d i c t i o n o f r a t i o o f p r o d u c t s which r e s u l t f rom s t e r e o

s e l e c t i v e n u c l e o p h i l i c a d d i t i o n s t o s t e r i c a l l y h i n d e r e d3 Uk e to n e s 9 ( s e e F i g u r e 1 ) .

3I n Wipke and Gund*s method , t h e t e rm 1s t e r i c

L i A I HOH

o b s e r v e d %

c a l c u l a t e d % 20 80

F i g u r e 1 . C o m p ar i so n o f t h e o b s e r v e d and c a l c u l a t e d

s t e r e o s e l e c t i v i t y f o r t h e r e d u c t i o n o f

2 - n o r b o r n a n o n e , a c o n g e s t e d k e t o n e .

c o n g e s t io n * a t a r e a c t i o n c e n t r e r e f e r s t o t h e s t e r i c

e n v i ro n m en t o f t h e i s o l a t e d s u b s t r a t e i n i t s ground

s t a t e , and i s i n d e p e n d e n t o f r e a c t i o n p a r t n e r s o r

t r a n s i t i o n - s t a t e s t r u c t u r e . The te rm * s t e r i c h i n d r a n c e *

r e f e r s t o s t e r i c e n v i r o n m e n t w i t h r e s p e c t t o t h e a p p ro a c h

- 1 8 8 -

o f a s p e c i f i c r e a c t i n g p a r t n e r . The Wipke and Gund

method g e n e r a t e s a cone o f p r e f e r r e d a p p ro a c h f o r e a c h

s t e r i c a l l y h i n d e r i n g atom and works i n t h e f o l l o w i n g

C o n s i d e r a t t a c k on a c a r b o n y l g roup by a r e a g e n t R whose

s i z e i s c o n s i d e r e d n e g l i g i b l e ( F i g u r e 2 ) . I f t h e r e a g e n t

a t t a c k s C a lo n g a l i n e p e r p e n d i c u l a r t o t h e p l a n eJL,

c o n t a i n i n g th e c a r b o n y l g ro u p , i t w i l l be h i n d e r e d by

t h e v a r i o u s atoms i above t h e p l a n e . A m easure o f e a c h

a to m ’ s a b i l i t y t o h i n d e r t h e in co m in g r e a g e n t i s i t s v a n

d e r Waals r a d i u s r ^ . F o r e a c h h i n d e r i n g atom i , a cone

o f p r e f e r r e d a p p r o a c h , c e n t r e d on t h e p e r p e n d i c u l a r and

t a n g e n t t o t h e s p h e r e o f v a n d e r Waals r a d i u s r ^ s u r r o u n d i n g

atom i , i s d e f i n e d . T h is cone i n t e r s e c t s a s p h e r e o f

u n i t r a d i u s c e n t r e d on t h e c a r b o n C , t o g e n e r a t e a s o l i dAa n g le A The m ag n i tu d e o f t h i s a n g le i s e q u a te d w i t hX.£L •th e a c c e s s i b i l i t y o f t h e c a r b o n atom w i t h r e s p e c t

• to atom i . I t c a n be s e e n t h a t l a r g e s o l i d a n g l e s a r e

found i n s i t u a t i o n s o f , h i g h a c c e s s i b i l i t y and c o n v e r s e l y ,

a s m a l l s o l i d a n g le i s i n d i c a t i v e o f low a c c e s s i b i l i t y .

From s o l i d g e o m e t ry :

Ax a ( i ) = 2TT(1“ 008 S ) *The c o n g e s t i o n a t CY c a u se d by atom i i s d e f i n e d as th e

i n v e r s e o f t h e a c c e s s i b i l i t y :

Cx a ( i ) = 1 /Ax a ( i )

The t o t a l c o n g e s t i o n a t C i s g e n e r a t e d by summing t h e

i n d i v i d u a l c o n g e s t i o n te rm s f o r a l l t h e atoms above t h e

F ig u r e 2 ; Cone o f p r e fe r r e d , approach o f r e a g e n t R t o c a r b o n x

d e f i n e d b y h i n d e r in g atom i . The a c c e s s i b i l i t y o f

x on s i d e a w i t h r e s p e c t t o i_ i s d e f i n e d b y t h i s s o l i d

a n g l e and i s n u m e r ic a l ly eq u a l t o t h e a r e a on a

u n i t s p h e r e c u t by t h i s con e ( sh a d e d a r e a ) .

- 190 -

c a r b o n y l p l a n e :

Cxa “ ^ Cx a ( i )

The c a l c u l a t i o n i s t h e n r e p e a t e d f o r a t t a c k be low t h e p l a n e

o f t h e c a r b o n y l g ro u p t o g iv e . The p r e f e r r e d d i r e c t i o n

o f a t t a c k o f t h e incom ing r e a g e n t i s t h a t w h ich g i v e s t h e

minimum v a l u e o f C. The p e r c e n t a g e o f p r o d u c t r e s u l t i n gt hfrom a t t a c k be low t h e p l a n e o f t h e j c o n f o r m a t i o n , p ^

i s g i v e n b y :

CPgi ~ ----- ££—

C + C . xa xb

S i m i l a r l y , t h e p e r c e n t a g e o f p r o d u c t r e s u l t i n g f rom a t t a c k

above th e p l a n e o f t h e j c o n f o r m a t i o n , p ^ i s g i v e n b y :

PAj CxbCxa + C xb

Angle 9 i s e a s i l y d e r i v e d :

' 9 = 90 - 01 - ©2

Awhere 9^ = sin )> <3i t ie d i s t a n c e o f atom i

—1f rom t h e c e n t r e o f a t t a c k , and 9^ = s i n ( h ^ / d ^ ) , h i i s

t h e d i s t a n c e o f atom i above ( o r be low ) t h e p l a n e o f t h e

c a r b o n y l g r o u p ,

Wipke and Gund have found t h a t t h e c a l c u l a t e d

c o n g e s t i o n s do r e f l e c t o b s e r v e d s t e r e o s e l e c t i v i t i e s i n a

s e m i - q u a n t i t a t i v e manner and t h a t s t e r i c c o n t r o l a p p e a r s

t o d o m in a te when t h e d i f f e r e n c e i n c o n g e s t i o n o f t h e two

s i d e s i s l a r g e and t h e l a r g e r o f t h e two v a l u e s i s

g r e a t e r t h a n c a .3 0 *

I t i s n o t e w o r t h y t h a t r e s u l t s f rom t h i s method may

he i n a c c u r a t e i n c a s e s where t h e s i z e o f r e a g e n t s , i n d u c t i v e

e f f e c t s , t r a n s i t i o n - s t a t e c o n f o r m a t i o n a l e f f e c t s o r

- 191 -

equilibration of products are dominant factors in determining the stereoselectivity of a given reaction.

5.2 Prediction of the Stereoselectivity in the Hydro- boration of Hindered Cyclohexenes using Molecular Mechanics Calculations and Steric Congestion Calculations.

3Wipke and Gund suggested that these types of congestion calculations may be extended to include electrophilic additions to double bonds by calculating the degree of steric crowding or congestion on each side of the mid-point of the double bond. However, in the case of hydroboration of an alkene, which involves a cis anti-Markovnikov addition of the B-H bond to the double bond of the olefin, the reaction does not therefore take place via reagent attachment to the mid-point of the double bond but through the four-centre transition state 1^.

1It therefore appeared more realistic to adopt a two-fold attack on two atomic centres (see Figure 3) rather than a bond centred approach as the latter approach would imply that the double bond can be considered as infinitesimally small compared with the rest of the reagent-substrate complex. This appears to be too gross an

- 192 -

approximation for general use and therefore it would "be preferable to treat this type of addition in terms of the sum of two atom centred congestions.

Figure 3* Simultaneous Attack on Two Atomic Centres.

The congestion function developed by V/ipke andGund was utilised in the SAUCE computer program, whichwas written at the University of Glasgow by M.J. Bovilland C.J. Gilmore and which has proved useful in the study

2of electrophilic attack on nitrogen lone-pairs and hydroboration of hindered cyclohexenes , which will be discussed fully in this chapter.

The recent publication of results of a series of hydroboration/oxidation experiments on hindered 1,3,5- tri- and tetra- substituted alkylcyclohexenes^ provides reference data for testing the applicability of summed atom centred congestion ratio’s (SACK’S) in the prediction of the outcome of stereoselective additions to hindered double bonds since hydroboration is known to be sensitive to the balance of steric hindrance to the two faces of the double bond (see Figure 4 ).

- 193 -

ane..ttack

Figure U •

Gordon and Robinson^ propose that the olefins 2-^ and 6-2 (Tahle 1) strongly prefer the half-chair conformation jHD while, for olefin conformations 1C_ and 11 are of comparative stability. These proposals are borne out by molecular mechanics calculations using the White-Bovill alkane/alkene force field, the development of which is described in Chapter 2. The results of these calculations on olefins 2 - 2 are given in Table 1 . Olefins 2 and 6-2 which adopt half-chair conformer 1_0 are found to be between 1 ,2 9 and 2 .^ 8 kcal/ mole more stable than when the same olefins adopt the other half-chair conformation (N.B. A difference in strainenergy of 1 , 2 9 kcal/mole corresponds to 90% of the more

- 1^4 -Table 1. Results of Molecular Mechanics Calculations

and Congestion Calculations

Rotamers which adopt half-chair conformation10 11

bo Sso

452926

6 . 0 0

5.375537

4.53 31 91 £ai2 21 35.40 15 91 5.36 16 94

i s Z 3 - -22 5.78 8 75

6 . 1 2

7 .2 6

1 6 . 0 2

6 . 1 2

38'3230

4 .81 43 57 6 . 4 9

5.05 29 405 .0 6 28 52

S i l l

5.3042

- 195 -

Es j d e n o t e s t h e s t e r i c e n e r g y ( i n k c a l / m o l e ) o f

t h e c o n f o r m a t i o n .

x i d e n o t e s t h e p e r c e n t a g e o f c o n f o r m a t i o n j J

amongst t h e v a r i o u s p o s s i b i l i t i e s .

P-j3-j r e p r e s e n t s t h e p e r c e n t a g e o f p r o d u c t r e s u l t i n gt i lf rom a t t a c k he low th e p l a n e o f t h e j

c o n f o r m a t i o n .

The u n d e r l i n i n g i s u sed t o i n d i c a t e t h e most

s t a b l e r o t a m e r o f e a c h ty p e o f h a l f - c h a i r

c o n f o r m a t i o n t h a t t h e o l e f i n c a n a d o p t .

- 196 -

- 197 -

s t a b l e c o n fo r m e r b e i n g p r e s e n t i n an e q u i l i b r i u m m ix t u r e

a t room t e m p e r a t u r e . ) I n t h e c a s e o f o l e f i n t h e

h a l f - c h a i r c o n f o r m a t i o n 1_0 i s c a l c u l a t e d t o be o n l y 0.22+

k c a l / m o l e l o w e r i n p o t e n t i a l e n e r g y t h a n t h e h a l f - c h a i r

c o n f o r m a t i o n 1J_. S in c e o l e f i n s 2-l± and 6.-2 w i t h h a l f -

c h a i r c o n f o r m a t i o n 1J_ a r e b a r e l y p r e s e n t , t h e y a r e n o t

i n c l u d e d i n f u r t h e r c o m p u t a t i o n s .

On a c c o u n t o f t h e p r e s e n c e o f t h e i s o p r o p y l g roup

i n e a c h o f t h e o l e f i n s 2-%, i t i s n e c e s s a r y t o c o n s i d e r

e a c h o f t h e t h r e e r o t a m e r i c s t a t e s t h a t t h e i s o p r o p y l

g ro u p c a n assume i n e a c h o l e f i n . M o le c u la r m ec h an ic s

c a l c u l a t i o n s i n d i c a t e t h a t e a c h ro tam er ic fo rm o f each

o l e f i n i s p r e s e n t t o an a p p r e c i a b l e e x t e n t ( s e e T a b le 1 )

and s i n c e t h e c o n g e s t i o n r a t i o w i l l depend s t r o n g l y upon

t h e e x a c t m o l e c u l a r c o n f o r m a t i o n , i t was c o n s i d e r e d v i t a l ,

f o r t h e v a l i d i t y o f t h e r e s u l t s , t h a t t h e SACR’s o f each

r o t a m e r i c s t a t e o f e a c h o l e f i n s h o u ld be t a k e n i n t o

a c c o u n t when d e t e r m i n i n g th e o v e r a l l SACR o f e a c h o l e f i n .

The r e s u l t s o f t h e SACR c a l c u l a t i o n s a r e compared w i t h t h e

e x p e r i m e n t a l r e s u l t s i n T a b le 2 where i s c a l c u l a t e d n

f rom PT3=0.01 p u .x . w i t h Pu . r e p r e s e n t i n g t h e p e r c e n t a g e ■d nJ J

o f p r o d u c t r e s u l t i n g f rom a t t a c k be low t h e p l a n e o f t h e+ Vi

d c o n f o r m a t i o n ( i . e . a l t e r n a t i v e h a l f - c h a i r s a n d / o r

r o t a m e r s ) and x . th e p e r c e n t a g e o f c o n f o r m a t i o n j amongstJ

t h e v a r i o u s p o s s i b i l i t i e s . The i n d i v i d u a l PBj and Xj

v a l u e s f o r e a c h c o n f o r m a t i o n a r e g i v e n i n T a b le 1•

T a b le 2 .

- 198 -

_BO bs . C a l c .

100 53

100 89

100100 58 8

O bs . C a l c .

3 5 U6

3 5 50

9 0 7 5 3 0 3 3

- 199 -

5*3 D i s c u s s i o n

Prom T a b le 2 , i t c a n be s e e n t h a t t h e c a l c u l a t e d

v a l u e o f Pg c o r r e l a t e s w e l l w i t h t h e e x p e r i m e n t a l l y

o b s e r v e d s t e r e o s e l e c t i v e s i n t h e h y d r o b o r a t i o n o f t h e s e

h i n d e r e d c y c l o h e x e n e s i n most c a s e s - f o r o l e f i n s 2 and

5. - 2.f 'the c a l c u l a t e d v a l u e o f Pg i s w i t h i n - 15% o f t h e

o b s e r v e d v a l u e . T h is c o m p a r i s o n i s f a v o u r a b l e when i t i s

t a k e n i n t o a c c o u n t t h a t e x p e r i m e n t a l r e s u l t s , f rom one

l a b o r a t o r y have a s s o c i a t e d e r r o r s and d i f f e r f rom t h e

r e s u l t s f rom d i f f e r e n t l a b o r a t o r i e s . In o l e f i n s 2 and

k> t h e d i f f e r e n c e i n a b s o l u t e c o n g e s t i o n v a l u e s o f t h e

two s i d e s i s n o t l a r g e (7 and 5 r e s p e c t i v e l y ) and th e

l a r g e r o f t h e two v a l u e s i s l e s s t h a n 30 i n b o t h c a s e s ,

w h ich would be i n t e r p r e t e d by Wipke and Gund as b e i n g

due t o s t e r i c c o n t r o l n o t d o m i n a t i n g . T o r s i o n a l e f f e c t s3

i n t h e s u b s t r a t e - r e a g e n t complex c a n be i m p o r t a n t , b u t ,

i n t h e c a s e o f 2 and k> would f a v o u r t h e r e v e r s e s t e r e o s e l

e c t i v i t y t o t h a t o b s e r v e d . F u r t h e r m o r e , s i n c e t h e m a jo r

p r o d u c t s o f t h e h y d r o b o r a t i o n o f o l e f i n s 2 ~ 2. a r e t *ie l e s s

s t a b l e p o s s i b l e p r o d u c t s and o l e f i n s an(3 5. a l s o p ro d u c e

s i g n i f i c a n t amounts o f t h e l e s s s t a b l e p r o d u c t s , t h i s

would im p ly t h a t t h e t r a n s i t i o n s t a t e i n t h e s e r e a c t i o n s

c l e a r l y r e s e m b l e s t h e s t a r t i n g m a t e r i a l s ( o l e f i n s ) r a t h e r

t h a n t h e p r o d u c t s and t h a t t h i s r e a c t i o n i s g o v e rn e d by9

’s t e r i c a p p r o a c h c o n t r o l 1 r a t h e r t h a n p r o d u c t d e v e lo p m e n t

c o n t r o l ( i . e . where t h e more t h e r m o d y n a m i c a l l y s t a b l e

p r o d u c t i s p r e f e r e n t i a l l y f o r m e d ) . * t i s t h e r e f o r e

d i f f i c u l t t o e n v i s a g e r e a c t i o n s o f o l e f i n s £ - k b e i n g

- 2 0 0 -

c o n t r o l l e d d i f f e r e n t l y as a l l t h e r e a c t i o n s a r e m e c h a n i s t

i c a l l y v e r y s i m i l a r . T h is t h e n p o i n t s t o t h e f a c t t h a t

t h e r e a s o n f o r t h e p o o r r e s u l t s i n t h e c a s e o f 2 and l i e

w i t h t h e g round s t a t e c o n g e s t i o n a l g o r i t h m o r w i t h some

o t h e r f a c t o r w h ich h a s "been so f a r n e g l e c t e d . One su c h

f a c t o r may he t h e i n d u c t i v e e f f e c t o f t h e a l k y l g r o u p .

I n t h e h y d r i d e r e d u c t i o n o f 3 - a l k y l h i c y c l o ( 2 . 2 . 2 ) o c t a n -

2 - o n e s , (1 2 ) , (R=I.de,Et j P r 1 ) t h e r e i s an u n e x p e c t e d l y l a r g e

p r o p o r t i o n o f t r a n s a l c o h o l (lj±.) formed i n t h e r e a c t i o n ,. i o

e s p e c i a l l y when I ^ P r 1 , i n c o n f l i c t w i t h c h e m ic a l

i n t u i t i o n and t h e o r e t i c a l c a l c u l a t i o n s . T h is h a s h e e n

a t t r i b u t e d t o an a n i s o t r o p i c i n d u c t i v e e f f e c t o f t h e a l k y l

g r o u p s , w h ich l e a d s t o an a n o m a lo u s ly h i g h r a t e o f a t t a c k

from t h e more h i n d e r e d s i d e ( i . e . t h e a l k y l s i d e ) o f t h e

o f t h e c a r b o n y l g r o u p . I n t h e c a s e o f t h e h y d r o b o r a t i o n

( e l e c t r o p h i l i c r e a c t i o n ) o f o l e f i n s , i t i s c o n c e i v a b l e

t h a t t h e r e i s a s i m i l a r f a c t o r o p e r a t i n g . The i n d u c t i v e

e f f e c t o f t h e e l e c t r o n - r e l e a s i n g g ro u p s ( m e th y l and i s o

p r o p y l ) i s . a l s o a n i s o t r o p i c and t h a t t h i s e f f e c t i s

a c t i v a t i n g on t h e s i d e o f t h e d o u b le bond rem o te f rom t h e

s u b s t i t u e n t s H0 and Rc i n o l e f i n s 2 - U. T h i s would * ? ~

a c c o u n t f o r t h e h i g h s t e r e o s e l e c t i v i t y o f o l e f i n s 2 - i . .

- 201-

T h is a n i s t r o p i c i n d u c t i v e e f f e c t , ( i f p r e s e n t ) would a p p e a r

t o e x e r t a r e l a t i v e l y weak i n f l u e n c e , s i n c e i n o l e f i n s ^ -

w h ich c o n t a i n an a x i a l R^ o r an a x i a l R^ g ro u p and a r e

t h e r e f o r e c o n g e s t e d on th e s i d e o f t h e d o u b le bond rem ote

f rom R£ and R^ g r o u p s , ’s t e r i c a p p ro a c h c o n t r o l 1 once

a g a i n d o m i n a t e s .

W h a tev e r t h e r e a s o n f o r t h i s f a i l u r e i n t h e p r e d i c t i o n s ,

t h e SACR’s c a l c u l a t i o n s l e n d s u p p o r t t o Gordon and

R o b i n s o n ’ s h y p o t h e s i s t h a t t h e h i g h s t e r e o s e l e c t i v i t y

shown by 2. - i s due t o t h e e f f e c t o f t h e R^ h i n d e r i n g

a t t a c k f rom th e u p p e r f a c t o f t h e d o u b le bo n d , o n l y when

Rc i s an i s o p r o p y l g ro u p ( a s i n 3) and n o t when Rc i s a 0 0

m e th y l g rou p ( a s i n 2 and i ^ ) .

I n c o n c l u s i o n , t h e c o n g e s t i o n f u n c t i o n i s r e l i a b l e

i n p r e d i c t i n g t h e s t e r e o s e l e c t i v i t y o f h i n d e r e d c y c l o -

h e x e n e s when t h e d i f f e r e n c e i n t h e c o n g e s t i o n o f t h e two

s i d e s i s g r e a t e r t h a n a b o u t 10 and th e l a r g e r o f t h e two

v a l u e s i s g r e a t e r t h a n a b o u t 3 0 . F u r t h e r m o r e , t h i s

method r e q u i r e s o n l y s m a l l amounts o f co m p u te r t im e as

e a c h SACR c a l c u l a t i o n f o r one o l e f i n t a k e s o n l y C.25

s e c o n d . I n c a s e s where s t e r i c c o n t r o l d oes n o t d o m in a t e ,

a more complex a p p ro a c h i s o b v i o u s l y r e q u i r e d . One su c h

a p p r o a c h i n v o l v e s t h e c o n s t r u c t i o n o f m odels o f c h a i r

l i k e and t w i s t - l i k e t r a n s i t i o n com plexes ( s i n c e i t i s

i m p o s s i b l e t o deduce th e c o n f o r m a t i o n o f t h e t r a n s i t i o n

s t a t e f rom t h e p r o d u c t s ) o f a lk y l c y c l o h e x e n e / B H ^ f o l l o w e d

by f u l l r e l a x a t i o n e n e r g y m i n i m i s a t i o n o f t h e complexo

k e e p i n g a B-H v e c t o r l o c k e d p a r a l l e l t o a n d , s a y 1 *5A

- 202 -

a b o v e , t h e d o u b le bond^ i n one c a s e , and th e same d i s t a n c e

be low i n t h e o t h e r . The r a t i o o f p r o d u c t s would t h e n

be e s t i m a t e d f rom t h e c a l c u l a t e d e n e r g y d i f f e r e n c e

b e tw e e n th e model c o m p le x e s . T h is a p p ro a c h a l l o w s t h e

s u b s t r a t e t o r e l i e v e and s p r e a d th e s t r a i n in d u ce d by

r e a g e n t a p p ro a c h and would i n c l u d e t o r s i o n a l , d i p o l a r ,

s o l v e n t , e n t r o p i c and r e a g e n t s i z e e f f e c t s as w e l l as

i l l u m i n a t i n g t h e n a t u r e o f t h e t r a n s i t i o n co m p lex .

- 2 0 3 -

5.1+ References

1. Reviews: (a) J.D. Morrison and H.S. Mosher, "AsymmetricOrganic Reaction'*, Prentice-Hall, Englewood Cliffs,

N.J., 1971 ;(b) L. Velluz, J. Vails, and G. Nomine,

Angew. Chem.. Int. Ed. Engl., 181 (1965);(c) L. Velluz, J. Vails and J. Mathiez,

ibid., 6, 778 Cl 9 6 7);(a) J.W. Scott and D. Valentine Jr., Science.

1 8h, 91+3 (197U).2. C.J. Gilmore, R.F. Bryan and S.M. Kupchan, J. Amer.

Chem. Soc.. 2 8 , 1 9U7 (1976).3. W. Todd Wipke and P. Gund, J. Amer. Chem. Soc..

28, 8107 (1976).P. Muller and J-C. Perlberger, Helv. Chim. Acta.

2 2 , 1880 (1976).5. H.C. Brown, R. Liotta and C.G. Scouten, J. Amer. Chem.

Soc.. 28, 5297 (1976).6. D.N.J. White and M.J. Bovill, Tetrahedron Lett.,

submitted (1977).7* M.H. Gordon and M.J.T. Robinson, Tetrahedron Lett..

3867 (1975).8. M.H. Gordon and Kwang-Ting Liu, J. Amer. Chem. Soc.,

25, 7335 (1971).9(a).W.G. Dauben, G.J. Fonkin and D.S. Noyce, J . Amer.

Chem. Soc., 78. 2579 (1956);(b).W.G. Dauben, E.J. Blanz, J. Jiu and R.A. Micheli,

ibid.. 28, 3752 (1956).10. M. Cherest, H. Felkin and P. Tacheau, J. Chem. Soc.

Cominun.. 372 (1977).

- 204 -

CHAPTER SIX

The c o r r e l a t i o n o f Raman o p t i c a l a c t i v i t y

i n m e t h y l t o r s i o n modes w i t h m o l e c u l a r

m e c h a n ic s c a l c u l a t i o n s o f c h i r a l h i n d e r i n g

p o t e n t i a l s .

- 205 -

6.1 I n t r o d u c t i o n

A m o le c u le i s s a i d t o . b e o p t i c a l l y a c t i v e i f i t

r o t a t e s t h e p l a n e o f p o l a r i z a t i o n o f a l i n e a r l y p o l a r i z e d

l i g h t beam. T h i s i s a t t r i b u t e d t o t h e f a c t t h a t an

o p t i c a l l y a c t i v e medium h a s d i f f e r e n t r e f r a c t i v e i n d i c e s

f o r l e f t and r i g h t c i r c u l a r l y p o l a r i z e d l i g h t , t h a t i s

r i g h t and l e f t c i r c u l a r l y p o l a r i z e d l i g h t t r a v e l t h r o u g h

t h e medium a t d i f f e r e n t s p e e d s . The n e c e s s a r y and

s u f f i c i e n t c o n d i t i o n f o r a m o le c u le to show o p t i c a l

a c t i v i t y i s t h a t s u c h a m o le c u le s h o u ld n o t be s u p e r -

im p o s a b le w i t h i t s m i r r o r image i . e . when a m o le c u le h a s

no e l e m e n t s o f symmetry o r h a s o n l y a s i m p le a x i s o f

sym m etry . C o n v e r s e l y , a m o le c u le t h a t h a s a p l a n e o f

sym m etry , a c e n t r e o f symmetry o r an a l t e r n a t i n g a x i s o f

sym m etry , i s s u p e r i m p o s a b l e w i t h i t s m i r r o r image and

o p t i c a l l y i n a c t i v e .

S i n c e a b o u t 1955, c h i r o p t i c a l e f f e c t s ( e f f e c t s

upon l i g h t p a s s i n g t h r o u g h an o p t i c a l l y a c t i v e medium)

i . e . o p t i c a l r o t a t o r y d i s p e r s i o n (CRD) and c i r c u l a r

d i c h r o i s m (CD) have b e e n o f g r e a t v a l u e a s a p ro b e o f

c h i r a l i t y i n s t e r e o c h e m i c a l s t u d i e s o f m o le c u l e s c o n t a i n i n g

a chrom ophore w h ich a b s o r b s i n a r e a d i l y a c c e s s i b l e r e g i o n

o f t h e u l t r a - v i o l e t and w h ich h a s a low e x t i n c t i o n

c o e f f i c i e n t •

R e c e n t l y , c o m p le te v i b r a t i o n a l o p t i c a l a c t i v i t y

s p e c t r a o f c h i r a l m o le c u l e s have b e e n o b t a i n e d f rom a

- 206 -

s m a l l d i f f e r e n c e i n t h e i n t e n s i t y o f Raman s c a t t e r e d

l i g h t i n r i g h t and l e f t c i r c u l a r l y p o l a r i z e d i n c i d e n t 1 -5l i g h t . T h is t e c h n i q u e i s p o t e n t i a l l y more p o w e r f u l

t h a n ORD and CD, s i n c e e v e r y p a r t o f a m o le c u le

c o n t r i b u t e s t o a v i b r a t i o n a l s p e c t r u m , w h ich i s t h e r e f o r e

c o n s i d e r a b l y r i c h e r i n s t r u c t u r a l i n f o r m a t i o n t h a n t h e

v i s i b l e o r n e a r u l t r a v i o l e t p a r t o f an e l e c t r o n i c s p e c t r u m .

The r e l e v a n t e x p e r i m e n t a l q u a n t i t y i n m easu rem en ts o f

R a y l e i g h and Raman o p t i c a l a c t i v i t y i s t h e d i m e n s i o n l e s s

c i r c u l a r i n t e n s i t y d i f f e r e n t a l (CID).

A = ( I E - I L ) / ( I R + I L ) ( 1 ) .

