Conformational Analysis

Carey & Sundberg: Part A; Chapter 3

• The different arrangements of the atoms in space that result from rotations of groups about single bonds are called conformations of the molecule.

CO2HMe

H

CO2HMe

H

CO2HMe

H

MeH

HO2C

HO

Et

Me

OH

Me

Et

Conformational analysis

CO2HMe

H

CO2HMe

H

CO2HMe

H

MeCO2H

H

HO

Et

Me

OH Et

Me

Different conformations

Different configurations

•An analysis of the energy changes that a molecule undergoes as groups rotate about single bonds is called conformational analysis.

Conformations of ethane

C C

H

HH

H

H

600

C C

H

HH

H

H

H

600

600

Staggered conformation Eclipsed conformation

Wedge-and-dash structures

Sawhorseprojections

Newmanprojections H

H

H

H

HH

H

H H

H

HH

H

H H

H

H HH

H H

H

HH

H

The single parameter differentiating such conformers is an angle between two planes that contain atoms ABC and BCD in themselves. This dihedral angle is called a "torsion" angle and is most frequently used for specification of the type of conformations.

Torsion or Dihedral angle

Potential energy of ethane as function of torsion angles

•staggered conformation has potential energy minimum •eclipsed conformation has potential energy maximum • staggered conformation is lower in energy than the eclipsed by 2.9 kcal/mole (12 kJ/mole)

•The H-atoms are too small to get in each other’s way-steric factors make up < 10% of the rotational barrier in ethane

Why is the eclipsed conformation higher in energy than the staggered conformation?

Torsional strain

Caused by repulsion of the bonding electrons of one substituent with the bondingelectrons of a nearby substituent

filled orbitals repel

Stabilizing interaction between filled C-H bond and empty C-H * antibonding bonding orbital

The real picture is probably a mixture of all 3 effects

• The rotational barrier is (12 kJ/mol) small enough to allow the conformational isomers to interconvert million of times per second

Conformations of butane

Potential energy of butane as a function of torsion angle

C

DB

A

A “synclinal” or “gauche”B “anticlinal” C “anti-periplanar” or “anti”D “syn-periplanar” or “fully eclipsed

No torsional strain as the groups are staggered and CH3 groups are far apart

van der Waals forces between two CH3 groups are repulsive: the electron clouds repel each other which accounts for 0.9 Kcal/mole more energy compared to anti conformer

Highest energy due to torsional strain and large van der waals repulsive force between the CH3 groups

D “syn-periplanar” or “fully eclipsed

C “anti-periplanar” or “anti”

A “synclinal” or “gauche”

B “anticlinal”

torsional strain and large van der waals repulsive forces between the H and CH3 groups

• Calculations reveal that at room temperature ~72% of the molecules of butane are in the “anti” conformation, 28% are in “gauche” conformation

n-Butane Torsional Energy Profile

+3.6

+5.1

+0.88Ref = 0

G

E1E2

H

C

Me

HHH

Me

C

Me

H H

H

Me

H

Me

C

Me

H

C

H

H

HH

HH

H

Me

Me

e n e r g yA

gaucheconformation

staggered conformation

E = +0.88 kcal/mol

CH

H Me

Me

H

H

CH

Me H

Me

H

H

H

H

H

H

CH3

H

H

H

H

H

H

H

H

CH3

H

H

staggered conformation

gaucheconformation

Butane in “Chair” Form

H

H

H

H

CH3

H

H

H

H

H

H

H

H

CH3

H

H

staggered conformation

gaucheconformation

H

H

H

H

CH3

H

H

H

gaucheconformation

CH3

H

HH

HH

CH3

H

HH

HH

H

H

H

H

H

CH3

H

H

staggered conformation

H

H

HH

HCH3

H

H

HH

HCH3

CH3

H1,3-diaxial

A 1,3-diaxial interaction is the same as a gaucheconformation!!

CH3

An equatorial substituent is more stable because it is in the staggered conformation.

Conformations and Conformers

Butane can exit in an infinite number of conformations (6 most important have been considered), but has only 3 conformers (potential energy minima)-the two “gauche”conformations and the “anti” conformations

• The preference for a staggered conformation causes carbon chains to orient themselves in a zig zag fashion, see structure of decane

n-Pentane

Anti-Anti

Gauche-Anti

Gauche-Gauchedouble gauche pentane or "syn-pentane"

Me Me

H Me

Me

H H

MeMe

H H

Me Me

The Syn-Pentane Conformation

G = –5.5 kcal/mol

syn-pentane = G– 2 gauche = 5.5 –2(0.88) = + 3.7 kca/ mol

CH3

CH3 H

CH3

CH3 H

CH3

CH3 H

CH3

CH3

CH3

CH3

CH3

CH3

H3C

H3C

fully staggered2 gauche and 1 syn-pentane

gauche gauche syn-pentane

The syn-Pentane Interaction - Consequences

Me

Me Me

OH

Me

O

OH Bourgeanic acid

Using our knowledge of acyclic conformational analysis, we can predict the conformation found in the crystal state of a bourgeanic acid derivative.

The syn-Pentane Interaction - Consequences

Me

Me Me

OH

Me

O

OH Bourgeanic acid

avoid syn-pentane!

Using our knowledge of acyclic conformational analysis, we can predict the conformation found in the crystal state of a bourgeanic acid derivative.

Conformation and hydrogen bonding

Conformation of butane-2,3-diols

CycloalkanesRing strain

No of atoms in ring

Internal angle in planar ring

109.50-internal angle*

345678

600

900

1080

1200

128.50

1350

49.50

19.50

1.50

-10.50

-190

-25.50

All internal angles 109.5 0C

* a measure of strain per C-atom

•Ring strain largest for 3-membered rings, then decreases through a 4-membered ring and reaches a minimum for 5-memberd ring.

•Prediction: planar 5-membered ring should have the minimum level of ring strain.

•The ring strain keeps on increasing as the rings get larger after the minimum at 5

109.50-internal angle

3 49.50

4 19.50

5 1.50

6 -10.50

7 -190

8 -25.50

H

• the difference between any two in series is very nearly constant at around –660 kJ/mole

• assuming there is no strain in the straight-chain alkanes, each extra –CH2 group contributes an extra 658.7 kJ/mole to the heat of combution

• if cycloalkane is strain free, its heat of combustion should be n X 658.7 kJ/mole. If there is some strain,more energy is given out on combustion

Look at the graph which shows, for each ring size: (a) angle strain per CH2 group(b) heat of combustion per CH2 group

• The greatest strain is in the 3-membered ring.• The strain decreases with ring size and reaches a minimum for 6-membered ring. • The strain then increases, but not as quickly as the angle calculation suggested: it reaches a maximum at 9 and then decreases.• The strain remains constant at ~14, not increases steadily as the angle-strain suggested.

Q • Why 6-membered ring is more strain free?• Why there is still some strain in 5-membered ring?

Cyclic compounds twist and bend to minimize the 3 different kinds of strain1. Angle strain 2. Torsional strain 3. Steric strain

• banana bonds poor orbital overlap

•Torsional strain

Good overlapStrong bond

Poor overlapWeak bond

Cyclopropane

Electron density diverts away from the ring by 21°

External orbitals: 33% S & 67% p sp2

Internal orbitals: 17% S & 83% p sp5

For sp3: 25% s & 75% p charectorHere the four hybrid orbitals of C are far from equivalent

HCH 115°

Cyclobutane

Cyclobutaneto reduce torsional angle

Interplanar angle 35°

HH

H H

H

H

HH

Cyclobutane

eq

ax ax

eq

ax

eq

eqax

Eclipsing torsional strain overrides increased bond angle strain by puckering.

Ring barrier to inversion is 1.45 kcal/mol.

n G = 1 kcal/mol favoring R = Me equatorial

n 1,3 Disubstitution prefers cis diequatorial to trans by only 0.58 kcal/mol for di-bromo compound.

n 1,2 Disubstitution prefers trans diequatorial to cis by 1.3 kcal/mol for diacid (roughly equivalent to the cyclohexyl analogue.)

•one carbon atom is bent upwards•The molecule is flexible and shifts conformation constantly •Hence each of the carbons assume the pivotal position in rapid succession .

•The additional bond angle strain in this structure is more than compensated by the reduction in eclipsed hydrogens.

•With little torsional strain and angle strain, cyclopentane is as stable as cyclohexane.

H H

H

HH

H

H

H

H

H

H

HH

H

H

H H

H

H H

Envelope Half chair

Cyclopentane

The energy difference is little

H

H

H

H

H H

HH H

H

Cyclopentane

Two lowest energy conformations of cyclopentane (10 envelope and 10 half chair conformations) differ by only 0.5 kcal/mol. They are in rapid conformational flux (pseudorotation) which causes the molecule to appear to have a single out-of-plane atom "bulge" which rotates about the ring.

Since there is no "natural" conformation of cyclopentane, the ring conforms to minimize interactions of any substituents present.

H

A single substituent strongly prefers the equatorial position of the flap of the envelope

(barrier ca. 3.4 kcal/mol, R = CH3).