R Lwhere I and I a r e t h e s c a t t e r e d i n t e n s i t i e s i n r i g h t

and l e f t c i r c u l a r l y p o l a r i z e d l i g h t .

The l a r g e s t Raman CIDf s a r e u s u a l l y found i n

m o le c u l e s w i t h r i g i d , t w i s t e d s k e l e t o n s e . g . oC - p i n e n e .

S in c e m i r r o r - i m a g e i s o m e r s g i v e i d e n t i c a l o p t i c a l

. ' a c t i v i t y s p e c t r a b u t w i t h r e v e r s e d s i g n s , as i l l u s t r a t e d

i n F i g u r e 1 , i t i s u s u a l l y b e s t t o r u n t h e two i so m e rs t o

have c o n f i d e n c e i n t h e m a r g i n a l e f f e c t s ; b u t f o r t h e

l a r g e r e f f e c t s , a s i n g l e i s o m e r s u f f i c e s .

A l th o u g h t h e i n t e r p r e t a t i o n o f d e p o l a r i z e d Raman

CID s p e c t r a i s s t i l l i n i t s i n f a n c y , i t h a s b e e n e s t a b

l i s h e d t h a t c h i r a l o r g a n i c m o le c u l e s c o n t a i n i n g m e th y l

g r o u p s o f t e n show l a r g e o p t i c a l a c t i v i t y i n b r o a d , weak

d e p o l a r i z e d Raman bands b e tw e e n 200 and 300 cm t h a t

o r i g i n a t e i n m e th y l t o r s i o n modes o f v i b r a t i o n ^ . I t h a s

- 2 0 7 -

F i g u r e l ( a ) : Part o f t h e Ptaman CID s p e c t r a o f t h e two enantiorr.ers o f t a r t a r i c a c i d *

OCO <0

ZT + ZT i a a1 2I - ZI1 A d A

SINnOO NOiOHd

- 208 -

.}■ (~k).: P ar t o f t h e Raman CID spectrum o f (-)c<- p h e n y l e t h y l am ine .

M U-iiSiNflOO NOlOHd

- 2 0 9 -

F i g u r e 1 (~b) : P a r t o f t h e Raman CIO spectrum o f ( + ) o ( - p h e n y l e t h a n o l •

- 210 -

"been s u g g e s t e d ^ t h a t t h i s Raman o p t i c a l a c t i v i t y c a n he

c o r r e l a t e d w i t h t h e c h i r a l p a r t o f t h e e l e c t r o n i c

p o t e n t i a l h a r r i e r h i n d e r i n g th e r e l a t i o n o f t h e m e th y l

g ro u p and as s u c h i t c o u ld p r o v i d e a n o v e l a p p ro a c h t o

c o n f o r m a t i o n a l a n a l y s i s and t o t h e a s s ig n m e n t o f a b s o l u t e

c o n f i g u r a t i o n o f c h i r a l m o l e c u l e s .

The d o m inan t p a r t o f t h e t h r e e - f o l d p o t e n t i a l

h a r r i e r t h a t h i n d e r s t h e r o t a t i o n o f t h e m e th y l g ro u p 8h a s t h e form

V(e) = i V (1 - c o s 30) (2 )

where V-. i s t h e h a r r i e r and 9 i s t h e t o r s i o n a n g l e w i t hj

t h r e e e q u i v a l e n t e q u i l i b r i u m v a l u e s 0 ° , 120° and 2 ^ 0 ° .

I n t h e p e r t u r b e d ha rm o n ic o s c i l l a t o r a p p r o x i m a t i o n

a p p r o a c h , i t i s s u g g e s t e d t h a t t h e b a r r i e r i n a c h i r a l3

m o le c u le c a n be w r i t t e n

V ( e ) = (1 - c o s 30) - V31 s i n 30 (3 )

■The s e co n d t e r m , V , s i n has t h e e f f e c t o f d i s p l a c i n gj

t h e p o s i t i o n s o f t h e maxima and minima t o one s i d e o r t h e

o t h e r o f t h e s y m m e t r i c a l p o s i t i o n ( F i g u r e 2 ) , so t h a t , i n

an e q u i l i b r i u m p o s i t i o n , t h e m e th y l g ro u p and th e

h i n d e r i n g g ro u p s now c o n s t i t u t e a c h i r a l s t r u c t u r e w i t h

a b s o l u t e c o n f i g u r a t i o n d e p e n d in g on t h e s e n s e o f

d i s p l a c e m e n t •

I n a d d i t i o n , u s i n g t h e e l e m e n t a r y t h e o r y o f t h e o n e

d i m e n s i o n a l h a rm o n ic o s c i l l a t o r , t h e b a r r i e r h e i g h t o u g h t

- 211 -

120 180 240

Zj-fture 2 : The g e n e r a t io n o f c h i r a l t h r e e f o l d p o t e n t i a l b a r r i e r s .

- 212 -

. , 8 t o be

V3 ( e r g ) = | TT 2 C 2 Vt 2 I r (!+)

— Awhere i s t h e t o r s i o n f r e q u e n c y i n cm and I r i s th e

r e d u c e d moment o f i n e r t i a f o r t h e i n t e r n a l r o t a t i o n .

T h i s f r e q u e n c y c o r r e l a t i o n i s n o t e x p e c te d t o be r e l i a b l e

b e c a u s e i t h a s b e e n assumed t h a t t h e m e th y l t o r s i o n d e e s

n o t c o u p le w i t h o t h e r modes, w h ic h i s p r o b a b l y n o t a

good a p p r o x i m a t i o n i n low -sym m etry m o l e c u l e s .

The f i r s t two t e rm s i n t h e s e r i e s e x p a n s i o n o f

t h e c h i r a l b a r r i e r (3 ) a r e

v(e) = 9/ h v3 92 i 3 v31 e ( 5 )

The p r e s e n c e o f t h e t e rm l i n e a r i n 9 means t h a t

( d v / £ e ) e = 0 so e = 0 i s no l o n g e r t h e e q u i l i b r i u m

p o s i t i o n : i n f a c t i f 9 = Oe i s now t h e e q u i l i b r i u m

p o s i t i o n , t h e n

V31 = + 3/ 2 v3 6 e (6)

-where i s t h e a m p l i t u d e o f t h e sym m etr ic p a r t o f t h eA

e l e c t r o n i c p o t e n t i a l b a r r i e r , i s t h e a m p l i t u d e o f

t h e ch ira l p a r t o f t h e e l e c t r o n i c p o t e n t i a l b a r r i e r and

Qe i s t h e d i s p l a c e m e n t o f t h e e q u i l i b r i u m p o s i t i o n o f

t h e m e th y l g ro u p from t h e sy m m etr ic p o s i t i o n . V ^ e

th u s g i v e s a m easure o f t h e c h i r a l p a r t o f t h e b a r r i e r

and i s t h u s p r o p o r t i o n a l t o t h e m e th y l t o r s i o n Raman

o p t i c a l a c t i v i t y .

At t h i s s t a g e , , m o l e c u l a r m e c h an ic s (MM) c a l c u l

a t i o n s were employed t o o b t a i n t h e c h i r a l p a r t s o f t h e

- 213 -

e l e c t r o n i c p o t e n t i a l b a r r i e r s h i n d e r i n g t h e m e th y l

t o r s i o n i n s e v e r a l m o l e c u l e s , w i t h t h e hope t h a t i t

would p ro v e p o s s i b l e t o o b t a i n a c o r r e l a t i o n b e tw e e n th e

o b s e r v e d m e th y l t o r s i o n Raman o p t i c a l a c t i v i t y and t h e

s i g n and m ag n i tu d e o f V^Ge s u p p l i e d by t h e MM c a l c u l

a t i o n s •

6 . 2 M o l e c u l a r Mechanics C a l c u l a t i o n s

The W h i t e - B o v i l l a l k a n e / a l k e n e f o r c e f i e l dQ A Q

(WBFF) and t h e m i n i m i s a t i o n p r o c e d u r e , w h ich v/ere

d i s c u s s e d i n C h a p t e r 2 , were u sed i n t h e MM c a l c u l a t i o n s .

S in c e ( + ) - 3 - m e t h y l c y c l o p e n t a n o n e and ( + ) - 3 - m e t h y l c y c l o -

hexanone c o n t a i n a c a r b o n y l g r o u p , i t was n e c e s s a r y to

r e p r e s e n t the^>C = 0 as a >C = CH^ i n t h e WBFF, w h ich i s11c o n s i d e r e d t o p r o v i d e a s u i t a b l e model • I n t h e c a s e

o f ( + ) - c a r v o n e , w h ich was i n c l u d e d i n t h e l a t e r s t a g e s o f1 2t h e c a l c u l a t i o n s , a c a r b o n y l f o r c e f i e l d w h ich was

b a s e d on t h e WBFF, was u s e d .

F o r e a c h o f t h e m o le c u l e s o f i n t e r e s t , a l l p o s s i b l e

c o n f o r m a t i o n s were b u i l t and m in im ised u n t i l t h e f i r s t

d e r i v a t i v e s o f t h e p o t e n t i a l e n e r g y w i t h r e s p e c t t o t h e“ 9c a r t e s i a n c o - o r d i n a t e s were l e s s t h a n 10 k c a l / m o l e to

e n s u r e a c r e d i b l e and r e p r o d u c i b l e minimum e n e r g y

g e o m e t r y . I n e v e r y m o le c u le e x c e p t ( + ) - 3 - m e t h y l c y c l o -

p e n t a n o n e , i t was fo u nd t h a t t h e r e was o n l y one m a jo r

c o n f o r m a t i o n p r e s e n t . F o r ( + ) - 3 - n i e t h y l c y c l o p e n t a n o n e ,

MM c a l c u l a t i o n s i n d i c a t e d t h a t two c o n f o r m a t i o n were

s i g n i f i c a n t l y p o p u l a t e d a t room t e m p e r a t u r e - 70% o f t h e

- 214 -

h a l f - c h a i r c o n f o r m a t i o n w i t h t h e m e th y l i n an e q u a t i o n a l

p o s i t i o n and 30% o f t h e h a l f - c h a i r w i t h t h e m e th y l i n an

a x i a l p o s i t i o n . The r e s u l t s f o r (+) - 3 - m e t h y l - c y c l o -

p e n t a n o n e i n T a b le 1 c o r r e s p o n d t o t h e B o l tz m a n n -w e ig h te d

mean o v e r t h e two c o n f o r m e r s •

E n e rg y mapping o f t h e m e th y l r o t a t i o n s t h r o u g h o o120 i n 10 s t e p s , i n a l l compounds, was a c c o m p l i s h e d

1 3by means o f t h e Wiberg-Boyd a l g o r i t h m . The r e s u l t i n g

p o t e n t i a l e n e r g y p r o f i l e V(9) f o r ( + ) - 3 - m e t h y l c y c l o -

hexanone i s p l o t t e d i n F i g u r e 3* In a d d i t i o n , t h e V(©) i s s u b t r a c t e d f rom t h e sym m etr ic p o t e n t i a l b a r r i e r

^ V ^ ( l - c o s3 © ) and th e r e s u l t a n t i s p l o t t e d as a f u n c t i o n

of 9 i n F i g u r e 3* I t c a n be s e e n t h a t t h e c h i r a l p a r t o f

t h e p o t e n t i a l b a r r i e r does in d e e d h ave t h e form s i n 3©>

as s u g g e s t e d by e q u a t i o n 3*

T a b le 1 l i s t s t h e c a l c u l a t e d d i s p l a c e m e n t 9e o f

th e e q u i l i b r i u m p o s i t i o n o f t h e m e th y l g ro u p s f rom t h e

’Symmetr ic p o s i t i o n i n t h e s e r i e s o f m o le c u l e s b e i n g

s t u d i e d , t o g e t h e r w i t h t h e c a l c u l a t e d h e i g h t o f t h e

c o m p le te d b a r r i e r w h ich we t a k e , f o r s i m p l i c i t y , t o be

V^. A p o s i t i v e 9e c o r r e s p o n d s t o a c l o c k w i s e d i s p l a c e m e n t

when v iew ed a lo n g t h e t h r e e f o l d a x i s o f t h e m e th y l g ro u p

to w a rd s t h e h i n d e r i n g s t r u c t u r e and t o n e g a t i v e Raman

o p t i c a l a c t i v i t y and v i c e v e r s a . I n t h e c a s e o f (+)-3- m e t h y l c y c l o p e n t a n o n e , i t i s t h e l e s s s t a b l e i s o m e r t h a t

shows t h e l a r g e s t c h i r a l p a r t o f t h e h i n d e r i n g p o t e n t i a l

and t h u s d o m in a t e s t h e m e th y l t o r s i o n Raman o p t i c a l

a c t i v i t y .

- 2 1 5 -

Zi&ure 1 : The c a l c u l a t e d p o t e n t i a l e n e r g y p r o f i l e V(©>) ( s o l i d l i n e )f o r r o t a t i o n o f t h e m e t h y l group i n ( + ) - 3 - m e t h y l - c y c l o h e x a n o n e . The minimum i s a t 5 8 .6 4 and t h e h a r r i e r h e i g h t V . , ( c a l c . ) i s 2 . 5 1 k c a l . / m o l e . The broken

. l i n e shows t h e r S s i d u a l -J -V^(calc . ) ( l + c o s 3 £ ) - V ( & ) .

- 216 -

« a • +

• a tn r r► M HX 3 2< o oC 2 Z z rum m z z

a a a2 C4 Cmto a a2 2 3 h i m m 2-4-4 O X I

<fl r» W0 X 0 ) "B WO X Z U C O XX o n 2 DH H z TO X -<

~ o oX -< -< ♦H O Oz to too o o

31 Xi m m m z xx-<

► z2 G

r- o z w z m m

TO TOX-<

a t a©Ww*- S w • • • • • •N U U U I O ^ >4 4k

fi S M N N • • • « •• o iu a iu i« t O N « * -

M l Ia »***y ® ut i w a o i o i • « •**,**

X —1o >to crTO toO TOcTOm •

O XX c*-« toX TO*►r»to CTX

TO!►

o XtoTO Xn TOc Oto XTO ►CD 2• w

O»■~ 4*>

X® XTO TOTOCD X

TO —«X

o -<>- TOTO

O oto cTO TO

<C•-*zCO

A >•(D

> 3BCD

« •TOX

n > hH X O TOH » z ca«<■ zw O o-4 O TO TO■< TO

-« OH 0O Cft>> TOr~ x

- 217 -

Figure 4 R LThe d e p o l a r i z e d Rojno.11 c i r c u l a r i n t e n s i t y sum (i^ + I xR L z z )

and d i f f e r e n c e ( i - I s p e c t r a o f n e a t ( + ) - 3 - m e t h y l -

c y c lo h exa n o n ep ^ oJ O N C O U N T St f - i i i M i

Lz *2• + +

O KJI'-CT'C D

TTTT TTTT

tftf 1 I I I 1------ 1------ 1------ T

- 218 -

Figure 5 • The depo lar ized Raman c i r c u l a r i n t e n s i t y cum and d i f f e r e n c esp ec tra o f neat ( + ) -3 -methylcyclopentanone.

- 219 -

Figure 6 : The depolarized. Raman c i r c u l a r i n t e n s i t y sura and d i f f e r e n c esp ec tra o f (- )-menthone d i l u t e d . w i t h about 30^ methanol.

- 220 -

Figure 7 : The depo lar ized Raman c i r c u l a r i n t e n s i t y sum and d i f f e r e n c esp ec tra o f ( - ) -menthol.

- 221 -

Figure 8 : The d epo lar ized Raman c i r c u l a r i n t e n s i t y sum and d i f f e r e n c esp ec tra o f neat ( - ) -m en th y l chloride*

- 222 -

Figure 9: The dep o la r ized Raman c i r c u l a r i n t e n s i t y sum and d i f f e r e n c esp ec tra o f neat ( - ) - i s o p u l e g o l .

- 223 -

Figure 1 0 : The d epo lar ized Raman c i r c u l a r i n t e n s i t y sum and d i f f e r e n c esp ectra o f neat ( - ) - l im o n e n e .

- 224 -

Figure 11: The depo lar ized Raman c i r c u l a r i n t e n s i t y sum and d i f f e r e n c esp ec tra o f neat (+)-carvone*

- 225 -

I n p r a c t i c e , h ow e v e r , i t has "been found t h a t t h e

o n l y method w h ich g i v e s a r e l i a b l e m easure o f 9e (and t h u s

t h e a b s o l u t e c o n f i g u r a t i o n o f c h i r a l m o l e c u l e s ) i s MM

c a l c u l a t i o n s as t h e y t a k e a c c o u n t o f a l l t h e s t e r i c

i n t e r a c t i o n s i n a m o le c u le and m in im ise t h e e n e r g y w i t h

r e s p e c t t o t h e g e o m e t r y . M oreover , MM c a l c u l a t i o n s can

a s s e s s t h e r e l a t i v e p r o p o r t i o n o f i s o m e rs t h a t compose an

e q u i l i b r i u m m ix t u r e o f a c h i r a l m o l e c u l e . M o le c u la r models

a r e i n e f f e c t i v e i n t h e d e r i v a t i o n o f t h e s e two f e a t u r e s

o f c h i r a l m o l e c u l e s .

6.3 Discussion

I t c a n be s e e n f rom T ab le 1 and f rom F i g u r e s 4 , 5 ,

7 ,1 0 and 1 1 , t h a t i n a l l m o le c u l e s s t u d i e d , t h e r e i s a

s t r o n g c o r r e l a t i o n b e tw e e n th e s i g n o f V^9e, w hich i s o b t a i n e d

f rom MM c a l c u l a t i o n s and t h e s i g n o f t h e c o r r e s p o n d i n g

m e th y l t o r s i o n CIDs. T here i s o n l y an a p p ro x im a te c o r r e

l a t i o n b e tw e e n t h e m a g n i tu d e s o f V^9e and t h e c o r r e s

p o n d in g m a g n i tu d e s o f t h e CIDs b u t t h i s i s d u e , i n p a r t , t o

t h e f a c t t h a t Raman i n t e n s i t i e s a r e n o t s t a n d a r d i z e d . As

a n t i c i p a t e d , t h e c o r r e l a t i o n b e tw e e n f r e q u e n c y o f t h e m e th y l

t o r s i o n band and th e b a r r i e r h e i g h t , Vy as im p l i e d by

e q u a t i o n 4 , i s n o t r e p r o d u c e d by t h e MM c a l c u l a t i o n s .

A l th o u g h t h e a s s ig n m e n t o f most Raman b a n d s i s

s t i l l t e n t a t i v e , t h e t o r s i o n modes o f m e t h y l g ro u p s

a t t a c h e d t o s a t u r a t e d r i n g sy s te m s c a n be a s s i g n e d w i t h a

c e r t a i n d e g r e e o f c o n f i d e n c e a s t h e y a r e u s u a l l y b ro a d

- 226 -

and weak , and o c c u r b e tw e e n 200 and 300 cm . I n t h e

Raman s p e c t r u m o f ( + ) - 3 - m e t h y l c y c lo h e x a n o n e ( F i g u r e k)A

t h e b r o a d , weak band a t a b o u t 260 cm p r o b a b l y o r i g i n a t e s

i n t h e m e th y l t o r s i o n . I n a s i m i l a r way, t h e band a t

290 cm i n ( + ) - 3 - m e t h y l - c y c l o p e n t a n o n e ( F i g u r e 5 ) i s

a s s i g n e d t o t h e m e th y l t o r s i o n mode. The f o r m e r band i s

l a r g e and n e g a t i v e , w h e reas t h e l a t t e r i s small and n e g a t i v e .

These r e l a t i v e s i g n s and m a g n i tu d e s a r e c o n s i s t e n t w i t h

t h e MM c a l c u l a t i o n s (T ab le 1 ) w h ich g iv e V^Ge o f t h e same

s i g n ( p o s i t i v e ) b u t much l a r g e r f o r t h e c y c lo h e x a n o n e t h a n

f o r t h e c y c l o p e n t a n o n e . The a s s ig n m e n t o f a h i g h e r

m e th y l t o r s i o n f r e q u e n c y i n t h e c y c l o p e n t a n o n e t h a n i n

t h e c y c l o h e x a n o n e i s s u p p o r t e d by t h e c a l c u l a t e d b a r r i e r

h e i g h t s , V^.

T h is t y p e o f c o r r e l a t i o n h a s b e e n e x t e n d e d ,

w i t h o u t c a l c u l a t i o n , t o some a d d i t i o n a l r e l a t e d m o l e c u l e s .

F o r e x a m p le , t h e m e th y l g ro up a t t a c h e d d i r e c t l y t o t h e

r i n g i n ( - ) - m e n t h o n e h a s a v e r y s i m i l a r s t e r e o c h e m i c a l

e n v i r o n m e n t and th e same a b s o l u t e c o n f i g u r a t i o n t o t h a t

i n ( + ) - 3 - m e t h y l - c y c l o h e x a n o n e . I t i s t h e r e f o r e p o s s i b l e

t o a s s i g n t h e l a r g e n e g a t i v e Raman o p t i c a l a c t i v i t y

a s s o c i a t e d w i t h t h e weak Raman band a t a b o u t 260 cm

i n ( - ) - m e n t h o n e ( F i g u r e 5) t o t h e m e th y l t o r s i o n mode.

MM c a l c u l a t i o n s on ( - ) -m e n th o l i n d i c a t e t h a t t h e

m e th y l g ro up a t t a c h e d t o t h e r i n g w i l l g i v e r i s e t o a

t o r s i o n mode w h ic h w i l l h ave l a r g e and p o s i t i v e Raman

o p t i c a l a c t i v i t y . These c a l c u l a t i o n s a r e i n a c c o rd w i t h

- 227 -

t h e e x p e r i m e n t a l o b s e r v a t i o n o f a weak, b ro ad Raman band

a t a b o u t 260 cm i n ( - ) -m e n th o l ( F i g u r e 7) w h ich shows

l a r g e p o s i t i v e o p t i c a l a c t i v i t y . S i m i l a r l y , t h e Raman

o p t i c a l a c t i v i t y s p e c t r u m o f ( - ) - m e n t h y l c h l o r i d e ( F i g u r e

8) shows band s h o u l d e r s a t a b o u t 260 and 230 cm"^ w h ich

show s m a l l p o s i t i v e o p t i c a l a c t i v i t y and th e Raman

o p t i c a l a c t i v i t y s p e c t ru m o f ( - ) - i s o p u l e g o l ( F i g u r e 9)_ - i

h a s a band a t a b o u t 260 cm which shows a p o s i t i v e

o p t i c a l a c t i v i t y . S in c e t h e s e t h r e e m o le c u le s have t h e

same a b s o l u t e c o n f i g u r a t i o n i n th e r e g i o n o f t h e m e th y l

g r o u p , i t seems t h a t t h e s e bands c a n be a s s i g n e d t o

t o r s i o n o f th e m e th y l g roup a t t a c h e d t o th e r i n g i n e a c h

m o l e c u l e •

The Raman o p t i c a l a c t i v i t y s p e c t r u m o f ( - ) -

l im o n e n e ( F i g u r e 10) shows a l a r g e n e g a t i v e e f f e c t_-l

a s s o c i a t e d w i t h a broad, weak Raman band a t 250 cm

I n a s m i l i l a r way, ( + ) - c a r v o n e ( F i g u r e 11) shows a l a r g e

• p o s i t i v e e f f e c t a s s o c i a t e d w i t h a Raman band o f s i m i l a r

shap e a t t h e same f r e q u e n c y . These e f f e c t s m igh t

o r i g i n a t e i n t o r s i o n s o f t h e i s o p r o p e n y l m e th y l g ro u p s

s i n c e t h e c o r r e s p o n d i n g p o t e n t i a l b a r r i e r s would be

v e r y s i m i l a r i n t h e two m o le c u l e s b u t w i t h o p p o s i t e

# c h i r a l p a r t s . T h is i s s u p p o r t e d by MM c a l c u l a t i o n on

' ( - ) - l i m o n e n e (T a b le 1) w h ich g i v e a p o s i t i v e V^9e

v a l u e (and i m p l i e s n e g a t i v e Raman o p t i c a l a c t i v i t y ) f o r

t h e i s o p r o p e n y l m e th y l g ro u p and a n e g a t i v e and s m a l l e r

V^9e v a l u e (and t h e r e f o r e p o s i t i v e Raman o p t i c a l

a c t i v i t y ) f o r t h e m e th y l g ro u p a t t a c h e d d i r e c t l y t o th e

r i n g . The t o r s i o n o f t h e l a t t e r m e th y l g ro u p may t h e r e

f o r e g i v e r i s e t o t h e Raman ban ds o f p o s i t i v e o p t i c a l

- 228 -

-1a c t i v i t y a t a b o u t 200 era o r b e tw een a b o u t 100 and 180

cm • MM c a l c u l a t i o n s on ( + ) - c a r v o n e g iv e a n e g a t i v e

V^9e v a l u e f o r t h e i s o p r o p e n y l m e thy l g roup and t h u s

im ply p o s i t i v e Raman o p t i c a l a c t i v i t y w h ich a g r e e s w i t h

t h e a s s i g n e d Raman band a t a b o u t 250 cm

An i l l u s t r a t i o n , w h ich d e m o n s t r a t e s t h e r e l i a b i l i t y

o f c o r r e l a t i o n s o f a b s o l u t e c o n f i g u r a t i o n s o b t a i n e d from

Raman o p t i c a l a c t i v i t y d a t a , i s a v a i l a b l e . The s i m i l a r i t y

o f a number o f Raman o p t i c a l a c t i v i t y f e a t u r e s o f m en tho l

and m en th y l c h l o r i d e , i n F i g u r e s 7 and 8 , i m p l i e d t h a t

t h e two c h i r a l m o le c u l e s sh o u ld have th e same a b s o l u t e

c o n f i g u r a t i o n . The m en th o l e n a n t i o m e r was known, w i t h

c e r t a i n t y , t o be t h e ( - ) - i s o m e r . R e f e r e n c e 1U, h o w e v e r ,

w ro n g ly a s s i g n e d th e m en th y l c h l o r i d e m o le c u le u sed as

t h e ( + ) - i s o m e r . T h is i n c o r r e c t a s s ig n m e n t was s u b s e q u e n t l y

found t o be due t o a t y p o g r a p h i c a l e r r o r and t h e i so m er

o f m en th y l c h l o r i d e u sed i n t h e Raman s t u d i e s was i n f a c t

t h e ( - ) - i s o m e r as t h e Raman o p t i c a l a c t i v i t y s p e c t r u m

s u g g e s t e d .

- 229 -

6 References

1 • L.D. Barron, M.P. Bogaard and A.D. Buckingham,J. Amer. Chem. Soc., 95, 603(1973)

2. L.D. Barron and A.D. Buckingham, Ann. Rev.Ph.ys .Chem.. 26, 381 (1975)-

3* L.D. Barron, Advances in Infra red and RamanSpectroscopy. (Edited by R.J.H. Clark and R.E. Hester), Volume 3, Heyden, London, in the press.

1+. W. Hug, S. Kint, G.F. Bailey, and J.R. Scherer,J. Amer. Chem. Soc.. 97 > 5589 (1975)

5. M. Diem, M.J. Diem, B.A. Hudgens, J.L. Fry andD.F. Burow, J.C.S. Chem. Comm.. 1028 (1976).

6. L.D. Barron, Nature, 255# U58 (1975)7* L.D. Barron, M.J. Bovill and D.N.J. White,

J.C.S. Perkin II, in preparation (1977)8. C.H. Townes and A.L. Schawlow, Microwave Spectroscopy.

McGraw-Hill, New York, 19559. D.N.J. White and M.J. Bovill, J.C.S. Perkin II.

in the press (1977)10. D.N.J. White, Computers and Chemistry, in the press

(1977)11. D.P. DeTar, J. Amer. Chem. Soc.. 96. 1254 (1974)12. D.N.J. White and H.P. Flitman, to be published.13* K.B. Wiberg and R.H. Boyd, J. Amer. Chem. Soc..

8426 (1972)14* W. KLyne and J. Buckingham, Atlas of Stereochemistry.

Chapman and Hall, London, 1974*

CHAPTER SEVEN

Some a s p e c t s o f c r y s t a l l o g r a p h y .

- 231 -

7 . 1 . H i s t o r i c a l

In 1912, Max von Laue p r e d i c t e d t h a t t h e a r r a y o f atoms

i n t h e l a t t i c e s t r u c t u r e o f a c r y s t a l c o u l d a c t a s a t h r e e -

d i m e n s i o n a l d i f f r a c t i o n g r a t i n g f o r X - r a y s , wh ich a r e

e l e c t r o m a g n e t i c waves h a v in g w a v e l e n g th s i n t h e r a n g e o f o

0 . 5 - 2 . 5 A. In t h e e x p e r i m e n t s o f F r i e d r i c h and K n ip p in g ,

a c r y s t a l o f z i n c b len d ew as ex p o sed t o X - r a y s and a

p a t t e r n c o n s i s t i n g o f a c e n t r a l image s u r r o u n d e d by s p o t s

was formed on a p h o t o g r a p h i c p l a t e . These d i f f r a c t i o n

p h o t o g r a p h s l e n t d e f i n i t e s u p p o r t t o t h e view t h a t X - r a y s

c o n s i s t e d o f waves a s w e l l a s s u p p o r t i n g t h e h y p o t h e s i s o f

t h e l a t t i c e s t r u c t u r e o f c r y s t a l s . W.H. Bragg and h i s s o n ,

W.L. Bragg assumed t h a t t h e X - r a y s w ere ’r e f l e c t e d ' from

f a m i l i e s o f r e g u l a r l y s p a c e d p l a n e s t h r o u g h o u t t h e c r y s t a l s

and t h e famous Bragg Law was d e r i v e d :

n X = 2d s i n 9 ;

where n i s t h e o r d e r o f t h e s p e c t r u m , X i s t h e w a v e le n g th

o f t h e i n c i d e n t X - r a y s , 9 i s t h e a n g l e o f i n c i d e n c e be tw een

t h e r a y s and t h e p l a n e and d i s t h e d i s t a n c e be tw een

a d j a c e n t l a y e r s o f a tom s i n t h e c r y s t a l . A p o w e r f u l and

p r e c i s e t o o l had now been p u t i n t h e hands o f s c i e n t i s t s

i n t e r e s t e d i n t h e s t r u c t u r e o f m a t t e r .

X - r a y s a r e so p e n e t r a t i n g t h a t t h e y c a n n o t be f o c u s e d

by any m a t e r i a l . To c i r c u m v e n t t h i s p ro b le m , v a r i o u s

c a l c u l a t i o n s , which w i l l be d i s c u s s e d i n s u b s e q u e n t s e c t i o n s ,

a r e s u b s t i t u t e d f o r t h e l e n s e s . From t h e i n t e n s i t i e s

o f t h e t h r e e - d i m e n s i o n a l a r r a y o f r e f l e c t i o n s c o l l e c t e d

- 232 -

from a g iv e n s i n g l e c r y s t a l e i t h e r p h o t o g r a p h i c a l l y o r from

an a u t o m a t i c d i f f r a c t o m e t e r , which h a s o n ly been in u se f o r

a b o u t f i f t e e n y e a r s , i t i s p o s s i b l e t o o b t a i n an eLect ron

d e n s i t y d i s t r i b u t i o n i n t h e c r y s t a l w h ich , i n t u r n , p r o v i d e s

d i r e c t images o f t h e a tom s i n t h e u n i t c e l l . X -ray

a n a l y s e s o f h u n d r e d s o f c r y s t a l s t r u c t u r e s have l e d t o

d e t a i l e d knowledge o f t h e g e o m e t r i c a l p r o p e r t i e s o f d i f f e r e n t

g ro u p s o f a to m s . The r e s u l t i n g s t e r e o c h e m i c a l p r i n c i p l e s

i n c o n j u n c t i o n w i t h t h e complex m a t h e m a t i c a l t e c h n i q u e s o f

modern c r y s t a l l o g r a p h y and t h e a d v e n t o f t h e d a t a - p r o c e s s i n g

c o m p u te r s h ave been o f g r e a t h e l p i n t h e d e t e r m i n a t i o n o f

t h e m o l e c u l a r a r c h i t e c t u r e o f c o m p l i c a t e d b i o l o g i c a l m o l e c u l e s ,

which a r e composed o f s m a l l b a s i c u n i t s , e . g . p r o t e i n s .

7 . 2 . C o r r e c t i o n s t o t h e m easu red i n t e n s i t i e s

B e f o re p r o c e e d i n g t o t h e a c t u a l s t r u c t u r e a n a l y s i s , i t

i s v i t a l t h a t c e r t a i n c o r r e c t i o n s , which a l l o w f o r v a r i o u s

g e o m e t r i c a l and p h y s i c a l f a c t o r s , be a p p l i e d t o t h e

i n t e n s i t y d a t a from t h e c r y s t a l .

(a) L o r e n t z - P o l a r i s a t i o n

L o r e n tz

D i f f r a c t i o n c o r r e s p o n d i n g t o a p a r t i c u l a r r e c i p r o c a l

l a t t i c e p o i n t h k l o c c u r s whenever t h a t p o i n t i n t e r s e c t s

t h e Ewald s p h e r e , b u t i n v iew o f t h e f a c t t h a t e a c h r e c i p r o c a l

l a t t i c e p o i n t i s sm eared o u t , t h e i n t e r s e c t i o n o f any g i v e n

p o i n t w i t h t h e Ewald s p h e r e i s n o t a p r e c i s e e v e n t o c c u r r i n g

a t t h e s i n g l e i n s t a n t when t h e Bragg c o n d i t i o n i s e x a c t l y

s a t i s f i e d . The t im e r e q u i r e d f o r a r e c i p r o c a l l a t t i c e

p o i n t t o p a s s t h r o u g h t h e s p h e r e o f r e f l e c t i o n d ep en ds on

- 233 -

b o th t h e Bragg a n g l e , 9 and on t h e t e c h n i q u e u s e d t o m easu re

t h e i n t e n s i t i e s . For t h e e q u i - i n c l i n a t i o n W eis sen b e rg

t e c h n i q u e , t h e L o r e n t z f a c t o r , L i s g i v e n by

L = r , ( i )2 2 2 s i n 29 ( s i n 9 - s i n ju)

where ja i s t h e e q u i - i n c l i n a t i o n s e t t i n g a n g l e . For d a t a

c o l l e c t e d on a f o u r c i r c l e d i f f r a c t o m e t e r , L i s g iv e n by

L = — ±----- . (2)s i n 29

P o l a r i s a t i o n

Most m ethods o f d a t a c o l l e c t i o n use an i n c i d e n t X -ray

beam which i s u n p o l a r i s e d . The em e rg en t r a d i a t i o n i s ,

however , p a r t i a l l y p o l a r i s e d b e c a u s e e l e c t r i c v e c t o r s which

a r e p a r a l l e l t o t h e s u r f a c e o f t h e r e f l e c t i n g p l a n e a r e

r e f l e c t e d more e f f i c i e n t l y t h a n e l e c t r i c v e c t o r s p e r p e n d i

c u l a r t o t h e a f o r e m e n t i o n e d p l a n e . The i n t e n s i t y o f t h e

r e f l e c t e d beam can be c o r r e c t e d by t h e p o l a r i s a t i o n f a c t o r ,

p , w hich i s i n d e p e n d e n t o f t h e mode o f d a t a c o l l e c t i o n

employed and which i s g iv e n by

p = £ (1 + c o s 2 29) . (3)

The combined L o r e n t z - P o l a r i s a t i o n f a c t o r , Lp, f o r a

f o u r c i r c l e d i f f r a c t o m e t e r may t h e n be w r i t t e n a s f o l l o w s :

2_ 1 + c o s 29 (ANLp = -------------------- (4)

2 s i n 29

(b) C o u n t in g Loss

In r e c e n t y e a r s , p r o p o r t i o n a l c o u n t e r s and s c i n t i l l a

t i o n c o u n t e r s have been u s e d i n t h e m easurem ent o f X - ray

- 234 -

i n t e n s i t i e s . I t h a s been p o i n t e d o u t t h a t , b e c a u s e o f t h e

dead t im e o f t h e c o u n t e r t u b e s , which i s a b o u t 0 . 2 5 j u s e c ,

t h e l i n e a r i t y o f c o u n t i n g r a t e w i t h i n t e n s i t y i s l i m i t e d t o r e g i o n s

below a c e r t a i n c o u n t i n g r a t e . For i n t e n s e r e f l e c t i o n s ,

i . e . g r e a t e r t h a n a b o u t 1 0 ,0 00 t o 2 0 ,0 0 0 c o u n t s / s e c , t h e

c o u n t i n g r a t e i s beyond t h e l i n e a r i t y l i m i t , and s o , i f

f u l l u s e i s t o be made o f t h e i n h e r e n t a c c u r a c y o f t h e

d i f f r a c t o m e t e r , t h i s c o u n t e r s a t u r a t i o n e f f e c t must be t a k e n

i n t o c o n s i d e r a t i o n and t h i s i s u s u a l l y a c c o m p l i s h e d by

r e d u c i n g t h e i n t e n s i t y o f t h e d i r e c t beam by i n t e r p o s i n g a

s u i t a b l e number o f c a l i b r a t e d f o i l s o r , more commonly, by

l o w e r in g t h e v o l t a g e . A number o f low o r d e r r e f l e c t i o n s

a r e t h e n r e m e a s u r e d an d , f rom an a n a l y s i s o f t h e c o u n t s o f

th e weaker low o r d e r r e f l e c t i o n s a t t h e r e d u c e d and no rm al

beam i n t e n s i t i e s , i t i s p o s s i b l e t o d e r i v e a c o n v e r s i o n

f a c t o r which may t h e n be a p p l i e d t o t h e more i n t e n s e

r e f l e c t i o n s .

The r e l a t i o n s h i p be tw een t h e i n t e n s i t y o f one r e f l e c t i o n

a t no rm al beam i n t e n s i t y , I , and t h e i n t e n s i t y o f t h e same

r e f l e c t i o n a t r e d u c e d beam i n t e n s i t y , J . i s g i v e n by

J = P XI + P2 I 2 , (5)

where P , , P a r e c o n s t a n t s t o be d e t e r m i n e d . Each 1 2

o b s e r v a t i o n J h a s an a s s i g n e d w e i g h t , W, which i s p r o p o r t i o n a l

to t h e i n v e r s e o f t h e s q u a r e o f t h e s t a n d a r d d e v i a t i o n o f

J, i . e .

w = i / ( a j )2

The residual A is the difference between the intensities for a given reflection under the two sets of conditions such

- 235 -

t h a t

A = j - ( p 1 i + p 2 i 2 ) . (6)

oBy t h e method o f l e a s t s q u a r e s , M i s s e t e q u a l t o X W A and t h e c o n d i t i o n s f o r M t o be a minimum a r e g i v e n by

6 M = &_M _ Q (7)a Pi ap2S o l u t i o n o f t h e r e s u l t i n g s i m u l t a n e o u s e q u a t i o n s p r o v i d e s

t h e v a l u e s o f and which can be r e s u b s t i t u t e d i n t o t h e

a p p r o p r i a t e e q u a t i o n , t o g e t h e r w i t h t h e c o u n t o f a s t r o n g

r e f l e c t i o n a t r e d u c e d beam i n t e n s i t y , J , t h u s making i t

p o s s i b l e t o o b t a i n c o r r e c t e d I v a l u e s f o r s t r o n g r e f l e c t i o n s .

7 .3 S t r u c t u r e F a c t o r s

The p r o p e r m easu re o f t h e s c a t t e r i n g power p e r u n i t c e l l

i s g i v e n by a complex q u a n t i t y known a s t h e s t r u c t u r e f a c t o r ,

r e p r e s e n t e d by F. The i n t e n s i t y I (h k l ) o f e ac h d i f f r a c t e d

beam i s p r o p o r t i o n a l t o t h e s q u a r e o f i t s a m p l i t u d e , i . e .

I ( h k l )c x f | F ( h k l ) l ^ _ where IF ( h k l ) I , i s t h e s o - c a l l e dobs obs" o b s e r v e d " s t r u c t u r e f a c t o r a m p l i t u d e and where F ( h k l )

r e p r e s e n t s t h e r a d i a t i o n s c a t t e r e d i n t h e o r d e r ( h k l ) by t h e

c r y s t a l . Each o f t h e d i f f r a c t e d beams a l s o h a s a p h a s e

(h k l ) a s s o c i a t e d w i t h i t which e x p r e s s e s t h e e x t e n t t o

which t h e d i f f r a c t e d beam i s i n p h a s e w i t h o t h e r d i f f r a c t e d

beams. I f t h e p o s i t i o n s o f t h e a tom s i n t h e u n i t c e l l a r e

known, b o t h t h e " c a l c u l a t e d " a m p l i t u d e I F ( h k l ) I c a l c and

" c a l c u l a t e d " p h a s e (h k l ) f o r e a c h r e f l e c t i o n c an be o b t a i n e d

from t h e s t r u c t u r e f a c t o r e q u a t i o n ,

- 2 3 6 -

nF ( h k l ) = X f exp 2 TT i ( h x . + k y . + l z . ) (8)J J J J

= A (h k l ) + i B (h k l ) ,

nwhere A (h k l ) = T f . c o s 2 TT (hx . + ky . + l z ) :

J J J jj = l

nB (h k l ) =T f . s i n 2 TT (hx . +ky . = l z . ) ;

J J J Jj = l

and i i s t h e im a g in a r y number V - 1 . The summation i s o v e r

a l l n a toms i n t h e u n i t c e l l , w i t h x . , y . z . r e p r e s e n t i n gJ <3 Jt h e f r a c t i o n a l c o o r d i n a t e s o f t h e j*'*1 atom. From t h e

s t r u c t u r e f a c t o r e q u a t i o n , i t f o l l o w s t h a t

| F (h k l ) | = N/ A ( h k l ) 2 + B ( h k l ) 2

and t a n oi ( h k l ) = B (h k l ) / A ( h k l ) . (9)

The t e rm f . i n e q u a t i o n (8) r e p r e s e n t s t h e s c a t t e r i n g power J

t ho f t h e j a tom and i s known f o r an a tom a t r e s t . At

z e r o a n g l e s c a t t e r i n g , f o r which a l l e l e c t r o n s s c a t t e r i n

p h a s e , f^ i s e q u a l t o t h e t o t a l number o f e l e c t r o n s i n t h e

atom ( v i z . t h e a to m ic n u m b e r ) . With i n c r e a s i n g d i f f r a c t i o n

a n g l e 0 , f . d e c r e a s e s r a p i d l y , i n t h e o r d e r o f s i n 9 / A J

due t o a g r e a t e r p h a s e d i f f e r e n c e be tw een t h e waves s c a t t e r e d

by t h e e l c t r o n c l o u d o f t h e a tom.

Atoms i n c r y s t a l s a r e v i b r a t i n g and t h i s r e s u l t s i n

t h e e l e c t r o n c l o u d b e in g s p r e a d o v e r a w id e r r e g i o n o f s p a c e .

- 2 3 7 -

A llow ance must be made f o r t h i s e f f e c t i n work o f even

m o d e ra te a c c u r a c y and t h i s can be a c c o m p l i s h e d by e f f e c t i v e l y

d i m i n i s h i n g f , t h e s c a t t e r i n g power o f t h e s t a t i o n a r y a tom.

Thus f o r i s o t r o p i c v i b r a t i o n , t h e s c a t t e r i n g f a c t o r f^ i s

g iv e n by

f j = f Q exp -B ( s i n 2 Q) / X 2J , (10)

2 2where B = 8TT U , t h e D ebye-W al le r f a c t o r o r t h e i s o t r o p i c

t h e r m a l p a r a m e t e r . I t u s u a l l y l i e s i n t h e r a n g e o 2

2 - 4 A f o r c a r b o n and oxygen a tom s i n a t y p i c a l

o r g a n i c c r y s t a l and i s t e m p e r a t u r e d e p e n d e n t .

— 2U = t h e mean s q u a r e a m p l i t u d e o f v i b r a t i o n p e r p e n d i

c u l a r t o t h e r e f l e c t i n g p l a n e and l i e s i n t h e r a n g e o^

0 . 1 - 0 . 0 1 A .

In g e n e r a l , how ever , a toms v i b r a t e w i t h d i f f e r e n t a m p l i t u d e s

i n d i f f e r e n t d i r e c t i o n s and a r e b e s t r e p r e s e n t e d by an

e l l i p s o i d o f e l e c t r o n d e n s i t y , r a t h e r t h a n a s p h e r e . To

d e s c r i b e su c h an e l l i p s o i d , s i x p a r a m e t e r s a r e r e q u i r e d -

t h r e e g i v e t h e r a d i i a l o n g i t s p r i n c i p a l a x e s and t h r e e more

t o d e s c r i b e t h e o r i e n t a t i o n o f t h e e l l i p s o i d i n s p a c e . Thus,

f o r a n i s o t r o p i c v i b r a t i o n ,

* * I /t> *2 *2 D . 2 . *2 , D , 2 * 2 + 2B, Qh l a * c *f j = V xp b ( 11 a 22 k b + B33 1 c 13

+ 2B k lb * c * + 2B12hka*b*) / 4 1 > ( U )2 3

where R 3 * *i j = t h e a n i s o t r o p i c t h e r m a l p a r a m e t e r ; a , b , c =

t h e l e n g t h s o f r e c i p r o c a l c e l l e d g e s .

A l t e r n a t i v e l y , e q u a t i o n (11) may be r e w r i t t e n i n t h e more

- 238 -

commonly u se d form:

f j = f Qexp [-2TT2 (Ul: lh 2a * 2 +U22k2 b*2 + U3g l 2 c * 2 + 2 u 13h la * c * +

2U23k lb * c * + ^U^2^ka*b*)_J ( 12 )

2 2where U. . ~ U. . = B. ./8TT , t h e t h e r m a l p a r a m e t e r s e x p r e s s e dJ %J J

i n t e r m s o f m e a n - s q u a re a m p l i t u d e s o f v i b r a t i o n s .

7 .4 S t r u c t u r e f a c t o r s and t h e e l e c t r o n d e n s i t y d i s t r i b u t i o n

S in c e t h e e l e c t r o n d e n s i t y i n a c r y s t a l v a r i e s

c o n t i n u o u s l y and p e r i o d i c a l l y i n t h r e e - d i m e n s i o n a l s p a c e ,

t h e e l e c t r o n d e n s i t y can be e x p r e s s e d a s t h e f o l l o w i n g t h r e e -

d i m e n s i o n a l F o u r i e r s e r i e s :

p (xyz) = V ^ X jE X F ( h k l ) exp Q-2 TT i (hx + ky + lz)Jh k l

w here p (xyz) i s t h e e l e c t r o n d e n s i t y a t t h e p o i n t w i t h

f r a c t i o n a l c o o r d i n a t e s x , y , z i n t h e u n i t c e l l o f Volume V.

The t r i p l e summation i s t a k e n o v e r a l l d i f f r a c t e d beams.

I t can be shown t h a t

F ( h k l ) = F ( h k l ) exp 2TTi cX ( h k l ) . (14)

Using e q u a t i o n ( 1 4 ) , i t i s now p o s s i b l e t o s u b s t i t u t e f o r

F (h k l ) i n e q u a t i o n (13) and t h u s o b t a i n a more u s e f u l form

of t h e F o u r i e r e x p r e s s i o n ,

p ( x y z ) = V_1I I X I F ( h k l ) | exp C - 2 TTi (hx + ky + h k l

l z - < X ( h k l 7 | ( 1 5 )

- 239 -

I f b o th t h e a m p l i t u d e F ( h k l ) and t h e p h a s e oC (h k l )

o f e ac h d i f f r a c t e d beam a r e known, t h e e l e c t r o n d e n s i t y

w i t h i n t h e u n i t c e l l o f t h e c r y s t a l can be c a l c u l a t e d

d i r e c t l y f rom e q u a t i o n (15) a t f r a c t i o n a l i n t e r v a l s a l o n g

e ach o f t h e c e l l e d g e s t o g i v e a t h r e e - d i m e n s i o n a l g r i d o f

e l e c t r o n d e n s i t y p o i n t s and t h e p o s i t i o n s o f t h e a tom s in

t h e u n i t c e l l may be deduced . E q u a t io n (15) s e p a r a t e s t h e

F ( h k l ) f s which can be o b t a i n e d e x p e r i m e n t a l l y from t h e

i n t e n s i t y d a t a f rom t h e p h a s e o C (hk l ) w h ich , u n f o r t u n a t e l y ,

c a n n o t be d e r i v e d from t h e e x p e r i m e n t a l d a t a and which must

t h e r e f o r e be d e r i v e d by some o t h e r s t r a t e g y , e . g . by t r i a l -

a n d - e r r o r , t h e h e a v y -a to m method, i som orphous r e p l a c e m e n t ,

P a t t e r s o n m ethods o r D i r e c t m ethods . T h i s s e a r c h f o r a

s e l f - c o n s i s t e n t s e t o f p h a s e s i s te rm e d t h e ’p h a s e p r o b le m '

o f c r y s t a l l o g r a p h y .

7 .5 D i r e c t Methods o f Ph ase D e t e r m i n a t i o n

D i r e c t m ethods s e e k t o d e t e r m i n e p h a s e i n f o r m a t i o n

o b j e c t i v e l y by e x a m i n a t i o n o f s t r u c t u r e f a c t o r m a g n i tu d e s

d e r i v e d f rom t h e s t u d y o f a s i n g l e c r y s t a l , w i t h o u t r e f e r e n c e

t o c h e m ic a l knowledge o r i so m orph o us d e r i v a t i v e s . S t a r t i n g

from t h e f u n d a m e n ta l p h y s i c a l f a c t t h a t t h e e l e c t r o n d e n s i t y

w i t h i n t h e u n i t c e l l can n e v e r be n e g a t i v e , a number o f

i n e q u a l i t i e s , e q u a l i t i e s and p r o b a b i l i t i e s may be d e r i v e d

which , i n f a v o u r a b l e c a s e s , a l l o w p h a s e s t o be d e t e r m i n e d .

D i r e c t m ethods i n v o l v e t h e c o m p a r i s o n o f t h e s t r u c t u r e

f a c t o r m a g n i t u d e s , and i n o r d e r t o g e n e r a l i s e t h e m a t h e m a t i c s ,

i t i s n e c e s s a r y t o d e f i n e t h e U n i t a r y S t r u c t u r e F a c t o r U (h ) ,

i n d i r e c t m ethod v e c t o r n o t a t i o n , a s

- 240 -

U( h ) =_ F(h)

NI f Jj = l

( 1 6 )

where t h e summation i s c a r r i e d o u t o v e r t h e N a tom s i n t h e

c e l l and f . i s t h e s c a t t e r i n g f a c t o r f o r atom j c o m p e n s a t in gJ —•f o r b o th t h e t a f a l l - o f f and t h e r m a l e f f e c t s .

S in c e ^

F (h ) = Z f . exp 2 H i h . r (17)J

t h e n | F ( h ) | ^ J f .

and so |u (h ) | ^ 1.

The maximum v a l u e o f 1 f o r U(h) o c c u r s when a l l a tom s s c a t t e r

i n p h a s e and U(h) ’ s o f 1 a r e r a r e l y i f e v e r fo un d . By

d e f i n i n g t h e U n i t a r y Atomic S c a t t e r i n g F a c t o r n . , i n t h eJ

f o l l o w i n g m a n n e r :f .

Jn i = N , (18)

I f . j = i J

i t i s p o s s i b l e t o w r i t e

U(h) = X n * exP 2 TT i (19)” ' Jj = l

I f a l l t h e a tom s i n t h e u n i t c e l l a r e a l i k e , n^ t h e n becomes

e q u a l t o t h e r e c i p r o c a l o f t h e number o f a tom s i n t h e u n i t

c e l l , N, i . e .

1n. - — *

and i t c a n be e a s i l y d e d u c e d t h a t , i n a r e a s o n a b l y s i z e d

- 241 -

o r g a n i c m o le c u l e , t h e r e may be so few l a r g e U(h)

among t h e d a t a t h a t t h e r e w i l l n o t be enough c o n s t r a i n t s

t o d e t e r m i n e t h e s t r u c t u r e . As a r e s u l t o f t h i s , K a r l e

and Hauptman f o r m u l a t e d a n o r m a l i s e d s t r u c t u r e f a c t o r ,

E ( h ) , which i s g iv e n by

2 F(h)E(h) = n 2 ( 2 0 )

e l f ii = l

where C i s an i n t e g e r , which i s n o r m a l ly u n i t y and which

c o r r e c t s f o r s p a c e g roup e x t i n c t i o n s . The a d v a n t a g e o fI I 2E(h) i s t h a t t h e a v e r a g e v a l u e o f |E ( h ) | i s u n i t y , and i t

h a s been shown t h a t t h e u s e o f E(h) i s t a n t a m o u n t t o r e g a r d

in g t h e a tom s w i t h i n a s t r u c t u r e a s p o i n t s which do n o t

s u f f e r t h e r m a l m o t io n .

I n e q u a l i t i e s

The f i r s t d i r e c t m ethods t o be i n t r o d u c e d were t h e

H a r k e r - K a s p e r i n e q u a l i t i e s , f rom w hich i t i s p o s s i b l e t o

o b t a i n c e r t a i n p h a s e i n f o r m a t i o n . In a c r y s t a l w h ich h a s

a c e n t r e o f symmetry , e q u a t i o n (19) may be r e w r i t t e n i n t h e

form N/2

U(h) = 2 X n - c o s 2 IT i h . r . (21)Jj - i

Using C a u c h y ' s i n e q u a l i t y , which s t a t e s t h a t

iz .Ai2 i2)'3 3 3

e q u a t i o n (21) t h e n becomes

U2 (h) ^ i f l + U (2h7j (22)

- 242 -

R e l a t i o n (22) r e l a t e s i n f o r m a t i o n c o n c e r n i n g t h e r e c i p r o c a l

l a t t i c e s i t e h t o t h a t f o r t h e s i t e 2h and s i n c e , b o th2t h e m a g n i tu d e and s i g n (+) o f U (h) a r e known, t h e s i g n o f

U(2h) may be unam b ig u ou s ly deduced i f t h e i n t e n s i t y a t h i s

s t r o n g enough .

In g e n e r a l , t h e y g i v e unambiguous i n f o r m a t i o n o n ly i f

t h e r e a r e a l a r g e number o f i n t e n s i t y maxima a s s o c i a t e d w i t h

u n i t a r y s t r u c t u r e f a c t o r s o f v a l u e o f a b o u t one h a l f o r

g r e a t e r . As m o l e c u l a r s i z e i n c r e a s e s , t h e p r o b a b i l i t y o f

any g e n e r a l U(h) b e i n g g r e a t e r t h a n one h a l f d e c r e a s e s , and

so t h i s r e d u c e s t h e a p p l i c a b i l i t y o f i n e q u a l i t i e s t o l a r g e r

s t r u c t u r e s . A l th o u g h d i f f e r e n t i n e q u a l i t i e s may be g e n e r a t e d

f o r a l l t h e 230 s p a c e g r o u p s , t h e g e n e r a l u se o f i n e q u a l i t i e s

i s r e s t r i c t e d t o c e n t r o s y m m e t r i c c r y s t a l s . The r e s o l u t i o n

o f t h e p o s i t i v e / n e g a t i v e a m b i g u i ty i s a f a r s i m p l e r p ro b le m

t h a n t h e i d e n t i f i c a t i o n o f a p h a s e a n g l e anywhere be tw een

0 and 2 , and no g e n e r a l i n e q u a l i t i e s f o r t h e n o n c e n t r o -

sym m etr ic c a s e have been found t o be u s e f u l .

E q u a l i t i e s

In 1952, c e r t a i n e q u a l i t i e s , which g i v e more s p e c i f i c

i n f o r m a t i o n t h a n do t h e i n e q u a l i t i e s , w ere i n t r o d u c e d . S a y re

d e r i v e d t h e f o l l o w i n g r e l a t i o n s h i p be tw een t h e s t r u c t u r e

f a c t o r s o f t h r e e r e f l e c t i o n s r e p r e s e n t e d a s h , k , h - k :

F ( h ) = 0 ( h ) Y. F C O . F C h - k ) , ( 2 3 )

where 0 ( h ) i s a c a l c u l a b l e s c a l i n g f a c t o r .

By c o n s i d e r i n g a s t r u c t u r e o f i d e n t i c a l r e s o l v e d a tom s ,

Sayre derived the following ’ Sigma two' relationships,

- 243 -

be tw een t h e s i g n s o f t h r e e r e f l e c t i o n s :

S(h) = S(k) . S (h - k) (24)

where S i n d i c a t e s ’ t h e s i g n o f ’ .