HH H

H

HH

H

H

H H H

H

H

H

H

H

H

H

H

H

HH H

H

H

H

H

H H

Half-ChairEnvelope

1,2 Disubstitution prefers trans for steric/torsional

reasons (alkyl groups) and dipole reasons (polar groups).

Me

Me

1,3 Disubstitution: Cis-1,3-dimethyl cyclopentane only 0.5 kcal/mol more stable than trans.

H

A carbonyl or methylene prefers the planar position of the half-chair (barrier 1.15

kcal/mol for cyclopentanone).

H H

H

HH

H

H

HO

Chair conformation

Sum of the van der Waals radii = 2.4 A0

Boat conformation

Newman projection of the

boat conformation

HA

HB

HB

HAring-flip

1.8 A0

H H

flagpole hydrogens

Cyclohexane

H

HH

H

H

H

H

H

Ha

Ha

Ha

Ha

Ha

Ha

He He

He

He

HeHe

He

He He

He

He He

Ha Ha

Ha

Ha Ha

HaRing flipping orinversion

Chair Half Chair Twist boat boat

Half Chair Opposite sense ChairTwist boatOpposite sense

Erel=10Erel=0.0 kcal/mol Erel=5.5 Erel=6.5

Planar Erel= very large >20 kcal/mol

Interconversions of Cyclohexane

Half chair

boat

Twist boat

Half chair

chair chair

H

Cyclohexane energy profile for cyclohexane ring reversal

• The energy difference between the chair, boat, and twist conformation of cyclohexane are low enough to make their separation impossible at r.t. At room temperature approx. 1 million introversions occur each other second.

• More than 99% of the molecules are estimated to be in chair conformation at any given time

1-1.15(4.2-6.3)

X

X

Monosubstituted cyclohexane

This conformation is lower in energyWhy?

X

H

H When X=CH3, conformer with Me in axial is higher in energy by 7.3 kJ/mol than the corresponding equatorial conformer.Result: 20:1 ratio of equatorial:axial conformer at 200 C

1,3-diaxial interaction

The black bonds are anti-periplanar (only one pair shown)

The black bonds are synclinal(gauche) (only one pair shown)

X

H

HH

H

XH

H

H

X

HH

H

HH

H

HX

X

X

K=Conc. of equatorial conformer

Conc. of axial conformer

X Equilibrium

constant

Energy diff. between axial and equatorial conformers

kJ/mol

% with substitutent equatorial

H 1 0 50

Me 19 7.3 95

Et 20 7.5 95

i-Pr 42 9.3 98

t-Bu >3000 >20 >99

OMe 2.7 2.5 73

Ph 110 11.7 99

OH

OH

OH

OH

H H

Disfavoured

Twist boat

t-butyl groupa locking group

Preferred Conformations

Me

i-Pr

OH

OH

Me

Me

OH

favoured

Write preferred conformation for

It exists as a dl-pair, but since barrier to rotation is low to allow separation.Therefore the ()- pair is inseparable and hence the compound is optically inactive.

CH3

CH3

CH3

CH3

CH3

CH3

1 gauche-butane interaction0.9 kcal/mol

4 gauche-butane interaction4 x 0.9 kcal/mol = 3.6 kcal/mol

CH3

CH3

CH3

CH3

CH3

H3C

CH3

CH3

This has 3 gauche-butaneinteractions

Difference in stability between the conformational isomers

3.6 - 0.9 = 2.7 kcal/mol

Diastereomeric, chiral and therefore resolvable

Enontiomeric, chiral and not resolvable

CH3

Very bad steric situation ~ 5.5 kcal/mol (4 x 0.9 = 3.6 kcal/mol + Methyl-Methyl interaction)

CH3

CH3 CH3H3C

CH3

CH3

CH3

CH3

CH3H3C

CH3

It is a resolavable molecule2-gauche-butane interaction = 1.8 kcal/mol

cis-isomer is stable than trans isomer

Diastereomers, achiral

Identical, chiral

CH3

CH3

CH3

CH3H3C

CH3

2-gauche-butane interaction, 2 x 0.9 = 1.8 kcal/mol

CH3

CH3

CH3

CH3

H3CCH3

Both have plane of symmetry, achiral

Trans is stable than cis

Identical, achiral

Diastereomers, achiral

OH

OH

OH

OH

OHOH

OH OH

OH

OH

OHOH

OH

OH

OH

OH

OH OH

OH

OH

Problem: Which of the following compounds are resolvable, and which are non resolvable?Which are truly meso?

a) cis-1,2-cyclohexane diol; b) trans-1,2-cyclohexane diol;c) cis-1,3-cyclohexane diol; d) trans-1,3-cyclohexane diol;e) cis-1,4-cyclohexane diol; f) trans-1,4-cyclohexane diol.