Thus knowledge o f t h e s i g n s o f two r e f l e c t i o n s p e r m i t t h e

s i g n o f t h e t h i r d r e f l e c t i o n t o be d e t e r m i n e d . These

p a r t i c u l a r r e l a t i o n s h i p s a r e t r u e o n ly f o r t h e h y p o t h e t i c a l

c a s e o f a s t r u c t u r e composed o f i d e n t i c a l a tom s . For

o r g a n i c c r y s t a l s , t h e p r e d o m in a n t components c a r b o n , oxygen

and n i t r o g e n have a b o u t t h e same a to m ic w e i g h t , and so

e q u a t i o n (24) h a s been shown t o h o l d i f t h e a s s o c i a t e d

s t r u c t u r e f a c t o r s a r e l a r g e .

’ S' may be u s e d t o d e n o te ' t h e p h a s e o f ’ , t h u s a l l o w i n g

t h e S a y re e q u a t i o n t o be u s e d f o r n o n - c e n t r o s y m m e t r i c c a s e s .

P r o b a b i l i t i e s

When t h e m a g n i tu d e s o f t h e s t r u c t u r e f a c t o r s a r e n o t

Targe enough f o r e q u a t i o n (24) t o be s t r i c t l y t r u e , i t h a s

been shown t h a t t h e y a r e p r o b a b l y c o r r e c t , a l t h o u g h i n some

c a s e s , t h e s i g n e q u a l i t i e s may b r e a k down and t h e ' e q u a l s ’

s i g n i n e q u a t i o n (24) s h o u l d be r e p l a c e d by ’ Z ' which

means ’p r o b a b l y e q u a l s ’ .

V a r io u s a n a l y s e s have been c a r r i e d o u t by Cochran and

Woolfson t o d e t e r m i n e t h e s t a t i s t i c a l i n t e r p r e t a t i o n o f

r e l a t i o n (24) and t h e p r o b a b i l i t y o f i t s b e i n g c o r r e c t may

be q u a n t i f i e d i n t e r m s o f E v a l u e s i n t h e f o l l o w i n g way:

- 244 -

P(E) = £ + \ t a n h ( | E (h) . E(k) . E (h -k ) | . N- ).. (25)

By regarding each phase indication as a vector of length |E(k).E(h - k) | and direction <J) (k) + <j>(h - «],t h e y may be summed v e c t o r i a l l y . T h is o p e r a t i o n l e a d s t o

t h e T angen t f o r m u l a :

For n o n - c e n t r o s y m m e t r i c s p a c e g r o u p s , i t i s o f t e n found o n ly

p a r t i a l s t r u c t u r e i n f o r m a t i o n i s o b t a i n e d . However, i f t h e

c a l c u l a t e d s t r u c t u r e f a c t o r s , b a s e d on t h e p a r t i a l s t r u c t u r e ,

a g r e e r e a s o n a b l y w e l l w i t h t h e o b s e r v e d a m p l i t u d e s , t h e n

t h e p h a s e s a s s o c i a t e d w i t h o t h e r l a r g e E v a l u e s may be

i n c l u d e d i n f u r t h e r t a n g e n t f o rm u la c a l c u l a t i o n s . T h is

r e c y l c i n g p r o c e s s may be r e p e a t e d u n t i l a l l t h e a toms a r e

l o c a t e d .

Phase D e t e r m i n a t i o n i n P r a c t i c e

Numerous com pute r programmes have been p r e p a r e d t o

d e t e r m i n e p h a s e s by u t i l i s i n g t h e s y m b o l ic a d d i t i o n

p r o c e d u r e o f t h e K a r l e s and e q u a t i o n s ( 2 4 - 2 6 ) . The MULTAN

sy s te m i s one su c h p a ck a g e o f c r y s t a l l o g r a p h i c com pute r

programmes w hich w i l l p e r f o r m a l l t h e n e c e s s a r y d i r e c t

methods c a l c u l a t i o n s . The main subprogrammes w hich com

p r i s e t h e c o m p le t e s y s te m a r e :

(a) The NORMAL programme com putes t h e n o r m a l i s e d

s t r u c t u r e a m p l i t u d e s , | E | ' s f rom t h e i n t e n s i t y d a t a .

tan (J) (h)

- 245 -

(b) The MULTAN programme c o n s i s t s o f t h r e e s e c t i o n s :

( i ) SIGMA 2 g e n e r a t e s t h e Sigma two i n t e r a c t i o n s

( E q u a t i o n ( 2 4 ) ) .

( i i ) CONVERGE f i n d s t h e s t a r t i n g r e f l e c t i o n s f o r t h e

T an gen t fo r m u la ( E q u a t io n (26)) by a p p l i c a t i o n o f t h e

Sigma one fo rm u la (which i s a s p e c i a l c a s e o f t h e

Sigma two r e l a t i o n s h i p i n which two o f t h e r e f l e c t i o n s

a r e t h e same) and by a s s i g n i n g p h a s e v a l u e s t o

r e f l e c t i o n s which d e f i n e t h e o r i g i n and e n a n t io m o r p h .

A s m a l l number o f r e f l e c t i o n s , which a p p e a r t o

p r o v i d e a good s t a r t i n g p o i n t f o r p h a s e d e t e r m i n a t i o n ,

a r e c h o se n and a r e g i v e n a l l p o s s i b l e c o m b i n a t i o n s o f + +- TT/4 o r - 3 TT/4 f o r n o n - c e n t r o s y m m e t r i c s p a c e g ro u p s

and 0 o r TT f o r c e n t r o s y m m e t r i c s p a c e g r o u p s , t h u s

p r o d u c i n g a m u l t i p l e s t a r t i n g p o i n t f o r t h e t a n g e n t

f o r m u la .

( i i i ) FASTAN g e n e r a t e s e ac h s t a r t i n g s e t o f p h a s e s

an d , by u s i n g a w e i g h te d v e r s i o n o f t h e T angen t fo rm u la

and t h e p h a s e r e l a t i o n s h i p s o u t p u t by SIGMA 2, i t

d e t e r m i n e s t h e p h a s e s o f o t h e r h i g h v a l u e |E |1s

and a f i g u r e o f m e r i t b a s e d on t h e d e g r e e o f i n t e r n a l

c o n s i s t e n c y f o r e ac h c o m p le t e p h a s e s e t .

(c) The FOURIER programme computes an E-map from a

s e t o f n o r m a l i s e d s t r u c t u r e f a c t o r s which h a s t h e h i g h e s t

combined f i g u r e o f m e r i t . From t h e E-map, i t i s p o s s i b l e ,

i n most c a s e s , t o d ed u ce t h e l o c a t i o n o f a tom s .

- 246 -

MULTAN i s most s u c c e s s f u l when d e a l i n g w i t h c e n t r o -

sym m et r ic c r y s t a l s o f s m a l l o r g a n i c m o l e c u l e s , and c o m p le te

s t r u c t u r e s s o l u t i o n s a r e o f t e n p o s s i b l e . The p ro b lem i s

more c o m p l i c a t e d f o r t h e n o n - c e n t r o s y m m e t r i c c a s e , b u t i t

i s n o t i m p o s s i b l e . Very o f t e n , f i g u r e s o f m e r i t can be

u n r e l i a b l e and i t i s n e c e s s a r y t o examine a l a r g e number

o f E-maps b e f o r e t h e c o r r e c t s o l u t i o n i s fo un d .

7 . 6 . F o u r i e r s y n t h e s i s

Once t h e i n i t i a l e s t i m a t e s f o r t h e p h a s e s c X ( h k l )

have been o b t a i n e d by some s t r a t e g y , t h e y can be u s e d , i n

c o n j u n c t i o n w i t h t h e o b s e r v e d s t r u c t u r e f a c t o r a m p l i t u d e s ,

t o compute a t h r e e - d i m e n s i o n a l e l e c t r o n d e n s i t y map, by

u s i n g e q u a t i o n (1 5 ) . I f t h e i n i t i a l p h a s e s a r e c l o s e

enough t o t h e t r u e v a l u e s , t h i s s y n t h e s i s w i l l a l l o w some

o f t h e s t r u c t u r a l i n f o r m a t i o n ’’l o c k e d ” i n t h e o b s e r v e d

s t r u c t u r e f a c t o r a m p l i t u d e v a l u e s t o be r e l e a s e d e i t h e r

by r e v e a l i n g p e a k s w i t h r e d u c e d d e n s i t y o f a d d i t i o n a l a tom s ,

which were n o t u s e d i n t h e d e r i v a t i o n o f t h e i n i t i a l s e t s

o f p h a s e s , o r by i n d i c a t i n g any minor e r r o r s i n t h e

c o o r d i n a t e s o f t h e a toms p r e v i o u s l y l o c a t e d . A new s e t

o f p h a s e s a r e t h e n r e c a l c u l a t e d from t h e c o r r e c t e d

c o o r d i n a t e s o f t h e p r e v i o u s s e t o f a tom s and t h e c o o r d i n a t e s

o f t h e newly l o c a t e d a to m s , u s i n g e q u a t i o n (8) and t h i s new

s e t o f p h a s e s r e p r e s e n t an improvement o v e r t h e i n i t i a l s e t

o f p h a s e s b e c a u s e t h e r e i s more, o r more p r e c i s e , i n f o r m a

t i o n u se d i n t h e i r d e r i v a t i o n . The r e i t e r a t i v e p r o c e s s

o f r e c a l c u l a t i o n o f t h e p h a s e s t o g e t h e r w i t h t h e s u b s e q u e n t

c o m p u t a t i o n o f a n o t h e r F o u r i e r e l e c t r o n d e n s i t y map (b a s e d

- 247 -

on t h e o b s e r v e d a m p l i t u d e s and c a l c u l a t e d p h a s e s ) i s known

a s " s u c c e s s i v e F o u r i e r s y n t h e s i s ” and i s c o n t i n u e d u n t i l

a model w hich r e p r o d u c e s i t s e l f i s o b t a i n e d .

H av ing o b t a i n e d a more r e l i a b l e s e t o f p h a s e s , we

t h e n c a l c u l a t e a F o u r i e r s y n t h e s i s u s i n g t h e q u a n t i t i e s

|F | - |F | . T h is g i v e s a d i f f e r e n c e F o u r i e r map whicho chas c e r t a i n f e a t u r e s which e n a b l e t h e c o r r e c t model t o be

f u r t h e r r e f i n e d and which may be e x p r e s s e d i n t h e form :

A p = V - ^ £ £ A F e x p - 2 TT i ( hx + k F + l z ) . C2?)h k 1

where. A F = I F I - I F II o I I c I

| Fq | = o b s e r v e d s t r u c t u r e f a c t o r a m p l i t u d e ,

o b t a i n e d from i n t e n s i t y d a t a ,

and | Fc | = c a l c u l a t e d s t r u c t u r e f a c t o r a m p l i t u d e ,

o b t a i n e d from s t r u c t u r e f a c t o r e q u a t i o n ( 8 ) .

S p e c i f i c a l l y , a d i f f e r e n c e F o u r i e r map i s p a r t i c u l a r l y u s e f u l

f o r t h e more p r e c i s e l o c a t i o n o f a to m ic p o s i t i o n s , f o r t h e

i d e n t i f i c a t i o n o f m i s s i n g a tom s and f o r r e f i n e m e n t o f

t h e r m a l p a r a m e t e r s .

7 .7 L e a s t s q u a r e s r e f i n e m e n t

T h i s i s a s t a t i s t i c a l t r e a t m e n t o f t h e d a t a so t h a t a

model , w hich r e p r e s e n t s t h e b es t : f i t w i t h t h e o b s e r v e d d a t a ,

i s o b t a i n e d .

The e l e c t r o n d e n s i t y maxima o b t a i n e d f rom t h e F o u r i e r

s y n t h e s i s , d i s c u s s e d i n t h e p r e v i o u s s e c t i o n , does n o t

- 248 -

n e c e s s a r i l y c o r r e s p o n d t o t h e b e s t a to m ic c o - o r d i n a t e s which

can be a t t a i n e d . T h is i s m a in ly due t o t h e f a c t t h a t , in

t h e s e F o u r i e r s y n t h e s i s , t h e summation i s o n ly t a k e n ove r

a l l t h e d i f f r a c t e d beam i n s t e a d t h e s e F o u r i e r s e r i e s s h o u l d

be i n f i n i t e . Thus t e r m i n a t i o n o f s e r i e s e r r o r s w i l l a lw ay s

be p r e s e n t . To overcome t h i s o b s t a c l e , t h e s t r u c t u r e can

be f u r t h e r r e f i n e d by t h e method o f l e a s t s q u a r e s . S in c e

t h e r e i s a l a r g e e x c e s s o f o b s e r v a t i o n a l d a t a (Fq ) o v e r t h e

numbers o f p a r a m e t e r s , e . g . a to m ic c o o r d i n a t e s , t e m p e r a t u r e

f a c t o r s , t h i s s i t u a t i o n i s s u i t e d t o l e a s t s q u a r e s a n a l y s i s ,

which i s w e l l a d a p t e d t o a u t o m a t i c com pu t ing . The com pu ta

t i o n i s s e t up so a s t o y i e l d s m a l l s h i f t s i n t h e p a r a m e t e r s

which w i l l m in im is e t h e q u a n t i t y D which i s g iv e n by

D = £ W ( | F q | - | F c | ) 2 = £ w A 2 , (28)h k l h k l

where W = a w e i g h t i n g f a c t o r f o r e ach o b s e r v a t i o n and t h e

summation i s o v e r a l l t h e o b s e r v e d r e f l e c t i o n s .

S in c e I Fc I i s a f u n c t i o n o f p a r a m e t e r s • • • pn >

which may be s c a l e , p o s i t i o n a l o r t h e r m a l p a r a m e t e r s , t h e

c o n d i t i o n s f o r D t o be a minimum a r e t h e e q u a t i o n s

A - ? = 0 = V w ^ ^ | Fc f o r J = 1, 2 , . . . n. (29)* Pj h k l “P "

There a r e n su c h e q u a t i o n s c o r r e s p o n d i n g t o t h e n p o s s i b l e

v a l u e s o f j . S in c e f o r e a c h atom which i s r e f i n e d

a n i s o t r o p i e a l l y , t h e r e a r e n i n e p a r a m e t e r s and f o r e ach

atom which i s r e f i n e d i s o t r o p i c a l l y , t h e r e a r e f o u r p a r a m e t e r s ,

i t can be s e e n t h a t n w i l l u s u a l l y be a l a r g e number i n most

- 249 -

c r y s t a l s t r u c t u r e a n a l y s e s . The F o u r i e r s y n t h e s e s p r o v i d e

s a t i s f a c t o r y e s t i m a t e s , a . , f o r t h e v a l u e s o f p a r a m e t e r s ,

P . , and t h u s p r o v i d e a good s t a r t i n g p o i n t f o r t h e l e a s t J

s q u a r e s a n a l y s i s , w h ich , i n t u r n , s u p p l i e s t h e v a l u e s f o r

t h e s m a l l c h a n g e s , A P . , i n t h e v a l u e s o f t h e p a r a m e t e r s ,

P . , su c h t h a t a b e t t e r a p p r o x i m a t i o n , a . , f o r t h e v a l u e J 3o f t h e p a r a m e t e r s , P , can be o b t a i n e d ,

i . e . a 7 = a . + A p . , j = 1 , 2 , . . . n (30)3 3 3

The f u n c t i o n | F | can now be e x p r e s s e d a s a T a y lo r s e r i e s ,owhich i s t r u n c a t e d a f t e r t h e l i n e a r t e rm t o make t h e

s u b s e q u e n t c a l c u l a t i o n s more m an a g ea b le :

Pc ^P 1 1^2* Pn I I Pc (a l * a 2 * a n^

+ £ Fc 1 £ p±. ( 3 D1 = 1 b p .i

S u b s t i t u t i n g e q u a t i o n (31) i n e q u a t i o n (29) g i v e s , on

r e a r r a n g e m e n t :

F i c . (32)

i = l h k l H dPj 1 ht i ^ p j

The s y s te m o f n e q u a t i o n i n (32) c o r r e s p o n d s t o t h e n

norm al e q u a t i o n s f o r t h e ’’b e s t ” v a l u e s o f A p ± and may

be r e w r i t t e n a s :

Z a . . A ? - “ C, (33)1J 1 Ji

o r , i n m a t r i x n o t a t i o n , a s :

A . A p = C (34)

- 250 -

H aving o b t a i n e d t h e l e a s t s q u a r e s s o l u t i o n from one

c y c l e , i . e . t h e v a l u e s o f s h i f t s A p ^, i t i s u s u a l l y n e c e s s

a r y t o p e r f o r m s e v e r a l c y c l e s o f l e a s t - s q u a r e s b e f o r e t h e r e

i s c o n v e r g e n c e . T h is i s b e c a u s e t h e T a y lo r s e r i e s , which

( e q u a t i o n (31 )) and so t h e ’ b e s t v a l u e s ’ o f t h e p a r a m e t e r s

a r e n o t g i v e n a f t e r one c y c l e .

The c r y s t a l l o g r a p h i c l e a s t s q u a r e s r e f i n e m e n t can

u t i l i s e e i t h e r b l o c k d i a g o n a l o r f u l l m a t r i x m ethods . The

l a t t e r i s t h e p r e f e r r e d a p p ro a c h a s t h e f u l l m a t r i x t e c h n i q u e

has b e t t e r c o n v e r g e n c e p r o p e r t i e s and a l s o s u p p l i e s u s e f u l

i n f o r m a t i o n on t h e i n t e r p e n d e n c e or c o r r e l a t i o n o f p a r a m e t e r s

u se d i n t h e l e a s t s q u a r e s a n a l y s i s , b u t i t i s i m p o r t a n t t o

n o t e t h a t i t p l a c e s g r e a t e r demands on com pu te r r e s o u r c e s .

Once t h e optimum v a l u e s o f t h e p a r a m e t e r s , P . , haveJ

been o b t a i n e d , i t i s i m p o r t a n t t o o b t a i n a m ea su re o f t h e

e r r o r i n su c h v a l u e s and t h i s i s a c c o m p l i s h e d by c a l c u l a t i n g

t h e s t a n d a r d d e v i a t i o n , O , f o r e ac h p a r a m e t e r i n t h e

f o l l o w i n g w a y :

r e l a t e s F t o t h e p a r a m e t e r s , P . , ha s been t r u n c a t e d c J

where G ( P . ) = e s t i m a t e d s t a n d a r d d e v i a t i o n o f p a r a m e t e r P .J J

1( a ” ) . . = t h e j d i a g o n a l e le m e n t i n t h e i n v e r s e

m a t r i x o f A ( s e e e q u a t i o n ( 3 4 ) ) .

m = number o f o b s e r v a t i o n s

n number o f p a r a m e t e r s .

- 251 -

From s t a t i s t i c a l c o n s i d e r a t i o n s , t h e p r o p e r w e i g h t , W, s h o u l d

be p r o p o r t i o n a l t o t h e i n v e r s e o f t h e s q u a r e o f t h e s t a n d a r d

d e v i a t i o n o f t h e a m p l i t u d e | f ( h k l ) | , i . e .

1W (h k l ) = -ry—---------- = , (36)

a | F o (hkl)_|

where t h e s t a n d a r d d e v i a t i o n s can be e s t i m a t e d by making

r e p e a t e d m ea su rem en ts o f e ac h r e f l e c t i o n , which i s c l e a r l y

n o t f e a s i b l e . I t i s t h e r e f o r e c u s to m a ry t o u s e e m p i r i c a l

w e i g h t i n g schemes which a r e d e s i g n e d so a s t o m in im is e t h eA 2

o ve r a r a n g e o f m a g n i tu d e s

o f I F land s i n 0 .1 o

The l e a s t s q u a r e s r e f i n e m e n t p r o c e s s i s f o l l o w e d by

com put ing t h e w e i g h te d r e s i d u a l R a t e ac h s t a g e :

R - I» ’I F„ I - 1 F, DI > " ' 2

I f t h e r e f i n m e n t p r o c e s s i s g i v i n g a p r o g r e s s i v e l y more

a c c u r a t e e l e c t r o n d e n s i t y map, t h e n R s h o u l d d e c r e a s e

s t e a d i l y .

- 252 -

CHAPTER EIGHT

An X - r a y a n a l y s i s o f 1 T8 - d i m e t h y l - 2 - n a p h t h y l a c e t a t e .

- 253 -

8 . 1 I n t r o d u c t i o n

In t h e n a p h t h a l e n e m o le c u l e , t h e 1-and 8 - p o s i t i o n s a r e

s a i d t o be p e r i t o e ach o t h e r and s u b s t i t u e n t s l o c a t e d a t

t h e s e p o s i t i o n s a r e i n much c l o s e r p r o x i m i t y t h a n s i m i l a r

s u b s t i t u e n t s l o c a t e d o r t h o t o e ach o t h e r . T h is c l o s e r

p r o x i m i t y h a s been r e s p o n s i b l e f o r t h e a p p e a r a n c e o f s e v e r a l

u n iq u e p r o p e r t i e s o f p e r i - s u b s t i t u t e d n a p h t h a l e n e s , e . g .

t h e r e l a t i v e e a s e o f a c i d - c a t a l y s e d i s o m e r i s a t i o n o f 1 , 8 -

d i m e t h y l n a p h t h a l e n e t o t h e 1 , 7 - i s o m e r compared t o o t h e r

d i m e t h y l n a p h t h a l e n e s h a s been a t t r i b u t e d t o t h e r e l i e f o f

s t r a i n i n t h e l e a d i n g t o t h e c a r b o n - 1 p r o t o n a t e d d e r i v a t i v e . ^

P e r i - s t r a i n can be r e l i e v e d by f o u r modes of m o l e c u l a r 2 , xd e f o r m a t i o n - (a) s t r e t c h i n g o f bonds C1-C9 and C8-C9,

(b) i n - p l a n e d e f l e c t i o n o f t h e s u b s t i t u e n t s su c h t h a t t h e

C9-C8-C16 and C9-C1-C11 v a l e n c y a n g l e s a r e i n c r e a s e d from

t h e i r e q u i l i b r i u m v a l u e s o f 120° , (c) o u t - o f - p l a n e b e n d in g

of t h e s u b s t i t u e n t s on t h e n a p h t h a l e n e n u c l e u s , 8 ^ , and

(d) a d i s t o r t i o n or b u c k l i n g o f t h e n u c l e u s i t s e l f . In

many p e r i - s u b s t i t u t e d n a p h t h a l e n e s , c o n s i d e r a b l e i n - p l a n e

and o u t - o f - p l a n e d e v i a t i o n s o f t h e e x o c y c l i c bonds o c c u r ;

r e p o r t e d c a s e s o f n u c l e a r d i s t o r t i o n s a r e r e l a t i v e l y l i m i t e d .

In such m o l e c u l e s , two c o m p e t in g i n f l u e n c e s a r e i n o p e r a t i o n ,

namely t h e l o s s on r e s o n a n c e e n e rg y due t o n u c l e a r d i s

t o r t i o n s and d e v i a t i o n o f s u b s t i t u e n t s f rom t h e mean

m o le c u l a r p l a n e on one hand and t h e d e c r e a s e i n s t e r i c s t r a i n

e n e rgy on t h e o t h e r .

In n a p h t h a l e n e , t h e d i s t a n c e be tw een t h e p e r i - c a r b o n

- 254 -

atoms i s o n ly a b o u t 2 . 4 - 2 . 5 8. In a r o m a t i c m o l e c u l e s , t h e

norm al nonbonded C . . . C d i s t a n c e i s a b o u t 3 . 0 A. I t i s

t h e r e f o r e l o g i c a l t o e x p e c t t h a t w i t h s u b s t i t u e n t s o t h e r

t h a n hy d ro g en a t t h e p e r i p o s i t i o n s i n n a p h t h a l e n e , t h e r e

w i l l be c o n s i d e r a b l e s t e r i c i n t e r a c t i o n .

The c r y s t a l l o g r a p h i c s t u d y o f 1 , 8 - d i m e t h y l - 2 - n a p h t h y l 3

a c e t a t e ( I ) was u n d e r t a k e n so t h a t some l i g h t may be th row n

on t h e n a t u r e o f t h e p e r i i n t e r a c t i o n and t h e mechanism by

which t h e s t e r i c s t r a i n i s m in im is e d . T h i s , i n t u r n , may

5 4Ih e lp t o e x p l a i n t h e e f f e c t o f t h e p e r i - s t r a i n on t h e r a t e

of t h e a u t o x i d a t i o n o f s u b s t i t u t e d 2 - n a p h t h o l s The o r d e r

of r e a c t i v i t y o f t h e 2 - n a p h t h o l s known t o a u t o x i d i s e was4

found t o b e ,

1 - M e ( in e r t ) « 1 - E t h y l « 1 - c - h e x y l < 1 - i s o p r o p y l

< 1 , 8 - d i m e t h y l < 1 - t - b u t y l .

Brady and C a r n d u f f ^ p r o p o s e d t h a t t h e m ajo r f a c t o r c o n t r o l l

in g t h e o v e r a l l r a t e o f t h e a u t o x i d a t i o n o f s u b s t i t u t e d

2 - n a p h t h o l s , which show t h e c h a r a c t e r i s t i c s o f a r a d i c a l

c h a in p r o c e s s , i s t h e d e g r e e o f s t e r i c s t r a i n w i t h i n t h e

m o le c u le , and e s p e c i a l l y t h e m ag n i tu d e o f t h e p e r i - i n t e r a c t i o n

between s u b s t i t u e n t s a t Cl and C8 a n d / o r C4 and C5. T h i s

- 255 -

p e r i - i n t e r a c t i o n i s a b s e n t i n t h e l - h y d r o p e r o x y - 2 ( 1 H ) -

n a p h t h a l e n o n e s (2) p ro d u c e d i n t h e a u t o x i d a t i o n r e a c t i o n s .

The r e s u l t i n g s t r a i n r e l i e f i s t h o u g h t t o be t h e f a c t o r

c o n t r o l l i n g t h e r a t e s .

° 2 , C6h 6

On a c c o u n t o f t h e f a c t t h a t l , 8 - d i m e t h y l - 2 - n a p h t h o l

w i l l a u t o x i d i s e r e a d i l y , t h e X -ray c r y s t a l s t r u c t u r e

a n a l y s i s was p e r f o r m e d on t h e a c e t a t e o f t h e n a p h t h o l , s i n c e

t h e f i r s t s t e p i n t h e r e a c t i o n i s t h e h o m o ly t i c f i s s i o n o f

t h e 0-H bond.

- 256 -

8 . 2 . E x p e r i m e n t a l

C r y s t a l DataCHc h .

•CH.

l , 8 - D i m e t h y l - 2 - n a p h t h y l a c e t a t e : ^ i 4 ^ 2 H14

U n i t C e l l D i m e n s io n s :

o9 .5 4 A

6 .6 3 A

= 1 9 .87 A

C* = 9 0 .0 °

P= 1 1 0 .2 °

y = 9 0 .0 °

Space Group

DmDcX[1 (Mo K*)

F (000)

P 2 i / C (C°h)

214 a .m .u .o ^

1180 A

1 .1 8 g cm

1 .2 1 g cm o

0 .7 1 0 7 A

0 . 8 6 cm

The s p a c e g ro up was u n i q u e l y d e t e r m i n e d by t h e s y s t e m a t i c

a b s e n c e s :

hOl when 1 = 2n +1 and OkO when k = 2n +1. The c r y s t a l

u se d i n t h i s a n a l y s i s was a n e e d l e o f d im e n s io n s 1 .5 x

1 .0 x 0 . 5 mm .

- 257 -

Data C o l l e c t i o n

P r e c e s s i o n p h o t o g r a p h s were u s e d t o m easu re t h e c e l l

d im e n s io n s and t o d e t e r m i n e t h e s p a c e g ro up . The c r y s t a l

was t h e n mounted and a l i g n e d on t h e g o n io m e te r h e ad o f a

H i l g e r and W at ts Y290 c o m p u t e r - c o n t r o l l e d f o u r - c i r c l e

d i f f r a c t o m e t e r . The c e l l d im e n s io n s q u o te d i n the c r y s t a l

d a t a a r e t h o s e o b t a i n e d from a l e a s t - s q u a r e s a n a l y s i s o f

t h e a n g u l a r s e t t i n g s o f 12 r e f l e c t i o n s . The i n t e n s i t i e s

were o b t a i n e d by t h e CJ-20 s t e p s c a n p r o c e d u r e which

c o n s i s t e d o f f o r t y s t e p s o f 0 . 0 2 ° a t 2 s e c . / s t e p w i t h b a c k

ground c o u n t s f o r 20 s e c o n d s a t e ach end o f t h e s c a n r a n g e

and p e r i o d i c m o n i t o r i n g o f two s t a n d a r d r e f l e c t i o n s . The

i n t e g r a t e d i n t e n s i t y , I o f a r e f l e c t i o n can be c a l c u l a t e d

from t h e p e a k , P, and b a ck g ro u nd B l , B2, c o u n t s u s i n g

e q u a t i o n (1) :t

I = P - (Bl + B2) . — £ (1)

w here t = c o u n t i n g t im e a t p eak

and t ^ = c o u n t i n g t im e f o r one o f t h e b a ck g ro u n d

c o u n t s (b o th t h e s a m e ) ,

and t h e s t a n d a r d d e v i a t i o n o f I ( O D > can be o b t a i n e d from

e q u a t i o n ( 2 ) :t 1

ax = ( P + (Bl + B2) ) 2 (2)

The i n t e g r a t e d i n t e n s i t i e s ( I ) o f 1877 in d e p e n d e n t

r e f l e c t i o n s (20 \< 52°) w i t h I >/2 0 ( 1 ) w ere o b t a i n e d .

Reduced beam i n t e n s i t y was employed t o r e m e a s u r e t h e

r e f l e c t i o n s f o r w hich 20 N< 16° i n o r d e r t o c o r r e c t f o r c o u n t e r

s a t u r a t i o n e r r o r s . No c o r r e c t i o n f o r a b s o r p t i o n was a p p l i e d .

- 258 -

n n n n n n j l + * TO—I — 4 C3Gh Ol CM IVJ —• O 3 X X •

X J C TO TOm X O 3

O TO TO C/>TO TO TO -HI

-» —1 3»#—* !—« -4o r H

MX MU XX X O #-• j » >• COTO TO TO O .TJ Z TO TO H

3333>3>>-"3»-i Mn - m z z z c n o TO TO o

r w n 3 TO COO 3 3J < < < z x om ^ n > > > « 33 33 TO

to to t o r r r o n > Or r r c c c o m n O TOTOrnTOTOTOTOTOTOCO TO Zo n n h 2 -«-9 —9 —f TO TO TO TO X H 33M M M O O O *HI 33 MOO □3J»3BT| X MOz z z a niROlO X Z Z 33

S X X O O O 33 X C X TO

H H - i r r j — i

x x x c: c x to s s o03 CO 09 TO • • • TO

X X X o 09 C9 MO C O O O 0 - 1 10 0X0O O O TO TO TOC X X 3r r r -*-* to to z c c *

09 C» 09

oi c a os n » o «-*■ *— ►** ro o • • • TO

o o o * z S S SIOTO TO TO M O Q G 3

w TO TO TO TO 1 33

*-> Zv i r v w n

t i io a s s s• • • • • • TOs s s O N O U

M U OO Ok 09

COm33 HnNNtfl© TO oto -nn(V) xv u n » * m o i n to-« xI I * * M >

u » * » * q co09 OB 04 «-»■ x mo♦ ♦

( 4 U U U U U UC3* 0k <Jk t3k Ok O Ov "Os s a a s s s x

>O O O D CO33 33 33 37 TO

CD a> 09 09T.OGG

MOIU 09 Ok •■* TO * % *» Ok09 09 "SI

N M U U N M U • • • • • • •O I O S S < J I> 4 * - N M J k S S O *

• • • atca 09 o

OB SI CB • • • TO I ^ S O iS

TABLE I

Sl'f’A.F’V

OF STRUCTURE

DETERMINATIO

- 259 -

S t r u c t u r e A n a l y s i s

The a to m ic c o o r d i n a t e s o f a l l t h e n o n -h y d ro g e n atoms

were o b t a i n e d by t h e m u l t i s o l u t i o n d i r e c t p h a s e d e t e r m i n i n g

programme MULTAN. I E I v a l u e s were d e r i v e d from t h e

i n t e n s i t i e s , on t h e b a s i s o f an o v e r a l l i s o t r o p i c t e m p e r a t u r e o ^

f a c t o r B 3 .8 0 A , and t r i p l e t r e l a t i o n s h i p s were g e n e r a t e d

f o r t h e 200 r e f l e c t i o n s w i t h I E I >, 1 . 5 . The s t a r t i n g

s e t o f 7 r e f l e c t i o n s , which c o n s i s t e d o f t h r e e t o d e f i n e

t h e o r i g i n and f o u r r e f l e c t i o n s t o which t h e v a l u e s o f 0 and

TT were g i v e n , were s e l e c t e d by t h e programme (T ab le 1 ) .

T h is p r o c e d u r e gave s i x t e e n p o s s i b l e p h a s e s e t s which were

t h e n c a l c u l a t e d f o r t h e 200 r e f l e c t i o n s w i t h t h e l a r g e s t

v a l u e s o f | E | and an E-map computed from t h e s e t show ing

t h e h i g h e s t combined f i g u r e o f m e r i t r e v e a l e d a l l t h e non

hyd ro g en a tom s .

The i n i t i a l s t r u c t u r e - f a c t o r c a l c u l a t i o n gave an R

o f 29.8% and t h r e e c y c l e s o f f u l l - m a t r i x l e a s t - s q u a r e s

r e f i n e m e n t , u s i n g t h e 1824 i n d e p e n d e n t s t r u c t u r e a m p l i t u d e s

f o r which | F | >, 4 O ( | Fq | ) w i t h i s o t r o p i c t h e r m a l

p a r a m e t e r s , l o w e re d R t o 16.7%. S u b seq u e n t c a l c u l a t i o n s

w i th a n i s o t r o p i c t h e r m a l p a r a m e t e r s r e d u c e d R f u r t h e r t o

10.4%. A f t e r making a l l o w a n c e f o r e r r o r s c a u s e d by c o u n t e r

s a t u r a t i o n , R was 9.7%. A d i f f e r e n c e e l e c t r o n - d e n s i t y

d i s t r i b u t i o n r e v e a l e d t h e s i t e s o f t h e h y d ro g en a to m s ,

which were t h e n i n c l u d e d i n t h e l e a s t - s q u a r e s c a l c u l a t i o n s

w i th i s o t r o p i c t h e r m a l p a r a m e t e r s and c o n v e r g e n c e was

r e a c h e d a t 6.6%. The w e i g h t i n g scheme employed was

CO = 1 / (A + B If I + C | f | 2 ) w i t h A = 0 . 1 5 0 8 , B = - 0 . 0 0 5 1

- 260 -

and C = 0 . 0 0 3 8 . The v a l u e s o f c o n s t a n t s A, B and C were2

c h o se n so t h a t t h e d e v i a t i o n from U) A o v e r t h e r a n g e o f

I F I and s i n 0 was m in im is e d . The r e f i n e m e n t then ' oc o n v e r g e d a t R = 6.1%. The r a t i o o f o b s e r v a t i o n s t o

p a r a m e t e r s was 9 t o 1.

8 . 3 R e s u l t s

The a to m ic c o o r d i n a t e s , t h e r m a l p a r a m e t e r s , bond

l e n g t h s , v a l e n c y a n g l e s , t o r s i o n a n g l e s , d e v i a t i o n s o f

t h e a tom s from t h e v a r i o u s p l a n e s i n t h e m o l e c u l e s and

a l i s t i n g o f t h e o b s e r v e d and c a l c u l a t e d s t r u c t u r e f a c t o r s

a r e g i v e n i n T a b l e s 2 - 8 . The m o le c u l a r and c r y s t a l

s t r u c t u r e s a r e shown i n F i g u r e s 1 and 2.

- 261 -

T a b le 2 : F r a c t i o n a l a to m ic c o o r d i n a t e s ( x 10^) w i t h e s t i m a t e d

standard, d e v i a t i o n s i n p a r e n t h e s e s *

The h y d r o g e n atom s a r e numbered a c c o r d in g t o t h e

atom s t o w h ich t h e y a r e a t ta c h e d #

The t a b l e sh o w s:

At om x y z

- 262 -

—* —* «•» a a Ar—4 H •H r-H rH p4 OJ (VI i~+ fH CVJw» *■-* w ■ w00 00 cvj r- n in NO 4 in iH 4 O 4o oo O' sO f—4 h- in QO O' CM fH Is- Is- >o 00O' in (Vi NO in O' 4 >n h- 00 rH 00 ro O'in in LO >o r r- sO 4) n£) m 4 4 4 in vO

ro m 4 ro 3 4 4 n n ro 4 4 3 r> n vCw» •w» w

Is- O' ro >0 Is- 4 cn (VI p- (*> sO fH rH n ro 4in Is- CO o *> (VI m n rH O' Is- O' vO >o in (VI(VI 00 v£> 00 in f—t 4 <-H in (VI (VJ in in r- 4 44 4 NO Is- CO 00 >o <n r> Is- (VI CVJ H m (VJ m

(Vi (M (VI CM m n en CM CM CM 4 “ CM 4 (M ?M m—* —■» '•-P N» W wO' 00 o nO 4 p-H CO 00 (M o nO O' e' O nO n£>sO sO 00 (M O' >0 o 00 O 00 m (*> en O' in C-00 4 f- in >0 o 00 »—t r-> O' 4 in X >0 pH fH4 co CM r> in e' Is- r - in 4 “ in #■* o CM fH 00

_ _ _ L o i-H CM CO 4 in n£>CM CO 4 in sO r-. CO O' fH «H r—i iH pH

—* w ■w>u o (J (J u o (J <J o o L> <J O O o u

- 2 6 3 -

cvj OJ (Vi 4 CO X XpH r—• pH fH

p w w «—* SP

00 CO vO H X CO O'4 o r - 0J x r - O00 ro OJ ih X X fHin X r - X r - in X

X o o CO fH f-H rHCO 4 4 4 4 in in>«p *-p W *—«■ —►X CO OJ 4 CO o fHin o Is- X X in oo o o o CO 4r - O' O' O' X 0J rH

O' in Is- o o o 0J0J OJ 0J ro eo 4 CO— **-p '■—p —f w pX 00 CO o 4 inIs- o CO (VI 0J Is- O'Is- fH in X CO r-•H CO X r- X X in

OJA A pH

CO 4 sO iH*-P w -p -p p p

X X X X X X X

X CO X O' In o oOJ pH ^H (VI CVJ iH>«p p” >—p -p w >pO' •H O' o X Is-X X X m 4 X OJ0J X O' O' OJ 4in CO 4 CO X Is- X

OJ X r—1 X i^ 0J COin X m in Is- X in-p p >-» w *»p4 X Is- X o in COo 4 f H CO o CO XO' X m 4 o X 4f H OJ O f H 00 CO CO

^H 4 Is- OJ X Is- r -4 m CO 4 in 4 co'-P >-p >«P ' -p ^P —fX 4 in CO X CO XO X in O' iH OJ XIs- O o 4 p- (VI OJ4 o o ^H r - O' X

CO 1—I (VI CO r"4 OJ COiH CO CO CO X X XfH iH r-4 pH

w —> **pX X X X X X X

- 264 -

T a b le 3 : Thermal pa ,ram eters (x lO ^) w i th e . s . d . ’ s i n p a r e n t h e s e s .

Carbon and o x y g en v a l u e s a r e a n i s o t r o p i c *

H ydrogen v a l u e s a r e i s o t r o p i c *

The a n i s o t r o p i c t e m p e r a tu r e f a c t o r e x p r e s s i o n u s e d was

o f t h e form d e s c r i b e d b y e q u a t io n ( 1 2 ) i n c h a p t e r s e v e n ,

t h e c o e f f i c i e n t s b e in g i n term s o f t h e mean sq u a r e

a m p l i t u d e s o f v i b r a t i o n

The t a b l e s h o w s :

Atom Uu or U U22 U12 U13 U23

- 265 -

—* «—* rx rx rxo o CM OJ o rx rx rvi o rx rx

00 iH rH fH fH 00 00 rH rH rH 00 o-r ■*—* "■t xr xr xr •X* ■x» >w xrCM in sO sO n 00 x 00 o X Is- 00 O'>* in o CD 4 IT) in X CVJ r- LO COi 1 K rH rH 1 1 CM1 rH1 1

->x, rx ■rx rx ffH rx rxrx r-» -X o rH OJ o —* rx r-t in o •n rx rxX X o fH *H rH O ' X X iH rH rH r- O'xr xr XT w >— ■w xr xr ■w Xr xr >r -O ' rH r- cr o x 4 OJ r» X CVJ in OJ ino LO CVJ (\J U") OJ o OJ >0 X rH X O ' X 4x CVJ CVJ ro ro OJ fH OJ OJ OJ 4 rH rH OJ X

rx rx rx •TX. r» rxrx —* o o rH 4 OJ rn rx rx OJ o O' rx ^HX o rH ^H rH fH rH O' X X fH ^H fH Xxr xr xr T» xr Hr w Hr fr x» •w ■%«*OJ ro £7* rH X in X X O' OJ X O' 4“ X OJX rH ro r- X X o rH ro 4 iH OJ X OJ OJ1 rH rH OJ rH 1 i 1 •H x X 41 1 i 1 I i 1 1

o o OJ OJ OJ X X OJ rx o OJ r- j~ _rxo

fH r-H r-H rH fH rH fH o rH r-H r-H f-H X Hw W xr W nr >r w <w w sr xr

o X o £ OJ OJ r- o O' o- rH Xo X X X in X o rH 4 X o- X OJ rH XX m X r - X X X r- in in X X X X Or

rx ^H 4 OJ X OJ o o OJ •4 X OJo rH »H rH rH fH »H rH fH f-H rH f-H OJ fH <-H<r •w xr r w w xr 'xr w* v w xr -w <wOJ in O' X o- OJ OJ in X 4 OJ o X O'X LO fH o OJ X OJ X o fH OJ r» 4- 0- X4- X X X X X O' X X m in fH r-H

r-Ho ^H

fH r-H o 0J X r**- OJ o o X OJ O' o OJfH rH r-H fH rH H rH O' ^H ^H rH rH fH rH

xr •w w xr —* w r xr wrH X X r-H in OJ X X 4" rH in X »HX rH 0- X rH 4 X r - in 4- O' X OJ O'X X in X O' O' X in in X O' X O' r - O'

a r-v o rH OJ X 4 inH OJ n 4 in X X O' ^H rH rH H rH rH***o a <-> U O a a o o o o (J o O o C(

- 2 6 6 -

__ _ Hro o CO >* sO o o

vD vO 0 - >£) H O '■w «-*

O ' >* CVJ O (\i ro00 >fr rH (\J ro f"- i—i

>* LD sO in 00

«■«>

O' 00 00 in in vOo m OJ f-H r*- OJ OH f H O' r-H ^H *-4w w w ■w w

OJ >0 TO ro 00 > *0 - ro 00 O' ro r H OJ00 OJ r- 00 >* 00

«—« H r-H

h 4 OJ ro r—H OJ ro r-H OJ ro<•>* Ok ^H * - * r-H ro ro ro vO sD

ro in kO ^H r-H r-H ^H r«H »—• ^H iHa> **■»

X X X X X X I X X X X I X X

- 267 -

Table 4 I n tr a m o le c u la r bonded d i s t a n c e s

sta n d a r d d e v i a t i o n s (a n g str o m s)

• —■r>— O Si > ro ro X f"- N. o 4 o rvj ro r>-cn S i X o cr in 00 CVI 4 CVJ ro r-H 00 m O•—« O - i o J* o o O' o o X o oo • • • • • • • • • • • • • • •TI H o o rH O rH o © r-H o -—4H

OJz rH CVJro f-H CVJro f H CVJo 4- x H H rH ro ro ro X >0f - H r H ro 4 in r - H f H rH rH r H r-H r—H

4 o o x x E x X r X X X X X X X

o CVJ CVJ rH r H f-H ro ro ro X(— rH H rO 4 X >0 i*- r H r-H r-H H r—H *H fH f-H

C J v j J U 3 o C J o C J u D 3 <-> X

OJ 0J ro <o M CVJ o OJ o O CVJ 4 OJ ro• v—r _ s r w '—r ■*—»» r "»’ *—*■

h- S ' CVJ 4" T' ro fH OJ 4 r - ■o o X o CVJJ) X 4* r-H X ■H X i-H 4 r—H O X ro rH CVJ >►H CO 4 ro 4 ro ro X ro 4 in 4 4a • • • • • • • • • • • • • • •

f-H r-H fH rH i—H r-H r-H »-H •-H r—H rH r-H H H r-H

4 3 3 3 3 3 3 3 3 3 3 o 3 3 X o

o <VII— —«—« ^ -\j \j o 4 -n x x r'- x x J* —«< -j o ■ j o j j o o j o u o s> u o

(a n g str o m s) w ith

in p a r e n th e s e s *

- 268 -

T a b le 5 s V a le n c y a n g l e s ( d e g r e e s ) w i t h t h e s ta n d a r d d e v i a t i o n s

( d e g r e e s ) i n p a r e n t h e s e s .

4 ro 4 X X OJ r*- r"> ro rH 4 X OJrH OJ OJ r-H OJ iH fH rH OJ •H <H rH rH rH rH OJ OJ OJ f H ro X OJ X ro

J j -W- wr "-r — —r —r —r r r-r ■— -w» wr •wr —r — -w- -wr3 —« X ro o © O ' X > O X *H OJ O' OJ x © X o © 4 ro X HX • • • • • • • • • • • • • . • • • • . . • • • . » •Z X X X i-«H X 4 X O o X X o X x 4 O OJ 4 X X OJ © X< t —* H

rH r-Hr Hr H

■Hf H

—«rH

OJr H rH

—«rH

■—« rH

r Hr H

> o jrH

r Hr H

xX f H OJ f H OJ f H OJo ro o © l"H OJ X CO X X1— OJ r H ro X X ^ JV H X 4 OJ 4 • H H N - X r H • H f H f H r H <H X f H f H< 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 X x 3 r x 3 x r

OJzo © © OJ 4 r H r H - H COXX X X Xt— r H OJOJ 4 X X X rH rH r H r H ro 4 X X r H rH r H r H r H H f H r H r-H< 3 3 3 3 3 3 3 3 3 3 3 o 3 3 3 3 3 3 3 3 3 3 3 3 3 3

X X OJ X OJ OJ X OJ OJ X3 rH 4 4 © X X OJ fH fH fH X X X X X XI— fH fH r-H rH r- fH X O O ' H rH X 4 X X f*- r-H fH r-H rH H fH rH fH r-H

< 3 D 3 3 3 3 3 3 3 3 3 3 x X x X X XX X XX XXXX

wr wr w wr wr wr wr wr wr w -w- wr wr wr wr wr wr w wr wr >w -w* -wr —*P*- -H o OJ O' 4* OJ ro X X p- rH X r*- r . > X X 4- n X © OJ X X OJ

r- 4 -0 X) o X *w X X © X © m -H •■H AJ X AJ H © X OJ O ' XrH OJ aj fH OJ CVJrH fH fH rH H OJ OJ AJ AJ fH AlH «-H O © rH © H © ©-H fH fH -H rH fH -H H H H H H -H -H -H -H rH fH H H H H H -H H *H

rozot— OJo H OJX X fH X 4

XrH4H OJX X X X —i

rH fHOJfH

fHXH X X

< 3 3 3 3 3 3 3 3 3 3 3 o 3 3 3 3 3 3 3 X 3 3 X 3 3 X

:\JO OJ OJ rH rH fH X X X X X X

r— H H OJ X X X O' H *H H X 4 X X S'N- fH H rH r-H -H —H rH H f H

< 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

T OJ fH X -H X X —< X XO fH O X © © 4 X rH rH fH X X X X X Xh- JN rH X 4 fH X fH H rH X rH H X 4 X X f'- fH rH rH —t H -H rH fH ■H

< 3 3 3 3 3 3 3 3 3 3 O o X X X X X X r X X X r X X X

- 269 -

T a b le 6 : T o r s i o n a n g l e s ( d e g r e e s ) with, t h e s t a n d a r d d e v i a t i o n :

(d .eg rees ) i n p a r e n t h e s e s .

- 270 -

__ _ L _ L __ _ >■—. C\J

j j —4 VJ M —4 - 4 VJ rsj x X X *—4 X VJ VJ OJ3 >«* —* *«» —• — ««*■ >— wX 'VJ oo O' o v j o O' O O X © "02 • • • • • • • • • • • • • • • •<t 4* *0 —4 x X O' VJ .-4 O X) /> H T' O' D

**> 1 —4

s*.—41

■!S»

1 —41

1 1 N- 41

1 ^—4 • -4

- 4 f- r--4 -4

II I i x xi o* n

—4 ■

4*xo 4- 4- O o VJ>— H -4 —4 —4 4- —4< o o u o 3 <3

<-• x vj vj 4 x vj -4 x»—4 <-4 «—< >D £ £ ro r*) ro

"4 ^ ”\J H ^ 4 ^ ^ ^ ^ ^ r*’- r*» H -H “4 <—4 <—4 —4 r 4

xzO 4"o oh- vj vjO'O'x —4 -—4 x iH< 3 o 3 3 3 D o 3 3

O 3 —4 —4 —4 X X) o X X X

rvjzo vj vj (\i vj

-4 - t H H T J 'V J t X X r'- X X T ' O' —4 ^-4 --4 —4 .VJ X X 4 - X -X X X V- X X X ) — J J J J J J ' J J J U J U U U J J U U U U U U U J J U U U J J J ' J U

zo r-4 --4 <f O X X 4^ .ft iXT 1 1-4 VJ —4 H X X '■4 vO X N «“4 '■4 00 H VJ C\J O ' r—4 (\J (X ^ J1 tX X X f*— Is- J ' ■J' >—4 1—4 r—43 3 3 3 0 3 3 3 3 3 o o 3 0 3 3 0 3 3 3 i : r r : E o : E i : 3 3 3 0 0 o

_L r-4 VJ ro r - Is - X) 4- X) 00 r - o i-4 X X X r4j jj oo rvj ro x \J ro JO M ro VJ \J VJ rH VJ ■o VJ VJ AJ -4 fH iH !\j H rH (—4 ro v j v j v j t\ j \ J

x> v j r - oo X) r*> X» o *—4 OJ JV ro S) VJ X) r“ 4 o ■> ro 4- 0^ - • VJ O ro O' O' X X rv. rs» S i X2 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •< O JO J* iH rH X) i-4 o o rvj r - VJ T> r - o X) VJ 4" O 4- VJ ^ i-4 3 s h - O' VJ —4 S i X X

1 h -c-4

>■>HI

1 oiH —4

I—*4 —4

1 1 VJ—41

fv. —1 1

1 V-Hl

1—4 f—4

r—4 4

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rvj-HL04-rvj^)0jr^o0'0'r0CVJ ro rH rH r-H f-H r—4 4 rH r-H r-H

I I I Ih N O h O'LDNOOO'NvDro r”H ro cvj in • o j cvj -h i-h ■—« -h

I t i l l00 m cvj cvi oo in1 i i

X 4(0 tV J4O f \ iN -«N M Of-H (\j i-H —H r-4 r—4 fH —H 4 H CVJ f-H

XBO«t>OXJOHV jH ®orvj i-h ro oj in f~• o j cvj i-h cvj f-H cvj >4

N 0 4 CVJ OO 4

so roo joo 'ooo-ro^ ro in 'or-H r-H r-H r-4 I I I I Il l l l

O' 00 0-fH f—4

in co O' in O' r - o ro co in o oj in —• o o ' o CO OJ O 00OJ r-4 r-4 OJ 0J 1 m in oj I—* i-h in ro 4 4 OJ ro ro oj o j

i i i i i 1 1 l l

-J -1 -J -Ji -H J O •> lH in co o •> O M \ l O •> ro in o j o r-4 cvj •> OJ i-h OJ OJOJ rH ro o j ro OJ r*— in oj ih r-H fH in ro 4 4 r -H O j o ro co cvj ro

I 1 i» » » s>

>0ao O ' r-H O 00 OJ cvj i-h o -h ro ro oj r-i o ro in 4 OJ OJ 4

OJ 0J r -H r - 4 CVJ OJ CVJ i-h i-h CVJ OJ OJ OJ r -H r-H OJ OJ r -H f—H

1 1 1 1 1 1 l l l l 1 1

vC in 4 OO rH M 00 v£> OJ M 'O OJ 4 o 0J 4 ro -H (VJ in o OJ 'Or-4 i 1 r-4 r-H in OJ r-H CO OJ f-H r-H 4 r-4 H 0JOJOJ OJ rH OJ so tn

1 1 1 1 1 I 1

M f 4 'O r-H r-H rH in (VJ -4 ro OJ f-t r-4 in 4 r-» f-H (VJ OJOI OJ r-4 OI 4 in in1 1 i 1» •> » »

1 » 1 1 1 i I I i i i

- 285 -

® 4 O O' O' co CT' Is- 4 o c- 4 -h rof—«(\j (\j I n ro oj co I —< ooi i i i i i i

v O 't H O O I M N r O n O H O »-« JOr—40jnj—4 ® ro — 4 O j r 0 r - 4 r - H r —t i cvj

® OJ r o 4 OJ r - 4 X) Oi r o J) OI ® OJLf> ® o r H i n OJ r^H OI f-H OJ r o o r—4 OJ1 r-H i i i 1 i I I r H 1I

® oj o- r- 4 Is - i—H O J •> 4 i f ) 4 4 4®o r—4 ® nj r—4 O J r-H o O J ro o r OJ

<-H •>

OI r-H o ®ro O I r—4 o O J ® 4 O I O 4r-H r H r—4 1 1 1 1 r-H r—4 —H f-H 1

1 1 1 1 1 1 1

® o ® ® 4 ® o ® ro O' o O' LO ro ro oj OI OJ cr r - OJ in ®< H J ) ro OJ OJ OJ r-4 ® 4 ro ro —4 OJ OJ f H r—4 1—H r—H r—4 ro ro r—4 OJi 1 l i 1 i 1 1 1 I 1 1

-J•>

o ® O OJ O' 4 ro — • 4 ® oi ro o ro ® ® r o ro 4 OJ r-H r—4 ® OJ L0 rHr-H LO ro OJ OJ 1 OJ OJ 4 4 ro i H ro 1 r-H OJ OJ r H r—4 r—4 f—4 OJ ro ro r—H ro

o or^H r—H

o ® NO ® ® r—4 0 0 N vO if) 4 ro in 4 OI r-H o ® Is - ® in OJ fH r—4OJ f H ^ H H 1 1 i l 1 l i H f-H r H r H r—4 1 1 1 i 1 1l i I i l l 1 l 1

to ro o ® in j) 4 O' Is- 4 r-H O' r H OI r - ro 9 9 r - ® ® ro m vOo ® r -rH CO r—H ro ® r- r—4 r—4 l fH r-H 4 OJ ro O J i rH h oi ro r H ro 4 «-H 4 f-H1 1 1 1 l 1 1 i I 1 I 1

_i _l4 O' ® 4 Is- O J o 4 4 r o OJ o ® OJ r-H <H >- ro ® 4 Is- 40 n OJ r*- cr-H O J r—4 ro v O ^ r—H OJ r—4 r—4 r-H O I

l® O J f-H CO O J r-H f-H r-H| »-H — 4 O J CO f-H CO 4 r H 4 r H

T' O'OJ ^ H 4 ro OJ r-H r—4 oi ro 4 in O' ® in 4 CO 4 Is- ^ H O O' ® m O J 4 in ® Is-r-H r—4 1 l 1 1 f H f-H r-H r-H OJ OI r-H r—4 *—41 1 i i i l i 1 1 1 i

® ro 4 in in r- in 4 ® O ' ® o ® 4 © Is - i-H r* - 4 ® r H ® O IO J 4 O J ro r H f H ^ f-H CO >“ 4 r—4 OI O J r H OJ ^ H r H ® ® CO O J — 4 CO1 1 i 1 1 l i I I i

-J•>c

O'O'OSoj 4- cvj ro

oj ao co oOJ •“* r—4I I

ni•>

O O' O'O N 00 !\1r—4 r—4 4 " r - H C O H *— 4

0 r**- ® in 4 ro oiH | I | | I I1

0 's0o»oo>04oors-| H O J r—4 r—4 r—4 1—4 f >* £ r *0

4 o j ^ s 0 i n 4 r o o i o jr-H r—l r—4 | | I | |

rol•>

O CO OJ 00oj r -* ro oj

oo «{> 4- ror—4 r—4 r—4 f 4

l l l l

C»C4'inr0r4iH(O0' ojrooj4--HOjrO'-H I I I I I

in oj ol \J H (\J H

Iuoo '4 r - r -^H 4 ro—•—i r o ^ ^ o j o j r oi

- oj •>4- o j roI I• —oo co

0 ' o o o j m r o o o 4 ' 0 ro oj 4 •“< oj ro <-h »-H

® f-® u n ro 4 tn r s»®r H r H r—4 r-H

l l l l

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r- 4 co oOJ • OJ •

O' 00 00 O'r H r H

4(7 'co r^ in® 4inH r H f l ' O ' t H M f O

l l l l

- 2 8 6 -

4 o O ro o CVJo - v O r o c v j n c v ji i

N o n |/) t >o cvj oj n rvj

4- !\l O ® >M Or-H r-H —H | |I I I

tvi n n H CVJ CVJ ’■” 4 r-H I

O CVJ o >t CVJ CVJ r-H r-H

x> 4 n ^ t i l l sO

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IT >}• ^ o SC Nr-H r-H r-H r-H | |l l l l

■—< CVJ >£> o O 4r-H r-H r-H (VJ CVJ r-H

l l l l

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OJ CVJ I CVJ

- 287 -

Figure 1 : A view of 1 ,8-dimethyl-2-naphthyl a c e t a t e .