Non resolvable (easily interconvertible by flipping)

Hint:

trans (resolvable)

cis (meso) trans (resolvable)

achiral (absence of chirality center)

Cycloheptane

Chair (+2.16 kcal/mol) Twist-Chair (0 kcal/mol)

Boat (+3.02 kcal/mol) Twist-Boat (+2.49 kcal/mol)

Hendrickson, J. B. JACS 1961, 83, 4537.

The easiest way to imagine cycloheptane is in chair-form:

Cyclooctane

Chair-BoatLowest-energy conformation

1

7

3

Ring strain originates in eclipsing interactions and transannular van der Waals interactions

Transannular strain between C3 & C7

5

1

7

3

Underside view of boat-chair C3 & C7 eclipsing interactions

3

7

1 3

7

5

Chair-Boat (BC)Lowest-energy conformation

1

7

3

5

O

Carbonyl is positioned at C3 or C7 Olefin is positioned at C3-C4 or C6-C7

Still, W. C.; Galynker, I. Tetrahedron 1981, 37, 1981.

Methyl position 1 2 3 4 5

1.8 2.8 >4.5 -0.3 6.1(pseudoeqatorial)

(pseudoaxial) (kcal/mol)G

Cyclooctane

Rigid molecules from cyclohexane conformers

Conformational equilibrium in 1-phenyl-1-methyl cyclohaxane

OH

CO2H

OH CO2H OO

CO2H

HO2CCO2HCO2H OOO

OH

OHOHOH

OOH H

Cyclic anhydride formation from 1,3-cyclohexanedicarboxylic acid

Intramolecular H-bonding in 1,3cyclohexanediol

Lactonization of 3-hydroxy cyclohexane carboxylic acid

Conformational Analysis of Bicyclic Systems

Me

Me

H

H

H

O

The steroid nucleus provided the stimulation for the development of conformational analysis, particularly of polycyclic ring systems. D. H. R. Barton

was awarded a Nobel prize in 1969 for his contributions in this area.

H

H

G° = +2.4 kcal/mol

rigid

Decalin Ring System (6/6)

mobile

H

H H

H

1

47

11

10

13

14

17

G°þ = 0 kcal/mol

Bicyclic Systems

H

H

H

H

1

2

3

4

Gauche-butane interactions

C1 C2C1 C3C4 C3

G°(est) = 3(0.88) = 2.64 kcal/mol

Can you estimate the energy difference between the two methyl-decalins shown below?

Me

H

Me

H

E2 eliminations have anti-periplanar transition states

In E2 eliminations, the new bond is formed by overlap of the C-H bond with the C-X * antibonding orbital

Two conformations with H and X coplanar

Reaction is stereoselective

Me groups anti-periplanarLess hindered

Me groups gauche (syn-clinal)more hindered

E2 eliminations have anti-periplanar transition states

Only one proton for removal

C6H5

C6H5

Br

CH3

OH

(faster)

C6H5H3C

C6H5 H

C6H5

C6H5

Br

CH3

OHC6H5H3C

H C6H5

(slower)

BrH

Ph

Ph

CH3

H

Br

H

Ph

CH3

H

Ph

H

Ph CH3

Br

PhH

BrH

Ph

Ph

HMe

Br

HPh

Ph

H

Me

H

Me Ph

Br

PhH

Whereas

C6H5

Br

H COC6H5

CO2HC5H5N

H

C6H5

H COC6H5

CO2HCO2HC6H5

H COC6H5

HO2C

Br

H COC6H5

C6H5 C5H5N

H

HC6H5

H COC6H5

C6H5

Br

H COC6H5

HC5H5N

CO2H

HC6H5

H COC6H5

Ph

Ph

BrH

HBr

H Br

HBrPh

Ph

Br

Br

HPh

PhH

Br

H

HPh

BrPh

Br

Ph

PhPh

Ph

BrH

BrH

H Br

BrHPh

Ph

Br

Br

HPh

HPh

Ph

Ph

Problem: On treatment with the aromatic base pyridine, racemic 1,2-dibromo-1,2-diphenyl ethane loses HBr to yield trans-1-bromo-1,2-diphenyl ethane; In contrast the meso dibromide loses Br2 to yield trans-1,2-diphenyl ethene. Suggets a mechanism?

Hnit:

Racemic

Br2 loss is not favored

meso

-HBr

-Br2