Apical values Bond angles (°)

Others Bond lengths ( X )

3- 288 -

- 289 -

Figure 2 : C r y s t a l packing;

A v i e w down t h e h a x i s

- 290 -

< dX 5

< h zH? *

H aP 2P o

- 291 -

8 . 4 D i s c u s s i o n o f R e s u l t s

The o v e r a l l geom etry o f 1 , 8 - d i m e t h y 1 - 2 - n a p h t h y l

a c e t a t e (1,8-DMNA) d i f f e r s s i g n i f i c a n t l y from t h a t o f5

n a p h t h a l e n e b u t i s v e ry s i m i l a r t o t h a t o b s e r v e d i n0

1 , 8 - d i m e t h y l - n a p h t h a l e n e (1,8-DMN) ( F i g u r e s 1 and 3 ) . T h is

would imply t h a t t h e a d d i t i o n o f s u b s t i t u e n t s on t h e n a p h t h a

l e n e n u c l e u s i n p o s i t i o n s 1 and 8 h a s i n t r o d u c e d a d d i t i o n a l

s t r a i n in to t h e s y s te m a s a r e s u l t o f t h e s t r o n g nonbonded

i n t e r a c t i o n s be tw een t h e m e th y l s u b s t i t u e n t s .

The most marked d i s t o r t i o n s o c c u r a t t h e j u n c t i o n o f

t h e two benze n e r i n g s i n t h e n a p h t h a l e n e n u c l e u s . The

C1-C9-C8 v a l e n c e a n g l e i n 1,8-DMNA i s 1 2 5 .9 ° compared t o

1 2 5 . 2 ° i n 1,8-DMN. The C1-C9 and C8-C9 bond l e n g t h s a r e

o b s e r v e d t o be s i g n i f i c a n t l y l o n g e r t h a n t h e c o r r e s p o n d i n g

bond d i s t a n c e s i n n a p h t h a l e n e , w h i l e t h e C4-C10 and C5-C10

bond l e n g t h s a r e fou n d t o be c o r r e s p o n d i n g l y s h o r t e n e d .

In 1,8-DMNA, t h e i n n e r v a l e n c e a n g l e s C9-C1-C11 and

C9-C8-C16 a r e i n c r e a s e d from t h e i d e a l 120° t o 1 2 4 .1 ° and

1 2 4 . 8 ° r e s p e c t i v e l y , w h i l e t h e o u t e r a n g l e s C2-C1-C11 and

C7-C8-C12 a r e d e c r e a s e d t o 1 1 8 .1 ° and 1 1 6 .2 ° r e s p e c t i v e l y .

The C9-C1-C11 v a l e n c e a n g l e i s s m a l l e r t h a n t h e C9-C8-C16

v a l e n c e a n g l e , i n 1,8-DMNA, b e c a u s e f u r t h e r o p e n in g o f t h e

fo rm er a n g l e would l e a d t o more r e p u l s i v e i n t e r a c t i o n s

be tw een t h e o u t e r h y d ro gen on C11(H113) and t h e s u b s t i t u e n t

on C2. In 1,8-DMN, t h e i n n e r a n g l e i s i n c r e a s e d t o 1 2 4 . 8 °

and t h e o u t e r a n g l e i s d e c r e a s e d t o 1 1 6 . 2 ° . The a f o r e

m e n t io n e d d e f o r m a t i o n s r e s u l t i n t h e Cl . . . C8 and C l l . . .o o

C16 nonbonded d i s t a n c e s b e i n g 2 .5 6 5 A and 2 .9 6 5 A r e s p e c t i v e l y

- 292 -

F ig u r e 3 1 1 8 - d i m e t h , y l - n a p h t h a l ene

A p i c a l v a l u e s Bond a n g l e s ( S )

O t h e r s Bond l e n g t h s ( ° )

~ 293 -

- 294 -o o

i n 1,8-DMNA, and 2 .5 4 3 A, and 2 .9 3 2 A, r e s p e c t i v e l y ino

1,8-DMN, a s compared t o 2 .4 4 A, which i s t h e c o r r e s p o n d i n g

v a l u e f o r t h e s e d i s t a n c e s i n n a p h t h a l e n e .

The n a p h t h a l e n e n u c l e u s i n 1,8-DMNA i s e s s e n t i a l l y

p l a n a r (T a b le 6) a s t h e maximum r i n g t o r s i o n a n g l e (CO)

i s 3 ° , w i t h t h e sum o f t h e a b s o l u t e v a l u e s o f t h e t o r s i o n

a n g l e s , Zliol, b e in g 18° and t h e sum o f t h e s i g n e d v a l u e s

o f t h e t o r s i o n a n g l e s , b e in g 0 ° . The l a r g e s t d i s -o

p l a c e m e n t s from t h e mean p l a n e o f t h e r i n g i s 0 . 0 4 A a t o

C6 and - 0 . 0 3 A a t C8 (T ab le 7 ) . The l a r g e s t d e v i a t i o n fromo

t h e b e s t l e a s t - s q u a r e s p l a n e i n 1,8-DMN i s c a . 0 . 0 2 A.

Thus t h e s t e r i c s t r a i n , r e s u l t i n g from p e r i - i n t e r a c t i o n s ,

w i l l n o t be r e l i e v e d by a b u c k l i n g o f t h e n a p h t h a l e n e

n u c l e u s , i n t h e s e m o l e c u l e s . The s u b s t i t u e n t s on C l , C2

and C8 i n 1,8-DMNA d e v i a t e f rom t h e mean p l a n e o f t h e

n a p h t h a l e n e n u c l e u s . The C16 atom d e v i a t e s from t h e meano o

p l a n e by - 0 . 1 3 4 A, t h e C l l a tom d e v i a t e s t o +0.099 A, ando

014 atom by - 0 . 0 5 8 A, i . e . t h e C16 and 014 a tom s d e v i a t e

f rom t h e mean p l a n e i n an o p p o s i t e d i r e c t i o n from C l l a s

t h i s would h e l p t o d e c r e a s e t h e r e p u l s i v e - i n t e r a c t i o n s

be tw een t h e s u b s t i t u e n t s . In a d d i t i o n , t h e c a r b o n a tom s

b e a r i n g t h e m e th y l g ro u p s a r e a l s o f o r c e d o u t o f t h e p l a n e

o f t h e m o le c u le i n t h e d i r e c t i o n o f t h e s u b s t i t u e n t (T a b le

7 ) , r e s u l t i n g i n s l i g h t n u c l e a r d i s t o r t i o n s . T h i s o u t - o f -7

p l a n e d e f l e c t i o n e f f e c t i s o b s e r v e d i n 1 , 8 - d i n i t r o n a p h t h a l e n e8and 3 - b r o m o - l , 8 - d i m e t h y l n a p h t h a l e n e b u t n o t i n 1^8-DMN.

T h is must be due t o t h e e x t r a nonbonded i n t e r a c t i o n s o f t h e

s u b s t i t u e n t i n p o s i t i o n 2 which a r e p r e s e n t i n 1,&-DMNA b u t

- 2 9 5 -

a r e a b s e n t i n 1,8-DMN. In 1,8-DMNA, t h e a n g l e be tw een t h e

p l a n e s d e f i n e d by C11,C1,C8 and C16,C8,C1 i s 6 ° , which

p r o v i d e s f u r t h e r e v i d e n c e o f t h e o u t - o f - p l a n e b e n d in g of

t h e s u b s t i t u e n t s on Cl and C8 on o p p o s i t e s i d e s o f t h e

mean p l a n e o f t h e n a p h t h a l e n e r i n g .

The c o n f o r m a t i o n o f t h e m e th y l h y d ro gen a tom s on C l l

and C16 i n 1,8-DMNA and 1,8-DMN i s u n e x p e c t e d . The two

h y d ro g e n s on t h e o u t s i d e o f t h e C . . . C i n t e r a c t ion p r a c t i c a l l y

l i e i n t h e p l a n e o f t h e a r o m a t i c r i n g s w h i l e t h e o t h e r f o u r

h y d r o g e n s f a c e e ac h o t h e r i n p a i r s su ch t h a t t h e H . . . Ho

d i s t a n c e s a r e c a . 2 . 0 A ( F i g u r e 4 ) . S t r a i n e n e r g y m in im iz a -g

t i o n c a l c u l a t i o n s have shown t h a t t h i s i s i n d e e d t h e most

s t a b l e c o n f i g u r a t i o n f o r t h e m e th y l g ro u p s . T h i s

c o n c l u s i o n was a r r i v e d a t by s t a r t i n g w i t h d i f f e r e n t s t a r t

i n g o r i e n t a t i o n s o f t h e m e th y l g ro u p s . The r e s u l t i n g

m in im iz e d g e o m e t r i e s a l l had t h e same o r i e n t a t i o n o f t h e

m e th y l g ro u p s a s found i n t h e two c r y s t a l s t r u c t u r e s . T h is

c o n f i g u r a t i o n t h e n must m in im ize t h e H . . . H i n t e r a c t i o n s .

The c a l c u l a t i o n s a l s o i n d i c a t e t h a t t h e f i x e d o r i e n t a t i o n

o f t h e m e th y l g r o u p s i n t h e c r y s t a l s t r u c t u r e s r e s u l t s

from i n t r a - r a t h e r t h a n i n t e r - m o l e c u l a r f o r c e s .

T a b le 9 shows t h e v a l u e s o f c e r t a i n g e o m e t r i c p a r a m e t e r s

which a r e c o n s i d e r e d t o be i n d i c a t i v e o f p e r i - s t r a i n , f o r a

s e r i e s o f i n c r e a s i n g l y crowded Cl a n d / o r C8 s u b s t i t u t e d

n a p h t h a l e n e s . The o u t - o f - p l a n e b e n d i n g , 15-| | +

a p p e a r s t o be a lm o s t random and a l t h o u g h t h e g e n e r a l t r e n d

o f t h e l e n g t h e n i n g o f bonds Cl - C9 and C8 - C9 i s u p w ards ,

i t i s i r r e g u l a r , a s i s t h e accom panying r e d u c t i o n i n t h e

- 2 9 6 -

F ig u r e 4? A v ie w o f 1 , 8-d im e t h y l - 2 -n ap h th .y l a c e t a t e th r o u g h

t h e n a p h th a le n e r i n g .

- .297 -

(4) Me

REFERENCCU (51

ork(61

REFERENCES

02/N0t

REFERENCE 7

(6) t-rtu/t-O

u REFERENCE

- 2 9 8 -

X X X N \ N — X Xa n“O

» 3 a J n n m -x -T!n n nX.TJ33r i n nn n n m m n<-• yisi

n HX >_r IX.■-» ■"> J-* »—» ITS »“S XJ I-

a* ni cn cj rc •— V — ix•_/ w u «*-» <_» v-» w> v_/ cz vO•

ClX Xr* I-* -XXI• jo -x• « n‘\jfOMrofo\>ro*v> • *17 O* • • • • • • * • M X

a> o» o» 'ji cn ju ^ r» o> nM M N N O M O J ^ 09 X —1 OD 00

CO M-i n■■4 T~

CD aHi *oi n ■><D z> oom ►» »-* >-» »-» *-• ►» ►* 1 »>s\jrjf\3Poro?OA>f\> OS X X«o ^ >«OI Ol 01 PO zz 4~% > IX• • • • • • • • o U H0 « Q « O C 3 ! 0 S M m x m

D H 00X CO >r~ hi m xx o1<e

to xw oM »\J JVJ M ro IO fV> PO + • X« • • • • • • « — -#© O 0 3 0 ® ODCJOD 00v O M ^ O N O l ^ l v i —i>4W t a o o s o o i o <e o

>»o 03m*--«zo

lO N M N I O M I O M 8 >*« • • • • • • « -#•a»a>a»a»a»a»c»a» t-tC 4 U « > I O N U U ^ in •cfooc9<oa»fN>a»Ok i

3e-xj>o

-71-omoo*-•

J5> •COcB & sx& c a c a ca c a 7 —1““ 39Ol M*>fOO> < 9 S O >•m 0 M w » o i n s «-•

- 2 9 9 -

C4-C10, C5-C10 bond l e n g t h s . In c o n t r a s t , 9 8 anc*

Cl . . . C8 i i c r e a s e sm o o th ly w i t h i n c r e a s i n g c ro w d in g o f t h e

s u b s t i t u e n t s and a r e t h e o n ly c o n s i s t e n t i n d i c a t o r o f

s t e r i c c ro w d in g f o r p e r i - s u b s t i t u t e d n a p h t h a l e n e s .

9 10The c r y s t a l s t r u c t u r e s o f 1 - m e th y l , 1 - i s o p r o p y l3

and l , 8 - d i m e t h y l - 2 - n a p h t h y l a c e t a t e s s u p p o r t t h e h y p o t h e s i s

t h a t t h e r a t e o f a u t o x i d a t i o n o f t h e c o r r e s p o n d i n g n a p h t h o l s4

i s d e p e n d e n t on t h e s t e r i c s t r a i n p r e s e n t . I t i s however

p o s s i b l e t h a t a l t h o u g h t h e r e a c t i o n i s d r i v e n by r e l i e f o f

s t r a i n when t h e i n t e r m e d i a t e i s fo rm ed , s t e r i c f a c t o r s , i n

p a r t i c u l a r t h e a c c e s s i b i l i t y o f t h e r e a c t i o n s i t e , may be

o f some i m p o r t a n c e . The d i f f e r e n c e i n c o n g e s t i o n a t t h e

r e a c t i o n s i t e would i n c r e a s e w i t h t h e s i z e o f t h e a l k y l g roup

and would show a c o r r e s p o n d i n g d e c r e a s e i n r a t e , i n c o n t r a s t

t o t h e o b s e r v e d i n c r e a s e i n r a t e . The Wipke and Gund12s t e r i c c o n g e s t i o n a l g o r i t h m , which was d i s c u s s e d i n

C h a p te r 5 , was u s e d t o c h ec k t h e l a t t e r p o i n t and no s i g

n i f i c a n t i n c r e a s e i n c o n g e s t i o n i n p r o g r e s s i n g from t h e 1-

m e th y l t o t h e 1 , 8 - d i m e t h y l - 2 - n a p h t h y l a c e t a t e was found .

In o r d e r t o g a i n some i d e a o f t h e r e l a t i v e e n e r g i e s o f t h e

1 - m e th y l and 1 , 8 - d i m e t h y l compounds were computed by3

M.H.P. Guy a t t h e U n i v e r s i t y o f Glasgow u s i n g an nd hoc

f o r c e - f i e l d and t h e 1 - m e th y l compound was fo un d t o be o f

l o w e s t s t r a i n - e n e r g y and 4 . 5 k c a l . / m o l e more s t a b l e t h a n

t h e 1 , 8 - d i m e t h y l compound.

F i n a l l y , t h e r e i s no e v i d e n c e t o s u p p o r t t h e p r o p o s a l

o f B r i g h t e t a l t h a t p e r i - s t r a i n be tw een Cl and C8

s u b s t i t u e n t s i s t r a n s m i t t e d t o H4 and H5 by a b u t t r e s s i n g

- 300 -

mechanism i n v o l v i n g H2, H3, H6 and H7. Were t h i s t h e

c a s e t h e n one would e x p e c t t o f i n d s y s t e m a t i c d i s t o r t i o n s

o f t h e bond a n g l e s i n v o l v i n g t h e s e l a t t e r f o u r a tom s .

A l th o u g h t h e h y d ro gen a toms a r e r e l a t i v e l y p o o r l y d e f i n e d

by X -ra y a n a l y s e s , t h e f a c t t h a t no su ch d i s t o r t i o n s a r e3 9 10fo u nd i n t h e t h r e e a l k y l - 2 - n a p h t h y l a c e t a t e s * * ,

6 21,8-DMN and 1 , 8 - d i (bromomethy1) n a p h t h a l e n e makes t h i s

a rgu m en t r e a s o n a b l y c o n c l u s i v e . In any c a s e , i t i s

e x t r e m e l y u n l i k e l y t h a t t h i s h y p o t h e t i c a l s t r a i n t r a n s m i s s i o n

s y s te m would c o n c e n t r a t e i t s e f f e c t a t H4 and H5 b u t would

d i s t r i b u t e i t , i n s o f a r a s was p o s s i b l e , amongst a l l t h e

n a p h t h a l e n i c h y d r o g e n s . The key t o t h e n o n - p a r a l l e l C4-H4

and C5-H5 v e c t o r s i s c o n t a i n e d i n t h e l e n g t h e n i n g o f t h e

C1-C9 and C8-C9 bonds w i t h a c o r r e s p o n d i n g s h o r t e n i n g o f

C4-C10 and C5-C10 - t h i s p u s h e s C l l and C16 a p a r t and H4

and H5 t o g e t h e r w i t h o u t a f f e c t i n g H2, H3, H6 o r H7, su ch

t h a t , f o r i n s t a n c e H5, C5, C8 and C16 s t i l l l i e on a

s t r a i g h t l i n e and such would n o t be t h e c a s e i f a b u t t r e s s i n g

mechanism was o p e r a t i v e .

- 301-

8 . 5 . R e f e r e n c e s

1. V. BALASUBRAMANIYAN, Chem.Rev. , 6 6 , 567 (1966) .

2. J . B . ROBERT, J . S . SHERFINSKI, R.E. MARSH and J .D . ROBERTS,

J .O rg .C h em . , 39, 1152 (1974) .

3. D .N .J . WHITE, J . CARNDUFF, M.H.P. GUY and M.J. BOVILL,

A cta C r y s t . , B33, i n p r e s s (1977) .

4 . P .A . BRADY and J . CARNDUFF, Chem.Commun., 816 (19 7 4 ) .

5. G.S . PAWLEY and E.A. YEATS, Acta C r y s t . , B25, 2009

(1 9 6 9 ) .

6. D. BRIGHT, I . E . MAXWELL and J . de BOER, J . C . S . P e r k i n I I . ,

2101 (1 9 73 ) .

7. Z . A. AKOPYAN, A. I . KITAIGORODSKII and Yu.T. STRUCHKOy,

Z h . S t r u c t . Khim. , 6 , 729 (19 6 5 ) .

8 . M.D. JAMESON and B.R. PENFOLD, J .C h e m .S o c . , 528 (19 6 5 ) .

9. D .N .J . WHITE, J . CARNDUFF, M.H.P. GUY and M. J . BOVILL,

A c ta C r y s t . , B33, i n p r e s s (1 97 7 ) .

10. D .N .J . WHITE, J . CARNDUFF, P .R . MALLINSON, M.H.P. GUY

and M. J . BOVILL, A cta C r y s t . , B33, i n p r e s s (1977)

11. H. EINSPAHR, J .B . ROBERT, R. E. MARSH and J .D . ROBERTS,

A c ta C r y s t . , B29, 1611 (1 9 7 3 ) .

12. W.T. WIPKE and P. GUND, J .A m e r . Chem.Soc. , 9 8 , 8107

(1 9 7 6 ) .

13. J . HANDAL, J .G . WHITE, R.W.FRANCK, Y.H. YUH and N.L.

ALLINGER, J .A m e r .C h e m .S o c . , 99 , 3345 (1 9 7 7 ) .

- 3 0 2 -

CHAPTER NINE

The c r y s t a l s t r u c t u r e o f b i c y c l o ( 4 * 4 «l ) '1J -n d eca n e-l16 - d . i o l «

- 303 -

9 . 1 I n t r o d u c t i o n

X -ray c r y s t a l s t r u c t u r e a n a l y s i s ha s p l a y e d an

i m p o r t a n t r o l e i n t h e dev e lo pm en t o f c o n f o r m a t i o n a l a n a l y s i s

o f common- and m ed iu m -s ize d c y c l o a l k a n e s . ^ T h is t e c h n i q u e

g i v e s v e ry d e t a i l e d i n f o r m a t i o n a b o u t t h e geom e try o f

s u i t a b l e c r y s t a l l i n e d e r i v a t i v e s and t h u s e s t a b l i s h e s t h e

most s t a b l e c o n f o r m a t i o n t h a t a p a r t i c u l a r c y c l o a l k a n e can

a d o p t i n t h e s o l i d s t a t e . On a c c o u n t o f t h e f a c t t h a t

i n t r a m o l e c u l a r f o r c e s a r e u s u a l l y much s t r o n g e r than i n t e r -

m o l e c u l a r f o r c e s , t h e c o n f o r m a t i o n a d o p te d i n t h e s o l i d

s t a t e i s q u a l i t a t i v e l y s i m i l a r t o t h a t i n s o l u t i o n o r i n 2t h e gas p h a s e . T h is s t r u c t u r a l i n f o r m a t i o n i s n o t o n ly

o f c h e m ic a l i n t e r e s t b u t i t a l s o p r o v i d e s a c c u r a t e d a t a

that a r e e x t r e m e l y u s e f u l i n t h e p a r a m e t r i s a t i o n o f f o r c e -

f i e l d s , which a r e u s e d i n m o l e c u l a r m e c h a n ic s (MM)

c a l c u l a t i o n s . The r e s u l t i n g f o r c e - f i e l d s can t h e n be u se d

t o p r e d i c t , w i t h a c e r t a i n d e g r e e o f c o n f i d e n c e , g e o m e t r i c

and therm odynam ic p r o p e r t i e s o f t h e r a p i d l y i n c r e a s i n g

number o f n a t u r a l l y o c c u r r i n g compounds t h a t i n c o r p o r a t e

c y c l o a l k a n e s i n t o t h e i r m o l e c u l a r f ram ework . T h i s l a t t e r

t e c h n i q u e o f c a l c u l a t i n g t h e p r o b a b l e p r e f e r r e d c o n f o r m a t i o n

i s much q u i c k e r and l e s s e x p e n s i v e t h a n d e t e r m i n a t i o n o f i t

by X - ra y d i f f r a c t i o n . M oreover , t h e p r e f e r r e d c o n f o r m a t i o n

o f a c y c l o a l k a n e r i n g c a n n o t be d e t e r m i n e d by X -ra y c r y s t a l

s t r u c t u r e a n a l y s i s w i t h c e r t a i n t y i n some c a s e s , a s many o f

t h e p o s s i b l e c o n f o r m a t i o n s a r e a p p r o x i m a t e l y i s o e n e r g e t i c

and t h e o b s e r v e d c o n f o r m a t i o n depend s on t h e n a t u r e and3 4p o s i t i o n o f t h e s u b s t i t u e n t s on t h e c y c l o a l k a n e r i n g . 1

- 304 -

I t i s now w id e ly a c c e p t e d t h a t c o n f o r m a t i o n s o f

c y c l o h e p t a n e e x i s t i n f a m i l i e s o f c h a i r s and b o a t s ( F i g u r e 1 ) .

The two f a m i l i e s a r e s e p a r a t e d by a p o t e n t i a l e n e rg y b a r r i e r

o f £ a . 8 k c a l . / m o l e and t h e y c o n t a i n a number o f f l e x i b l e5

form s which a r e r e a d i l y i n t e r c o n v e r t i b l e . The C form o f—st h e c h a i r h a s an e x t r e m e l y s e r i o u s H . . . . H r e p u l s i o n

a c r o s s t h e a x i a l C3 and C6 p o s i t i o n s which i t may r e l i e v e

by p s e u d o r o t a t i o n t o t h e C,2 t w i s t - c h a i r . T here seems t o 5 6be a g re e m e n t * t h a t t h e most s t a b l e c o n f o r m a t i o n o f

c y c l o h e p t a n e i s a c t u a l l y t h e Cg t w i s t - c h a i r form, which h a s

l e s s t o r s i o n a l s t r a i n and l e s s nonbonded r e p u l s i o n s t h a n

t h e C c h a i r . For s i m i l a r r e a s o n s , t h e C0 t w i s t - b o a t form—Si s more s t a b l e t h a n t h e C§ b o a t . The b o a t f a m i l y i s l e s s

s t a b l e t h a n t h e c h a i r f a m i ly by a b o u t 3 -4 k c a l . / m o l e .

W i th in e ach f a m i l y , t h e C b o a t o r C c h a i r c o n f o r m a t i o n s—s —sa r e e n e rg y maxima 1-2 k c a l . / m o l e above t h e t w i s t - m i n i m a .

On t h i s b a s i s , H e n d r ic k s o n p r e d i c t e d t h a t c y c l o h e p t a n e

p s e u d o r o t a t e s i n t h e gas p h a s e a t room t e m p e r a t u r e and t h e

f a c t t h a t t h e c r y s t a l s t r u c t u r e s o f c a l c i u m c y c l o h e p t a n e -7

c a r b o x y l a t e p e n t a h y d r a t e and 1 - a m i n o c y c l o h e p t a n e - l -g

c a r b o x y l i c a c i d h y d ro b ro m id e m onohydra te a r e d i s o r d e r e d

and a p p e a r t o c o n t a i n a m i x t u r e o f c o n f o r m a t i o n s o f t h e

7 - r i n g s u g g e s t t h a t t h i s p r o c e s s may a l s o o c c u r i n t h e

s o l i d s t a t e when t h e h y d r o c a r b o n i s l i g h t l y o r n o n - s u b s t i t u t e d .

S e v e r a l X -ray a n a l y s e s o f n a t u r a l l y o c c u r r i n g g u i a n o l i d e s ,

which c o n t a i n c y c l o h e p t a n e r i n g s f u s e d t o c y c l o p e n t a n e and9 -1 3Y - l a c t o n e r i n g s , have been p e r f o r m e d and t h e r e s u l t s

i n d i c a t e t h a t t h e c y c l o h e p t a n e r i n g does n o t a lw a y s a d o p t

Chair Boat

F ig u r e 1 I

T w i s t - c h a i r T w is t - b o a t

Major c o n f o r m a t i o n s o f c y c l o h e p t a n e .

- 306 -

t h e C2 t w i s t - c h a i r form and , r e g a r d l e s s o f t h e a c t u a l

c o n f o r m a t i o n assum ed, a p p r e c i a b l e d e v i a t i o n s f rom t h eg

s y m m e t r i c a l fo rm s have been n o t e d - t h e s e two f e a t u r e s o f

t h e c y c l o h e p t a n e r i n g in c r y s t a l s t r u c t u r e s r e s u l t f rom t h e

s t e r i c r e q u i r e m e n t s o f t h e g r o s s s t r u c t u r e s b e in g

accommodated.

I t would t h e r e f o r e seem t h a t t h e minimum e n e rg y

c o n f o r m a t i o n (MEC) o f c y c l o h e p t a n e i s o n ly l i k e l y t o be

o b s e r v e d i n t h e c r y s t a l s t r u c t u r e o f a s u i t a b l e d e r i v a t i v e

i n which t h e 7 - r i n g i s l o c k e d i n t o t h e C2 t w i s t - c h a i r MEC.

I n s p e c t i o n o f D r e i d i n g m odels r e v e a l s t h a t two MEC

c y c l o h e p t a n e r i n g s can be 1 , 3 - f u s e d , i n a c i s m anner , t o

fo rm b i c y c l o ( 4 . 4 . l ) u n d e c a n e w i t h m in im a l c h a n g e s i n t h e

i n d i v i d u a l 7 - r i n g c o n f o r m a t i o n s . The c y c l o h e p t a n e r i n g s .

w i l l be l o c k e d i n t o t h e C2 - s y m m e t r i c t w i s t - c h a i r form and ,

b a r r i n g t h e i n t r o d u c t i o n o f any s e r i o u s s t e r i c c o m p r e s s io n

by 1 , 3 - f u s i o n , t h i s h y b r i d c o n f o r m a t i o n s h o u l d a l s o be t h e

MEC o f b i c y c l o ( 4 , 4 , l ) - u n d e c a n e .

An X - ray c r y s t a l s t r u c t u r e a n a l y s i s o f b i c y c l o ( 4 , 4 , 1 ) - 14u n d e c a n e - 1 , 6 - d i o l t h e r e f o r e n o t o n ly p r o v i d e s d e t a i l s o f

t h e MEC o f t h e p a r e n t h y d r o c a r b o n b u t a l s o p r o v i d e s

s t r u c t u r a l d e t a i l s o f t h e MEC o f c y c l o h e p t a n e . One m ig h t

e x p e c t a l s o t h a t t h e c o n f o r m a t i o n o f t h e 1 0 - r i n g would

c o r r e s p o n d t o one o f t h e p r e v i o u s l y s t u d i e d p o s s i b i l i t e s

. „ 9f o r c y c l o d e c a n e .

- 307 -

9 . 2 E x p e r i m e n t a l

C r y s t a l Data OH

OHB i c y c l o ( 4 , 4 , 1 ) u n d e c a n e - 1 , 6 - d i o l : C HQ 0

U n i t C e l l D im ens ions

a = 1 1 .7 3 A C* = p = y = 9 0 . 0 °

b = 1 1 .7 3 X

c = 1 5 .4 7 %

Space Group P 4 32 12 (D®) o r P 4 12 12 (D^)

M 1 8 4 .3 a .m .u . o 3

V 2129 A

Dm 1 .1 7 g cm"3

Dc 1 .1 5 g cm"3

X 0 .7 1 0 6 9 A

|l(M0 Ko. ) 0 . 8 3 cm"*

F (000) 816

The p o s s i b l e g ro u p s were d e t e r m i n e d by t h e s y s t e m a t i c

a b s e n c e s :

hOO when h = 2n +1, OkO when k = 2n + 1 and 001 when 1 ^ 4n.

The c r y s t a l u s e d i n t h i s a n a l y s i s was o f d im e n s io n s3

c a . 0 . 8 x 0 . 5 x 0 . 3 mm .

- 303 -

Data C o l l e c t i o n

I n i t i a l v a l u e s f o r t h e c e l l d i m e n s i o n s , o b t a i n e d from

p r e c e s s i o n p h o t o g r a p h s , were s u b s e q u e n t l y a d j u s t e d by a

l e a s t - s q u a r e s a n a l y s i s o f t h e a n g u l a r s e t t i n g s f o r a number

o f r e f l e c t i o n s m easu red on a H i l g e r and W at ts Y290 f o u r -

c i r c l e c o m p u t e r - c o n t r o l l e d d i f f r a c t o m e t e r . The i n t e n s i t i e s

o f 1087 in d e p e n d e n t r e f l e c t i o n s (9 < 30°) w i t h I * >, 3 (j ( D

w ere m ea su re d by means o f GO - 2 9 s c a n s which c o n s i s t e d o f 40

s t e p s o f 0 . 0 2 ° a t 2 s e c . / s t e p , w i t h b a ck g ro u n d c o u n t s f o r

20 s e c o n d s on e ach s i d e o f p e ak maximum and two s t a n d a r d

r e f l e c t i o n s b e i n g m easu red a f t e r e v e r y 40 i n t e n s i t y m e a s u r e

m en ts .

The d a t a i n t h e r a n g e 29 >,< 16° were a l s o c o l l e c t e d

w i t h r e d u c e d beam i n t e n s i t y so t h a t a l l o w a n c e c o u l d be made

f o r c o u n t e r e r r o r s . No c o r r e c t i o n s were made f o r

a b s o r p t i o n .

S t r u c t u r e A n a l y s i s

The c o o r d i n a t e s o f a l l t h e c a r b o n and oxygen a toms

were o b t a i n e d from an E-map c a l c u l a t e d w i t h t h e s e t o f p h a s e s

h a v i n g t h e h i g h e s t combined f i g u r e o f m e r i t p r o d u c e d by t h e

MULTAN d i r e c t p h a s i n g p ro g ram f o r t h e s p a c e g roup P4g2^2.

N o r m a l i s e d s t r u c t u r e f a c t o r s were d e r i v e d f rom t h e i n t e n s i t i e s ,o

on t h e b a s i s o f an o v e r a l l i s o t r o p i c t e m p e r a t u r e B2.0013 A

and t h e t r i p l e t r e l a t i o n s h i p s f o r t h e 240 r e f l e c t i o n s w i t h

E >/ 1 . 2 . The s t a r t i n g s e t o f 4 r e f l e c t i o n s (T a b le 1)

was s e l e c t e d by t h e p ro g ram on t h e b a s i s t h a t p h a s e s w i t h

a p r o b a b i l i t y i n e x c e s s o f 0 . 9 5 w ere a c c e p t a b l e and gave

OF STR

UCTURE

- 309 -

u i • • •SCQG

O O O f v ID • • •

bJ ^ V Ok CO CM Q—• on^gr s s• ■ • • • • • KCOO

O IO CM CM CM CM CM M. • •- •o ltl«4 0 KX IO IO IO

V) IO «B IO ID<onio

r> io iook« SOSUI • • • • • •

cr cc 52 CC CO O CM IOo o Ui «-» A A A

2 *•IO IO DC 1 LJUI UICM CM SSG UJ

■It O CM Si CM 0 * 0 0 O CML.Uk.cc cc »■ n&Gts 2 * G O G

UI wD ’-•IO Ui • * • O CM *<n io r> w* «-* U « biOIOO?

cr*-* cc -r-# * w-Z5 3 Z>X mo «*o «. 2 Ui u*_j _> _JCL (S3 fO ID IO O ~ ZD ZD

o> wqm str CO AO CM •HI u. u u o o cO CO *-• 1- C O O 0 3 0

»<K C & o r x xUI • • • Ui CO CO CO63 & C£ —1 2 3 ZD X X X

U J J Jt-Hh-Ui Z> ZD X MUMor OQ Q XX X

G C Go +■ or x x x c o o oUi X O GO 2 2 2co c r> IO WO C3 CM OM rkKCKGCC-< •-t wHI M Cc *-i o o o »-••-« *-«X 1- d i- 2 LiUUU»-KKn. u CM IS CM *• K 2 H u u u

Ui X Ui Ob.U.UiUIUiUJUiUIfaL —1 Ui o y y o 3 3 3 j j jo IL CM IO -*K O* CM o < UI O _I_I_IU U u.

Ui DC CO < < < Itt U U1- cr a: or o c r > > > oror erIU cr? c c UiH_iCO u lL h. 0 0 3 2 Z Z U U UM h C<<<CCO_ J f- _i _J Zir C k! u u<< «o -C '•r kox t r rM H Ci o1— *~ M •-»H t—t-~2 Ui Ui Uiht (O tr ac o0 0 2 •

UI Ui S3 o• • X X o O *HI CM ro ^ ID M>< CO H *—* U- « 4-2 LJUtUI UtUJUJ

- 310 -

r i s e t o 64 p h a s e s e t s .

The i n i t i a l s t r u c t u r e - f a c t o r c a l c u l a t i o n u s i n g t h e 1060

i n d e p e n d e n t s t r u c t u r e a m p l i t u d e s f o r which | Fq | ^ 4 q | F |

gave an R o f 22.2% and f u l l - m a t r i x l e a s t - s q u a r e s a d j u s t

ment o f t h e p o s i t i o n a l and i s o t r o p i c t h e r m a l p a r a m e t e r s o f

t h e n o n -h y d r o g e n a toms c o n v e r g e d a t R 12.4%. R was lo w e re d

t o 9 .6% when a n i s o t r o p i c t h e r m a l p a r a m e t e r s f o r t h e s e a toms

w ere u s e d . The p o s i t i o n s o f t h e h y d ro g en a tom s were

l o c a t e d i n a d i f f e r e n c e map and l e a s t - s q u a r e s r e f i n e m e n t

c o n t i n u e d w i t h t h e p o s i t i o n a l and i s o t r o p i c t h e r m a l

p a r a m e t e r s o f t h e h y d ro g en a tom s i n c l u d e d i n t h e model . A

w e i g h t i n g scheme o f t h e form W = 1 Io{ \ F q I ) was

employed and t h e r e f i n e m e n t c o n v e r g e d a t R = 3.8%. The

r a t i o o f o b s e r v a t i o n s t o p a r a m e t e r s was 5 . 3 t o 1.

9 . 3 . R e s u l t s

The c r y s t a l and m o l e c u l a r s t r u c t u r e s a r e shown i n

F i g u r e s 2 and 3 and t h e a to m ic c o o r d i n a t e s , t h e r m a l p a r a m e t e r s ,

bond l e n g t h s , v a l e n c y a n g l e s , t o r s i o n a n g l e s a l i s t i n g o f

t h e o b s e r v e d and c a l c u l a t e d s t r u c t u r e f a c t o r s a r e g i v e n

i n T a b l e s 2 - 7 .

Figure 2: The crystal packing viewed, down b.

I n t e r - m o l e c u l a r h y d r o g e n bonds a r e i n d i c a t e d

by b r o k e n l i n e s .

- 312 -

Figure 3 a) and (b) : Two views of the molecule in approximately

p e r p e n d i c u la r d i r e c t i o n s .

2)- 314 -

T a b le 2 : F r a c t i o n a l a to m ic c o o r d i n a t e s ( x 10^) w i t h e s t i m a t e d

s ta n d a r d d e v i a t i o n s i n p a r e n t h e s e s »

The h y d r o g e n a.toms a r e numbered a c c o r d in g t o t h e

atom s t o w h ich t h e y a r e a t t a c h e d *

The t a b l e sh o w s:

Atom x y z

- 317 -

0m* 0m* ««*

(VJ (VJ (VJ (VJ (VJ (VJ<-»

(VJ n ro eo ro (VJw ****

H r- ro O' Oo ro sD O' vO v£)00 OJ O' fH (VJ 400 GO vO vO vO p-

<—*AJ n fO ''O ro (VI

■***

CO ro vO 4 ’ o oro o o CO r^ (VJ(VI ro >o m o00 00 00 r - f - «o

<~k —>it— t (VJ ( 0 4 t i l *>*** «—« ■w »— •

u ( J o O u o

(VJ (VJ (VJ (VJ (VI (VJ>»»■—4 o (VI p - COo 00 4 o r—4 ro—H O' in ro 4 O'(VJ fH (VJ (VJ

ro ro (VJ (VI (VJ'w* No*00 r^ o *0 (VJ OvO ro CO ro (0 *—4O' (VJ O' o (VJ (VIp- O' O' o

jHGO O'

(VJ GO n GO rvj (VJ—-(VJ in O' >0 r-4 r -

h - CO o r - 30r - in (0 sO p-*- rolO in sO p" O'

o fH (VJp*- oo O' fH fH fH

O O u u o o 0(13

- 318 -

-r^ -»-*k

cr CM oo r*- CM ro 4 4 O' in CO COr>* CM O ro 4 —h o ro CM in 4 o 4ro 4 in 4 oo CM 00 4 r- o fH CM rHro ro CM ro CM ro r—1 pH CM CM rH ro

3 r- 4 3 3 rH r- CO 4 o p* O' r-CM CM ro CM ro CO CM CM CM ro CM CM CM

•w »»«' '»»■CM in CO CM o 4 O CM 4 r- r«- fH COrH ro xO 4 r- 00 o 00 rH CM sO o mro >0 CO f - CO CO CO O' CO in CO 4 xOCO 00 vO xO LO O in in r» O ' O' O'

a .*■* <“»00 O' V0 xO o o O' o in O' o o ccAJ CM fO AJ CO CO AJ <o AJ CM O CO AJw —* —» —* —*h- CM 4 CM 4 'O 4 O' r - CO CM 4 r-r—• n CM CM 00 O' CO O' rH 00 O in r-xO CO CM O' Is- O' CO in O ' o 00 xO CMr- 00 O' CO r- n >0 r- in in 4 in n£>

A *•1 r~V r~. —»r-H CM rH CM ^H CM rH CM fH AJ fH AJ r-H

AJ CM CO CO 4 4 n m f— r»- CO T> O'•w w w ^-r -■*X X X X X X X X X X X X X

- 319 -

H 30 ■4 30 O 4 h-rvj (VJ (V) (VJ***ro o o r - LO (VJ 00o (VJ O' 4 rH 00 inLO 00 vO CT' 0J ^4 in(VJ (VJ 1—t o (VJ O

00 2 00 sO Is- ro vO(VI (VJ (VJ (VJ (VJ ro cow W W4 in ro >0 H o ox> 4 4 00 sD 00 o

4 4 r- Is- 4 fHo o o 00 Is- o Is-

30 Is- o in Is- 4 ro(VJ (VJ ro (VJ (VJ (O ro-»-» —* w —» —-4 o (V sO Is- 0000 oo (VJ O Is- Is- 4o O' Is- X) ro in m>0 Is- r- Is- 30 0s vO

r H C\J rH OJ(VJ o o ^H rH 0J no f-H f-H f-H rH H H

X X X X X X X

- 320 -

T a b le 3 : Thermal p a r a m e te r s ( x 10^) w i th e . s . d . ! s in p a r e n t h e s e s .

Carbon and o x y g en v a l u e s a r e a n i s o t r o p i c *

H ydrogen v a l u e s a r e i s o t r o p i c *

The a n i s o t r o p i c t e m p e r a tu r e f a c t o r e x p r e s s i o n u s e d was

o f t h e form d e s c r i b e d by e q u a t io n ( 1 2 ) i n c h a p t e r s e v e n ,

t h e c o e f f i c i e n t s b e in g i n term s o f t h e mean sq u a r e

a m p l i t u d e s o f v i b r a t i o n U . .*

The t a b l e sh ow s:

Atom or' U U22 U33 U12 U13 U23

- 321 -

00 n (VJ (VI CO ro r H ^ t (VJf-H i—i rH i—• » H i—4 r-( fH— w w w •*-r — ' w - w w

o 4- O' X in (VJ >* f - 4 inro ro (VI r - r*- r*- in O' 00 >0 m >t O'i (VJ i i i i ^4

l1 i 1 H

o ro CO X o f-H in p>* o f H (VIi H i H #-H H r-H f-H ( H fH f H ^H fHw *—» ■— w ■*— —» —- w - w —r w V

(VJ i—i GO 0 0 i H (VJ o o sO o > t (VI ini H o fH (VJ ro r-H (VJ ro r-H ro ^ t (VI ro

i i H1

1 1 i i 1 i

fH vO 5 rH (VJ in in ro r-H •“4 infH fH rH rH r-H »H >H ^H rH Hw w w» w w ■—f —— w-in o (VI in O' r - o rvj in x ro (VI fH

#—4 fH in f-H I i X (VI r-H no (VI1 rH 1 (VJ fH fH

F k(VJ ro iH (VJ o fH ro o rH in in (VJfH rH (VI (VJ (VJ ^H H CVJ ru f—« fH rH fH^Ff ■W w» w» W N-TX >t in CO vO ro rH r-H O ' r*- 00 x O 'in r - ro x © ro (VI <t cr (VI x O'ro ro X r*- X ro ro X X >t ro in ro

X) r-H r - in <tF—Kr^ O 00 5 >t x CO

fH rH rvj fH rH r H fH CVJ r-H —« i-H r-H —«w — w w •—F •—» w "W — —F

(VJ O' 00 O' rH X r-H f-H o in r^- ro f-HX (VI o O in CO CVJ & x ro >t rH 00ro in X <r ro ro in n ft ro n X) sD

(VJ X) ao rH X ro ro X X h- ro (VJ Xf-H ^H fH (VJ rH rH fH ^H «“H rH F-H ^H rH—F ■r w W w •f-Ff —«■ w wo j X X © h - r - ^H f-H X o (VJ nr - r - ro X r*> o r - ro X X o - t (VJ(VI ro >t in >t ro (VJ ro >t >t ro ro in

o <-H (VJ rorH (VJ ro >* X X X o rH H H rH

s r r '—r

u O U O U O u o (J u O o o

J—L JrH o CO CO

r*- CO rH r - O' O ''rrr ««r

CD CVJ r - o inrHrH

rH oCVJ

r -CVJ

•—« (\J r-« fVJ ^ (\Jcvj (\j ro ro H- <fr

X X X X X X

o >£) CVJ CVJ in fH00 00 r - 00 00 O ' 00

CVJ in LO ru r- *> >*r - O ' r*- i H r - CO r-r H f H rvj r-H CVJ r-H

r H CM CM r H CM r-Hin in r**- r - 00 CO O'

X X X X X X X

_ _ __ #—H Xro X O' 3 C\jX r- X r- r- r—1 i— i'— ■— • •—• ■— — » — <•

X , \ J j r H oX fV <r J ' J- o y

— i r “ H \j —1 ■----4

- 324 -

T a b le 4 s I n t r a m o le c u la r bonded d i s t a n c e s (a n g s tr o m s) w i th

s ta n d a r d d e v i a t i o n s (a n g s tr o m s) i n p a r e n th e se s * .

O' rO 4 roro ro 4 4 CO roroo 00 o —•X)oCVJro roro ro c\jrororo ro COCVJCO CVJ CO ro 4-• 1—1 >-* •—* —It— ro "\J XT o 4 TO TO TO X) o CVJ 4- X> r-. 4“CO to O' O' X) O' TO S i fx. r—4 r* 4 in O 4 4 »“H

4—( TO O' O'O' O' O' o o O o o o o O O' n in3 • • • • • • • • • • • • • • • • •

o o o o 00 o o i—4 I—4 o 1—4 f—4 00 o o

c\jn r—* cvj <“■* rvj

<x r r r x r r r r x r r r E X i : i ; i :

xO o o -4 »-* rvj ro

< ' J U U J ' J J U J ' J U ' J J D U J 3 0

__ _ __ AJ o* TO ro 'O 4 /> /v 4 'O "0 TO t 4 4 "0 ro 4

• ■—« ■w >—• w w —* •—» >-»J— x» X. 3 \J o X) — 4 xv — 4 3 X. o o 1—4 XV o x>v/) CVJ ro ro n *V rvi 4 ro OJ 4 4 0J iH -o X) o o1—4 XV XV S i 4 n r> /V xv .0 Si 4 Si _n -0 o 3 o3 • • • • • • • • • • • • • • • • •

o o (V J 1—4 C O o r-H (VJ i—4

>— CVJ H i-S r-H -o 4 XV X ) fx. ^ -4 i—4 X) O v\J rvj ro4 3 3 3 o o CJ CJ o o CJ —> 3 o o r r r

^ >h \ j ro 4 in xt X) XT r - x> O' rvj \ j roO O O O -JC JO C JC JC JO O O O O O O

- 325 -

T a b le 5 : V a le n c y a n g l e s ( d e g r e e s ) w i t h t h e s ta n d a r d d e v i a t i o n s

( d e g r e e s ) i n p a r e n th e se s * .

—- —» —» —» —- —» r*- CO 3 r o OJ O O (T 00 3 X 4' O ' O ' 00 00 -0 h -CJ n j CVJ CVJ rvj rvj OJ CVJ (VJ OJ f-H f-H OJ OJ OJ OJ OJ OJ f-H rH f-H f-H OJ rH r-H f-H i-H 0 J rH rH

3 —• —» — — —r —r w w w w w w w — w w3 4 o CVJ CVJ vO r^- S> OJ f-H 00 OJ 3 OJ f-H 4 r o x 0 - X X O J ' x O' X 003 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •Z X —«4 4 sO rH 4- 3 r o o O ' rH 3 JO f-H r«- r-H X) f-H X) 4 X) X X 4 sO ro<L -h o -H 1—» rH «-H O —i f-H ■—H 3 H —4 o —H o -H 3 •-H o 3 o 3 o o 3 o o

C—« f—» f-H <H rH rH f-H f-H f-H i-H r-H r-H r-H f-H f-H r-H rH 4 f-H rH rH rH f-H f-H rH —H f-H

coz3 o f-H rH *H rH fH o rH>- OJ f-Hf-H 4 s r- f-H t—H r-H roOJ4 OJX3 4 4 x 3 X) O' 1 f-H x O' —• O'

3 3 3 3 3 3 3 3 3 3 3 3 X3 3 3 3 X3 3 3 3 X3 3 3 3 X3 3

cvjzO 3 o o►- H f H r H roXX £ XX r H 0 J 0 J 0 J roro 4 4 4 JO IX r - r - X X O' O' O' r H f-H< 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

r Hz rH f-Ho rH r H 0 J f-H r H -3 r H rH CVJ rH r H —4 f H v\J r H r H r H r H O J r H r H f H *H 0 J o o

r H r H 4 X rH f-H f H O ' O 0 J 0 J O J m r o 4 4 4 in JO r - 0- Is- XXO' O' O' f-H --H< 3 3 3 3 3 3 3 o 3 3 XXXXXXXXXXXX XXXXXXXX

—*. f— —N — X X O ' o o 3 o O ' O r ^ O' 3 X X X O ' O ' O ' X

', 1O j iVJ0J0J 0J OJ vOj OJ OJ 0J OJ f—H f-H f-H 0J r o OJOJ#H 0J <\j f-H OJrH rH OJfH rH rH rH

-U3 X o 4 3 X o X 4 XOJfs, 4 O X t ro X OJ 4

X 0J O ' r o H rO 4D • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •z f-H X X XX rH XXiV. > — i Xfs- 4 3 XX3 X X3 c ro X X4 o " 0< f-H z> ~3 f-H r-H *H 3 3 rH -H rH 3 —H 3 3 3 r“ H 3 3 rH 3 3 rH 3 <-H 3 3 H H 3

— i —4 -H ■-H ■—t H •—« —i H —i H —1 -H r—\ —H —H ---t -H -H H —4 — t rH -4 -H —4 —4 •H -H H

O r H r—I r H o(M f\| D H 00 > <“•3 3 3 3 0 3 3 0 3 3 3 3 3 3 3 r u d u u i u o u u x o o o o

cu3 — « O 3

_ _« -\J .4- £. £ £) N » ,-1 \ i \ J r ) -T) r t 4< 0 0 0 0 0 3 3 0 0 0 0 3 3 0 3 0 3 3 3 3 0 3 3 3 3 3 3 3 3 3

rHZC O 0 J O Jh— •H *H r-H4 3 o o

0 J \ JO OJ O J r n m O O j O j ( \ j O J O j O J O J O « O J { \ j O j ( \ ; O j O j O j r V O > i C O

-oojojcofOfr>44XiX;xr^rs-x x. x 0s o f-* —• o o o o o o o o o o o x r x r x x r x T X T T x r r x x r x

- 326 -

r- J5r—4 r-H oj J-

-d ■— •—-I O X) sD d

0 • • • •Z 0 0 00 ■£> v O

0 0 O 3v— < rH f H

roX f-H0 rHh- r-H X? r-H X X 0

CVJX0 rH f-H — » roi— r-H rH r H rH< 0 O U O

X rH OJD r-H rH f-H rof— H rH rH <Hc X X E X

* 00 O' rHCVJ r— ! rH— ' '— -<+) 00 > \J

m • • •D X) E> >*-H 0 O 0H H f—H — »

roX -1O O

rH r-H \jQ r-H

< X o u 0

rvjX3 O rH rH CVJ

—t rH rH rH

< 3 O 3 O

HX -VJ \J \J0 O rH rH 0JH- ~H H <-H -H

< X X X X

- 327 -

T a b l e 6 : T o r s i o n a n g l e s ( d e g r e e s ) w i t h t h e s t a n d a r d d e v i a t i o n s

( d e g r e e s ) i n p a r e n t h e s e s .

- 328 -

o» O 30 X X O J ' o ro 4 O' X f H (VI in (VI 0 0 r H Ox J CO ro rvj O J ro 4 ro cm ro ro ro ro - H r H - H r-H r-H —4 ( H r-H » H 4 (VI (VI ro (VJ (VI < o ro OJ OJ ro_ i ■"•T *—* H r H r H r H r H r n r H r H r H r n r HT HT w H r H r — * H r H r w —r

4 0 X s O 4 rvj O 0 O 00 N O 4 l / l 0 X X (VI (VI (VI X <jv (VI i n i n O H r H ro r-H ro X 4Z • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •4 X 4 n - x i f ) 4 r»- X> N r H 1 ) r-H —4 O 4 rvj X X X ro 0 X —4 (VI N- O J 0 - ro X r - X N- X

ro 0 n- 0 0 30 X sO x> r^ . 4 30 X N- X) 4 N> X X s. ID4 X 4 4 N- X X x N- 4 N- ro- n1 1 1 1 r-H 1 1 1 1 r H r H 1 1 1 1 r-H

11 • H

11 i—4

4x OJ OJ 0J OJ OJ 0J0 r—« (VI 0J OJ 0 0 0 r-H r-H r-H 0J r H OJ r H r-H OJ r-H rH 0Ji— .0 ; > 0 X 4 X i—H X O0 r H O r-H (VI OJ (VI r^H <—H r-H r-H r H r H r H ro 4 ro ro 4 >n 4 4 X X X< 0 0 CJ CJ CJ CJ CJ 0 CJ O CJ CJ x X X X X X X X X X X CJ X X X CJ X X X CJ X

<ox0 O o H —H 0 0 0 © f-H f H r H OJh — 0J ^H f H f-H ro X N- »-H 00 r-H 0J 0J OJ r H r H r H rH f H f H pH CO CO ro ro 4 4 4 4 x x x4 CJ CJ 0 CJ CJ <J J CJ CJ CJ CJ CJ CJ CJ CJ CJ CJ CJ CJ CJ CJ D J CJ CJ CJ J J J CJ j CJ J

rvjTO i —4 i - h —« —* rvi v\J C\J rvj "O ro CO >0 4 4 44 CJCJCJCJCJCJCJCJCJCJCJCJCJCJCJCJCJCJOCJCJCJCJCJCJCJIJIJCJCJCJOCJ

21r H OJ 0 ro 0 r H 0J r H 0J 0 OJ 0 r H f H 0J f H f H 0J r H rH- H OJH r-H r-H CO 4 if) r H r- x oo ^H f H r H OJ r H f H (VJr H r H r H r H (VI (VIOJOJ ro ro CO CO 4 4u u 0 CJ CJ CJ CJ CJ O CJ CJ CJ CJ CJ 0 CJ CJ 0 0 CJ 0 CJ CJ X r X CJ X X X CJ X X

,_, 0 O' N- N- N- N-JJ OJ CO CO ro 0J ro CO OJ CO 0 J 0 J (O -H fH fH r—» pH fH fH_JCO in «—• m 0 O X X © 4 rH 3 9 X 3 2 X XXXz • • • • • • • • • • • • • • • • • • •4 CO rH (X CO 0J OJ OJ X X XN- O XrH ( \ J © XXN-

XCD X4 X N» Xn- ro X X N- X (J' X X N» XXfH 1 rH 1 rH

11 rH 1 rH rH

l1 •H

X ao n (VJ o h o xr H r-4 < * 4 OJ O \ J OJ

'H m o ^ <h ^\ j . 0 OJ VI \ j cvj

N >0 N t/l >0 ^ ^ >C >£1 .0 X/ X)| | —H r H r H r H | rH

4X rH • H rH i H r H *“H0 © r H r H fH 0 O O rH f H f H 0J OJ OJ rH CM 0J rH OJ OJ rH*— .0 CO J ' X X X N- «"H X f H pH f H tVi OJ OJ f H H rH H r H H f-H f H CO O 4 O 4 4 x 4 X X4 - j CJ CJ CJ CJ CJ 0 CJ J J CJ x r X X -L_ X X X r X X X X J X X X CJ X X X

<"021O © —i - H r-H H 0 0 © —«r-H rH OJ OJt— OJ (VI rH r-H r H 4 X x r- r-H r H OJ OJ OJ r-H r H r H r H r-H rH r H r H >0 <0.0 ro 4 4 4 4 X X4 CJ CJ CJ CJ CJ CJ CJ CJ CJ O CJ 0 CJ CJ 0 CJ O CJ CJ CJ CJ O O CJ CJ CJ CJ CJ O CJ O CJ CJ

rvj51O(— rH iH H H H r'l /l l / l 'C 'O SO 30 rHHrHrHrHrHrHrHrHjHrHfVlfVJ OJ OJ (O (O (0 (O 4 44 a u u o u o o u o j o o u u u o u o ' j u o u ' j u o u ' J J u O u u o

X0 O (VI rH (VI HI CO 0 —• (VI H 0J O (VI H OJ OJ rH<VJ (VI rHH- rH «*H HH(VI fH (VJ 4 4 —» i i h n fH <H H (VI rH#H0J rH 0J H rH (VJ 0J 0J OJ (O (0 (O (O 44 CJ O CJ CJ o u u CJ CJ CJ 0 0 0 CJ 0 CJ CJ O 0 O O CJ CJ CJ X X X CJ X X X CJ X

IN ANNIES

U)- 329 -

O ' O ' O ' O X X p - X X X X**“»*X O r T O X X 0 O' (Jv X 0 X

A l OJ rH rvj —4 rH rH pH rH rH 4 4 rH OJ OJ OJ OJ OJ OJ OJ rH OJ OJ OJ- J w w —r w '—r *-» w - r—r w <«r v w >-»0 rH vO 0 X rvj < f OJ IX 0 —4 r o 4 X OJ 0 r o O OJ IX rH Xz • • • • • • • 0 • • • • • • • • • • • • • • • •< 4 rH X X ) r-H X X O ' OJ x O' O ' O' O ' X O 4 X O 4 X O 0 OJ

X X) in x 4 X X 4 X X 4 X X f^r X X X X X X X r*- X1 1 1 1 -H rH 1 1 1 rH 11

1 1 rH 1

T pH r H r H OJ -* OJ0 - H X —4 * H r H r H r-H r-H r^H X X OJ H OJ OJ f-H 0 OJ0 0 0»— ■X 1 H H r- N*. Is- i H r-H r H r H r H XXO' XO' 0 r-H O' r-H » H <H r-H< r cj 0 cj X X X X X X X X X X O X X X 0 X X x 0 X

xT0r- X X X X r-~ Is- Is-

• Hr-H

Xr-H X X X X O' J' 0 O'

< t 0 cj 0 0 0 u <J cj O CJ 0 O O •J CJ cj -J •J 0 J CJ j 4J 0

OJXO(—< CJCJCJCJCJCJCJCJCJ<JCJCJCJCJ<JCJCJCJ<J<JCJCJCJCJ

Xo OJ r-H r—i fVJ rH X X »—4 r-H OJ OJ r H OJ OJ r H OJ OJ

4 X X X X r-H r H X P-- r-H X f-H X Is- h - X X X X O'O' O'X X X X cj 0 0 CJ 0 O CJ 0 CJ X X X O X X X (J X X X

r H 0 O ' O O 0 0'"'K

O ' O ' O ' X 0 X O ' O ' O O ' CO P - O ' r - X■OJ X —1 O J OJ \ J O J O J r—H f-H r-H 4 OJ r-H lOJ OJ r—H OJ O J OJ rH r H OJ 01*«r —T * ■w —r "T' —- w - w - W - r* T *W »— —- -— —»

r H r - O ' O X X X X 0 O ' £> OJ X X X X X rH O O 0 O '• • • • • • • • • • • • • • • • • • • • • • • •

Is- r4 X 4 X f-H O X X OJ r—H O ' 4 O ' X 4 O ' r H « 0 rH O' f ' - 4 — 4X O r

X P -r H r H

X P -1

4 X XrH

X Xr-H

P- 4rH |

1—rH

X r -r-H1

4Xo rvj rH X OJ O) o j rHsO n r—* N - r-H |^ - ^c j r d u d r i

OJ OJ OJ r H OJ r-Hr-H r-H r-H X rH OJ r H r-H 0 OJ rH O 0 0H H r-H H X O' X X O' r H O' O' r-H f H rH Hr X X x r 0 x r r 0 r 1: r 0 X r

roXo »“H — 4 rH X

r H f-H r H r-H

CJ CJ CJ 0_n_n sDvO sD>- — rH -h r—t —t xjx)X)jo cj' 0 0 j 'u u u u u u u u u u u o u u u u u u u u u u u u

0 CJ O 0rH rH f-H »—HCJ CJ 0 CJ

OJXo 44X X X '0 'O X sO v o X '£> rs' f s-rs-fs- x x x x O ' O ' O ' O 'CJCJCJ<J<J<JCJ<JCJCJCJCJCJCJCJCJCJCJCJCJCJCJCJCJ

OJ OJ r H OJ OJ i H X X pH r H OJ r H r H OJ pH • H OJ4 4 X X X X »-« r H x f H h» X F- Is- r^ r- X X X X O' O' O'X X X X X U CJ O 0 0 O CJ u X X X u X X X CJ X X X TH

E ANGLE

IS OEfINEU

AS POSI

VIEWED

BOND *

ROTATED

ECLIPSE

- 330 -

T a b le 7 ? F i n a l s t r u c t u r e f a c t o r s

The t a b l e sh ow s:

L* F Fo c P h ase (° )

* r e f l e c t i o n s s o r t e d i n t o g r o u p s w i t h common

H,K i n d i c e s (show n i n each group h e a d in g )

- 331 -

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9.4 Discussion of Results

T h i s X - r a y c r y s t a l s t r u c t u r e a n a l y s i s o f b i c y c l o ( 4 , 4 , 1 )

u n d e c a n e - 1 , 6 - d i o l r e v e a l s t h a t t h e r i n g s y s t e m c o n s i s t s o f

t w o c y c l o h e p t a n e r i n g s , b o t h i n a t w i s t - c h a i r c o n f o r m a t i o n ,

f u s e d b a c k - t o - b a c k t o o n e a n o t h e r a c r o s s p o s i t i o n s 1 a n d 3 ,

a s d e f i n e d i n F i g u r e 1 . T h e m o l e c u l e p o s s e s s e s a n

a p p r o x i m a t e s y m m e t r y a x i s p a s s i n g t h r o u g h C ( l l ) n o r m a l

t o t h e p l a n e o f l e a s t i n e r t i a ( F i g u r e 3 ) .

M o l e c u l a r m e c h a n i c s c a l c u l a t i o n s , u s i n g t h e W h i t e -

1 5B o v i l l a l k a n e / a l k e n e f o r c e - f i e l d a n d a t w o - s t a g e N e w t o n -

R a p h s o n m i n i m i s a t i o n p r o c e d u r e w e r e p e r f o r m e d o n a n u m b e r

o f p l a u s i b l e c o n f o r m a t i o n s o f b i c y c l o ( 4 , 4 , l ) u n d e c a n e . T h e

g a s p h a s e MEC a p p e a r s t o b e a n e x a c t l y Cg s y m m e t r i c s t r u c t u r e

c o r r e s p o n d i n g v e r y c l o s e l y t o t h a t i n t h e s o l i d s t a t e a n d

t h e c a l c u l a t e d a n d o b s e r v e d g e o m e t r i e s a r e c o m p a r e d i n

F i g u r e 4 . T h e s h o r t e s t o b s e r v e d t r a n s a n n u l a r H . . . Ho

c o n t a c t s a r e 2 . 1 5 a n d 2 . 1 4 A b e t w e e n H ( 2 1 ) . . . H ( 9 1 ) a n d

H ( 4 2 ) . . . H ( 7 1 ) (C-H b o n d v e c t o r s c o r r e c t e d t o a l e n g t ho „ o

o f 1 . 0 8 A f r o m t h e f o r e s h o r t e n e d l e n g t h o f 0 . 9 9 0 A, w h i c h

i s o b s e r v e d i n t h e X - r a y a n a l y s i s ) a n d t h e c o r r e s p o n d i n go

c a l c u l a t e d v a l u e s a r e 2 . 2 1 A. T h e r e i s n o e v i d e n c e o f1 7 , 1 8

a n o m a l o u s m e t h y l e n e s c i s s o r i n g m o d e s i n t h e IR s p e c t r u m

o f s o l i d b i c y c l o ( 4 , 4 , 1 ) u n d e c a n e a n d s o by a n a l o g y w i t h

9 - t h i a b i c y c l o ( 3 , 3 , 1 ) n o n a n - 2 , 6 - d i o n e w h e r e t h e e f f e c t i s

a l s o a b s e n t a n d t h e d i s t a n c e i s k n o w n t o b e 2 . 0 7 8 f r o m a

1 9r e c e n t n e u t r o n d i f f r a c t i o n s t u d y , i t s e e m s r e a s o n a b l e t o

c o n c l u d e t h a t t h e a c t u a l d i s t a n c e s i n b i c y c l o ( 4 , 4 , 1 )o

u n d e c a n e a r e , a t l e a s t , g r e a t e r t h a n 2 . 0 7 A.

F i g u r e 4 ( a ) : The c a l c u l a t e d t o r s i o n a n g l e s ( d e g r e e s ) f o r t h e

b i c y c l o ( 4 « 4*1 ) u n d ec an e s y s te m a r e shown t o t h e

l e f t - h a n d s i d e o f each s e t o f num bers . The o b s e r v e d

t o r s i o n a n g l e s f o r b i c y c l o ( 4 « 4 * 1 ) u n d e c a n e - 1 f 6 - d i o l

a r e g i v e n t o t h e r i g h t o f each s e t o f numbers,

a l o n g w i t h t h e c o r r e s p o n d i n g e . s . d . ' s ( i n p a r e n

t h e s e s ) , M u l t i p l e t o r s i o n a n g l e s a r e d i s t i n g u i s h e d

by a p p e n d in g t h e l a b e l o f t h e f o u r t h atom t o t h e

v a l u e .

F i g u r e 4 ( b ) : The bond l e n g t h s ( 8 ) w i t h e , s . d . * s x 10^ and bond

a n g l e s ( d e g r e e s ) w i t h e . s . d . ’ s x 1 0 ,

- 348 -

- 349 -

Fiprare 4(*0

- 350 -

T o r s i o n a n g l e s a n d r e l a t i v e e n e r g i e s f o r t h e o t h e r

c a l c u l a t e d c o n f o r m a t i o n s a r e g i v e n i n T a b l e 8 . C o n f o r m a t i o n

I c o r r e s p o n d s t o a t w i s t - c h a i r c y c l o h e p t a n e r i n g f u s e d t o

a c h a i r c y c l o h e p t a n e r i n g a n d i s 4 . 8 8 k c a l . / m o l e h i g h e r

t h a n t h e MEC, o n a c c o u n t o f t h e u n f a v o u r a b l e t o r s i o n a l

i n t e r a c t i o n s , m a i n l y a s s o c i a t e d w i t h t h e c h a i r , a n d t h e

r e p u l s i v e n o n b o n d e d i n t e r a c t i o n s o f a t o m s a c r o s s t h e r i n g .

T h e s e s t r a i n c o m p o n e n t s a r e m i n i m i z e d , t o a l a r g e e x t e n t ,

b y b o n d a n g l e d e f o r m a t i o n . C o n f o r m a t i o n I I r e l a t e s t o a

t w i s t - c h a i r b e i n g 1 , 3 - f u s e d t o a b o a t a n d i s 4 . 3 4 k c a l . / m o l e

h i g h e r i n s t e r i c e n e r g y t h a n t h e MEC. T h i s d i f f e r e n c e c a n

b e a t t r i b u t e d , i n l a r g e p a r t , t o t h e n o n b o n d e d i n t e r a c t i o n s

a n d t o r s i o n a l s t r a i n t h a t c h a r a c t e r i s e t h e b o a t c y c l o

h e p t a n e r i n g , w h i c h i s c a l c u l a t e d t o b e 3 . 7 9 k c a l . / m o l e

l e s s s t a b l e t h a n t h e t w i s t - c h a i r 7 - r i n g . C o n f o r m a t i o n I I I

r e p r e s e n t s a t w i s t - c h a i r , w h i c h i s 3 , 5 - b r i d g e d by a t w i s t -

b o a t s a t u r a t e d 7 - r i n g a n d i s 6 . 4 3 k c a l . / m o l e l e s s s t a b l e

t h a n t h e MEC. Two c y c l o h e p t a n e b o a t s f u s e d b a c k - t o - b a c k ,

a s i n C o n f o r m a t i o n IV r a i s e s t h e s t e r i c e n e r g y w i t h r e s p e c t

t o t h e MEC b y 8 . 2 6 k c a l . / m o l e , w h i c h i s a p p r o x i m a t e l y t w i c e

t h e c a l c u l a t e d e n e r g y d i f f e r e n c e b e t w e e n t h e t w i s t - c h a i r

a n d b o a t c o n f o r m a t i o n s o f c y c l o h e p t a n e . Two c y c l o h e p t a n e

c h a i r c o n f o r m a t i o n s f u s e d t o g e t h e r r e s u l t i n t w o e x t r e m e l yo

s e r i o u s H . . . H i n t e r a c t i o n s ( c a . 1 . 0 A ) , w h i c h i n v o l v e t h e

f o u r 4 - a h y d r o g e n s ( s e e F i g u r e 1 ) o f t h e t w o c y c l o h e p t a n e

r i n g s , a n d a s s u c h , w o u l d a p p e a r t o b e e n e r g e t - i c a l l y u n s t a b l e .

T h e c o n f o r m a t i o n o f t h e t e n - m e m b e r e d r i n g i n b i c y c l o

( 4 , 4 , l ) u n d e c a n e - l , 6 - d i o l i s i n t e r e s t i n g b e c a u s e i t a p p e a r s

t o b e r e p r e s e n t a t i v e o f a c l a s s w h i c h h a s s o f a r e s c a p e d

- 351 -

TABLE 8: T o r s i o n a n g l e s ( d e g ) a n d s t e r i c e n e r g i e s r e l a t i v e

t o t h e MEC ( k . c a l . m o l ~ ^ ) f o r s o m e l o w - e n e r g y c o n f o r m a t i o n s

o f b i c y c l o ( 4 , 4 , 1 ) u n d e c a n e •

I I I I I I I V

wl 0 , l , 2 , 3- 5 6 - 1 6 2 - 1 5 1 - 1 5 6

“1 , 2 , 3 , 4 - 5 9 7 3 7 2 6 8

w2 , 3 , 4 , 5- 8 - 6 - 1 3 0

* 3 , 4 , 5 , 67 0 - 6 9 - 6 4 - 6 8

* 4 , 5 , 6 , 7 5 7 1 7 0 1 6 8 1 5 5

“ 5 , 6 , 7 , 8- 1 2 0 - 1 0 8 - 5 3 - 1 5 6

* 5 , 6 , 1 1 , 16 0 5 0 51 6 4

* 6 , 7 , 8 , 958 49 - 3 4 6 8

* 7 , 8 , 9 , 1 0 - 8 7 - 8 8 - 3 3 0

u;8 , 9 , 1 0 , l 6 3 7 0 7 6 - 6 8

* 9 , 1 0 , 1 , 2 8 5 7 8 6 0 1 5 5

" 1 0 , 1 , 1 1 , 6 7 5 7 6 6 8 6 4

E 4 . 8 8 4 . 3 4 6 . 4 3 8 . 2 6s

- 352 -

a t t e n t i o n . T h e l o w - e n e r g y c o n f o r m a t i o n s o f c y c l o d e c a n e

5 2 0s t u d i e d by H e n d r i c k s o n a n d o t h e r s , a r e e i t h e r a s y m m e t r i c

o r h a v e m i r r o r p l a n e s / t w o - f o l d a x e s b i s e c t i n g b o n d s a n d / o r

p a s s i n g t h r o u g h a t o m s . I n t h e p r e s e n t i n s t a n c e , t h e s o l e

s y m m e t r y e l e m e n t i s a t w o - f o l d a x i s p a s s i n g t h r o u g h t h e

c e n t r e o f t h e r i n g a n d t h e c o n f o r m a t i o n r e s e m b l e s a t r a n s ,

t r a n s - c y c l o d e c a - 1 , 6 - d i e n e v a r i a n t w h i c h w a s d i s c u s s e d i n2 i

C h a p t e r 3 a n d w h i c h i s o n l y 2 . 4 0 k c a l . / m o l e l e s s s t a b l e

t h a n t h e MEC c o n f o r m a t i o n o f c y c l o d e c a n e , t h e BCB. T h e

g e o m e t r y ( d e r i v e d f r o m MM c a l c u l a t i o n s ) o f t h e o b s e r v e d

1 0 - r i n g c o n f o r m a t i o n i s s h o w n i n F i g u r e 5 .

22An a l g o r i t h m , d e r i v e d by C r e m e r a n d P o p l e , p r o v i d e d

a m e a n s w h e r e b y i t w a s p o s s i b l e t o c o m p a r e t h e v a r i o u s

o b s e r v e d a n d c a l c u l a t e d c y c l o h e p t a n e s t r u c t u r e s w i t h t h e

c a l c u l a t e d C2 s y m m e t r i c t w i s t - c h a i r MEC w h i c h i so

c h a r a c t e r i s e d b y a m p l i t u d e s q 2 = 0 . 4 9 9 , = 0 . 6 7 3 A a n d

p h a s e a n g l e s <|>2 = 2 7 0 ° , = 2 7 0 ° . T h e g e o m e t r y i s n o t

s i g n i f i c a n t l y d i f f e r e n t t o t h a t c a l c u l a t e d by o t h e r w o r k e r s ,

a n d t h e r e f o r e f o r m s a v a l i d r e f e r e n c e p o i n t f o r t h e f o l l o w

i n g d i s c u s s i o n . T h e a m p l i t u d e s a n d p h a s e a n g l e s f o r t h e

t w o o b s e r v e d 7 - r i n g s o f b i c y c l o ( 4 , 4 , 1 ) u n d e c a n e s y s t e m a r e

° o ° o0 . 5 1 2 , 0 . 6 4 4 A, 2 7 3 , 2 7 1 ° a n d 0 . 5 3 5 , 0 . 6 3 0 A, 2 7 1 , 2 7 0

oa n d t h e c o r r e s p o n d i n g c a l c u l a t e d v a l u e s a r e 0 . 5 1 2 , 0 . 6 5 6 A,

2 7 6 , 2 7 2 ° . A l t h o u g h t h e v a l u e s o f q 9 a n d q v a r y s l i g h t l y( 2 \ ^

f r o m 7 - r i n g t o 7 - r i n g , t h e v a l u e o f Q J f o rm

+ oe a c h r i n g i s n e a r l y c o n s t a n t a t 0 . 8 3 - 0 . 0 1 A , s o t h a t 1 , 3

f u s i o n a p p e a r s t o h a v e l i t t l e e f f e c t o n t h e t o t a l p u c k e r i n g

a m p l i t u d e . T h e d i f f e r e n c e s b e t w e e n t h e c a l c u l a t e d q a n d (j)

- 353 -

f i g u r e 5 » 'The c a l c u l a t ed c y c l o d e c a n e c o n f o r m a t i o n d e r i v e d from

t h e l O - r i r # o f o i c y c l o ( 4 . / r. l ) u n d e c a n e .

- 354 -

f o r c y c l o h e p t a n e a n d b i c y c l o ( 4 , 4 , 1 ) u n d e c a n e s y s t e m i n d i c a t e

a s m a l l a m o u n t o f d i s t o r t i o n c o n s e q u e n t u p o n f u s i o n o f t h e

t w o t w i s t - c h a i r 7 - r i n g s t o f o r m t h e b i c y c l i c m o l e c u l e , s o

t h a t t h e o b s e r v e d c o n f o r m a t i o n s p r o b a b l y d o n o t c o r r e s p o n d

e x a c t l y t o t h e MEC o f c y c l o h e p t a n e a l t h o u g h t h e d e v i a t i o n

i s s m a l l .

D i f f e r e n c e s b e t w e e n t h e t w o o b s e r v e d 7 - r i n g s a m o u n t t o

< A l > = 0 . 0 0 8 A, <AQ>= 0 . 5 ° a n d <,A<*>> = 1 . 5 °

c o m p a r e d w i t h 3 < C J ( l ) > = 0 . 0 1 2 8 , 3 < O (0)^>= 0 . 6 ° a n d

a n g l e a n d t o r s i o n a n g l e . I t c a n t h e r e f o r e b e d e d u c e d

t h a t , w i t h o n e e x c e p t i o n , t h e d e p a r t u r e o f b i c y c l o ( 4 , 4 , 1 )

u n d e c a n e - 1 , 6 - d i o l f r o m C^ m o l e c u l a r s y m m e t r y a r e p r o b a b l y

n o t s i g n i f i c a n t i n t h e s o l i d s t a t e . T h e e x c e p t i o n c o n c e r n s

t h e o r i e n t a t i o n o f t h e 0 - H b o n d v e c t o r s ( s e e F i g u r e 3 ) w h i c h

m i g h t b e e x p e c t e d t o v a r y i n d e p e n d e n t l y i n o r d e r t h a t t h e

i n t e r m o l e c u l a r h y d r o g e n b o n d i n g i s o p t i m i s e d .

2 3An a n a l y s i s o f t h e t h e r m a l m o t i o n p a r a m e t e r s o f t h e

n o n - h y d r o g e n a t o m s o f b i c y c l o ( 4 , 4 , 1 ) u n d e c a n e - 1 , 6 - d i o l w a s

c a r r i e d o u t a n d t h e c o m p o n e n t s o f t h e t r a n s l a t i o n ( T ) ,

l i b r a t i o n (L) a n d s c r e w ( S ) t e n s o r s a r e g i v e n i n T a b l e 9 .~ — o b s

T h e r e a s o n a b l e a g r e e m e n t b e t w e e n t h e r . m . s . G ) o f

0 2 o b s c a l c g J0 . 0 0 1 5 A a n d t h e c a l c u l a t e d v a l u e ^ ( U j j ~ ^

2*= 0 . 0 0 2 4 A i m p l i e s t h a t t h e b i c y c l i c s y s t e m b e h a v e s a s

a r i g i d b o d y a n d i s n o t d i s o r d e r e d . T h e e i g e n v e c t o r

c o r r e s p o n d i n g t o t h e l a r g e s t e i g e n v a l u e o f t h e L t e n s o r i s

a l m o s t e x a c t l y p a r a l l e l t o t h e v e c t o r b e t w e e n t h e t w o

o x y g e n a t o m s , s o t h a t t h e i n t e r m o l e c u l a r h y d r o g e n b o n d s a r e

- 355 -

TABLE 9 : C o m p o n e n t s o f t h e t r a n s l a t i o n ( T ) , l i b r a t i o n ( L ) a n d

s c r e w (jS) t e n s o r s d e s c r i b i n g t h e r i g i d b o d y m o t i o n o f

b i c y c l o ( 4 , 4 , 1 ) u n d e c a n e . A l l v a l u e s x l O 4

C o m p o n e n t s E i g e n v a l u e s E i g e n v e c t o r s

3 0 7 33 28 3 4 8 7 1 6 6 4 6 6 8 5 1 8 3

T. . 2 5 5 3 9 2 6 5 - 6 8 4 6 3 2 8 6 6 5 0 6

2 7 5 2 2 3 1 3 3 4 - 8 2 1 1 5 5 5 0

7 1 - 9 6 7 6 9 0 2 2 - 2 7 0 1 3 3 6 3

L . . 41 - 5 5 4 - 3 6 4 3 - 5 9 7 9 2 9 4

56 3 8 - 2 3 0 9 - 9 6 1 0 - 1 5 2 3

- 1 5 0 2

S . .*3

o b s y c a l c x i j ~ i 3 ( U ° b S ) ) 2 >2

° 2 2 4 A

° 2 1 5 Az

o 2 2 ®T h e t e n s o r c o m p o n e n t s a r e i n u n i t s o f A ( T ) , r a d ( L ) a n d r a d A ( s )

e i g e n v e c t o r s a r e r e f e r r e d t o t h e m o l e c u l a r i n e r t i a l a x e s s h o w n

i n F i g u r e 2*

- 356 -

minimally perturbed by this librational mode in a similar24way to those in cyclodecane-1,6-diol.

- 357 -

9.5. References

1 . J . D . DUNITZ, P e r s p e c t i v e s i n S t r u c t u r a l C h e m i s t r y , 2 ,

l - » 7 0 ( 1 9 6 8 ) . ( J . D . D u n i t z a n d J . A . I b e r s , e d i t o r s )

New Y o r k : J o h n W i l e y .

2 . E . HULER a n d A. WARSHEL. A c t a C r y s t . , B 3 0 , 1 8 2 2 ( 1 9 7 4 ) .

3 . M. BIXON, H. DECKER, J . D . DUNITZ, H. ESER, S . LIFSON,

C.MOSSELMAN, J . SICHER a n d M.SVOBODA, Chem .Com m un. ,

3 6 0 ( 1 9 6 7 ) .

4 . J . D . DUNITZ a n d H.M .M . SHEARER, H e l v . C h i m . A c t a , 4 3 ,

18 ( 1 9 6 0 ) .

5 . J . B . HENDRICKSON, J . A m e r . C h e m . S o c . , 8 9 , 7 0 4 7 ( 1 9 6 7 ) .

6 . R . PAUNCZ a n d D. GINSBURG, T e t r a h e d r o n , 9 , 4 0 ( 1 9 6 0 ) .

7 . W. M. J . FLAPPER a n d C. ROMERS, T e t r a h e d r o n , 3 1 , 1 7 0 5 ( 1 9 7 5 )

8 . K. K. CHACKO, R . SRINIVASAN a n d R . ZAND, J . C r y s t .

M o l e c . S t r u c t . 1, 2 1 3 ( 1 9 7 1 ) .

9 . ; A . T . McPHAIL a n d G . A . SIM, T e t r a h e d r o n , 2 9 , 1 7 5 1 ( 1 9 7 3 ) .

1 0 . J . D . M . ASHER a n d G.A,. SIM, J . C h e m . S o c . , 1 5 8 4 ( 1 9 6 5 ) .

1 1 . MAZHOR-UL-HAQUE a n d C . N . CAUGHLAN, J . C h e m . S o c . , B . , 9 5 6

( 1 9 6 9 ) .

1 2 . MAZHOR-UL-HAQUE a n d C . N . CAUGHLAN, J . C h e m . S o c . , B. , 3 5 5

( 1 9 6 7 ) .

1 3 . A . T . McPHAIL a n d K . D . ONAN, J . C h e m . S o c . , P e r k i n I I ,

i n p r e s s f ( 1 9 7 7 ) .

1 4 . D . N . J . WHITE a n d M . J . BOVILL, A c t a C r y s t . , B 3 3 , i n p r e s s

(1977).

1 5 . D . N . J . WHITE a n d M . J . BOVILL, J . C h e m . S o c . , P e r k i n I I ,

i n p r e s s ( 1 9 7 7 ) .

1 6 . D . N . J . WHITE a n d 0 . ERMER, C h e m . P h y s . L e t t e r s , 3 1 , 1 1 1

( 1 9 7 5 ) .

1 7 . J . MARTIN, P h . D . T h e s i s , U n i v e r s i t y o f G l a s g o w , 1 9 7 4

1 8 . R . K . MACKENZIE., D . D . MACNICOL, H. H. MILLS, R .A .RAPHAEL,

F . B . WILSON a n d J . A . ZABKIEWICZ, J . C h e m . S o c . , P e r k i n I I ,

1 6 3 2 ( 1 9 7 2 ) .

1 9 . M . J . BOVILL, P . J . COX, H . P . FLITMAN, M . H . P . GUY, A . D . U .

HARDY, P .McCABE, G . A . SIM a n d D . N . J . WHITE, A c t a C r y s t . , B ,

i n p r e p a r a t i o n ( 1 9 7 7 ) .

2 0 . 0 . ERMER, S t r u c t u r e a n d B o n d i n g , 2 7 , 1 6 1 ( 1 9 7 6 ) .

B e r l i n : S p r i n g e r - V e r l a g .

2 1 . D . N . J . WHITE a n d M . J . BOVILL, T e t r a h e d r o n L e t t e r s , 2 2 3 9 ,

( 1 9 7 5 ) .

2 2 . D. CREMER a n d J . A . POPLE, J . A m e r . C h e m . S o c . , 9 7 , 1 3 5 4

( 1 9 7 5 ) .

2 3 . V. SCHOMAKER a n d K . N . TRUEBLOOD, A c t a C r y s t . , B 2 4 , 6 3

( 1 9 6 8 ) .

2 4 . 0 . ERMER, J . D . DUNITZ a n d I . BERNAL. A c t a C r y s t . ,

B 2 9 , 2 2 7 8 ( 1 9 7 3 ) .

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