Indian Journal of Chemistry Vol. 42B, July 2003, pp. 1716- 1722

The role of orbital symmetry in Bergman cyclization

Sandip Kumar Kundu , Twishasri Das Gupta, Suven Das & Animesh Pramanik*

Department of Chemistry, Calcutta University, 92 A.P.C. Road, Kolkata 700009 E-mail:animesh@cucc.ernet.in

Received 8 August 2002; accepted (revised) 21 January 200]

In Bergman cycli zation the anLisy mmetric combination (nl -n2) of th hybrid orbitals at the radical sites in 1,4-dehydrobenzene is pre ferenti ally stabilized via through-bond interactions. The resultant splitting between the frontier orbi ­tals is cruc ial in making Bergman cyclization a thermally sy mmetry allowed process. 1,4-Pentadiyne and 1,6-heptadiyne have been used as model systems to explore theoretically the role of orbital sym metry in Bergman cyclizat ion.

The series of natural anticancer, antitumor antibiotics, such as Esperamicin l

, Calicheamkin2, Dynemicin3 are found to have the ability of cleaving DNA. It is known that these molecules possess a central enedi­yne moiety, typically in a cyclic framework. The mechanism of action has been postulated to involve the selective binding of the molecule via its oligosac­charide unit to the minor groove of DNA4, followed by a suitable activated triggering device (e.g., a nu­cleophilic attack) which initiates a cascade of reac­tions that leads to the generation of a highly reactive species5

. The critical step is the cyclization of the enediyne moiety to form the 1,4-dehydrobenzene bi­radical. The biradical is capable of abstracting hydro­gen atoms from the sugar unit of DNA, generating a new radical, which undergoes oxygenation under aerobic condition leading to cleavage. It is evident that the DNA cleaving ability of thi s class of antican­cer, antitumor anibiotics is crucially controlled by the ease of formation of the 1,4-biradical in these sys­tems. The key cyclization process mentioned above has been known in organic substrates for over two decades. Bergman et al.

607 have reported that (Z)-hexa-1,5-diyn-3-ene 1 undergoes a thermal degenerate rear­rangement (Scheme I) via a cyclic biradical interme­di ate 2 with a new C2 sy mmetry ax is. In order to de­sign synthetic analogues of the natural compounds, it is important to know the various factors controlling the cyclization process.

The mechanistic details of Bergman cyclization have been studied theoretically by different groups. In 1983 Dewar et al. 8 reported MINDO/3 and MNDO calculated reaction profiles for the reaction of the par­ent substrate 1 (Scheme I). By both procedures the reaction was predicted to take place via a stable in-

o 200C

•

1 2 Scheme I - Bergman cyclization of

(Z)-hexa- l ,S-diyn-3-ene 1

termediate 1,4-benzenediyl 2, in agreement with the mechanism suggested by Bergman6

. Koga et al. 9 have carried out ab initio Complete Active Space Self Con­sistent Field (CASSCF) and Multi-Reference Single and Double Configuration Interaction (MRSDCI) cal­culations with different basis sets on Bergman cycli­zation. Some more ab initio studies re lated to Berg­man cyclization also have been reported 10. In all these calculations, the HOMO of the intermediate 1,4-benzenedi yl 2 has been recognized as the antisymmet­ric combination (n,- 11 2) of the hybrid orbitals at the radical sites. However, the potential importance of thi s orbital ordering fo r the Bergman process has not been emphasized . In this paper, we analyze the orbital correlation diagram fo r the cyclization reaction to hi ghlight the ro le of orbital sy mmetry and through­bond interactions.

Orbital Analysis The orbital correlation diagram for the prototype

Bergman cyclization can be constructed (Figure 1) taking into account the symmetry elements which are conserved during the process II. The formation of the l,4-biradical 2 from (Z)-hexa-l,S-diyn-3-ene 1 in­volves significant electronic reorganization . However,

KUNDU el af.: THE ROLE OF ORBITAL SYMMETRY IN BERGMAN CYCLIZATION 1717

"

A

--- ____ s_ a

. g s ----

Figure 1-Orbital correlation diagram for Bergman cyclization of 1

the key changes correspond to the conversion of the two in-plane 1t bonds of the triple bonds into a new C-C a-bond and the HOMO of the biradicaloid inter­mediate. The symmetry properties of these orbitals can be distinguished on the basis of the mirror plane perpendicular to the molecular plane, bisecting the newly formed C-C bond in the product, 1,4-dehydrobenzene 2. The two filled in-plane 1t MO's of (Z)-hexa-l,5-diyn-3-ene transform as a symmetric (S) and an antisymmetric (A) combination with respect to reflection about the mirror plane. The newly formed a- bond obviously is a symmetric MO. For the overall orbital symmetry to be conserved for all the filled MO's, it is therefore imperative that the HOMO of the biradical be an antisymmetric combination of the hy­brid orbitals (nl-n2) at the radical centers. The thermal cyclization would be electronically forbidden if the symmetric combination (nl +n2) is lower in energyl 2.

In biradicaloids such as 2 the separation between HOMO and LUMO may be substantial, nearly 6.7 eV

computed at the HF/6-31G* level 12. Two modes of

orbital interactions can lead to orbital splitting. Direct overlap or through-space interaction between the radical sites would lead to stabilization of the sym­metric combination, nl+n2 (Figure 2). However, in 2,

Figure 2-Through-space interaction between the hybrid orbitals at the radical sites of 2

the direct overlap between the back-lobes of the hy­brid orbitals may not be large. A more significant in­teraction between the hybrid orbitals occurs via through-bond interactions mediated by the intervening C-C a-bonds. The symmetric MO nl + n2 can have interaction with the filled orbital combination (al + a2). The net result is destabilization of the n I + n2 MO. The antisymmetric combinations nl-n2 and al-a2 cannot interact in view of their nodal characteristics (Figure 3). Hence, the A-type orbital nl-n2 would be lower in energy than the symmetric counterpart.

The operation of strong through-space interactions in l,4-dehydrobenzene and related systems is well established l3. We suggest that the same electronic factors are also crucial in making the Bergman cycli­zation a thermally allowed process. The validity of this proposal can be evaluated by examining the po­tential energy (PE) surface for Bergman type cyC\iza­tion in a few model systems in which 'the relative con­tributions of through-space and through-bond interac­tions have been altered .

It is known that through-space and through-bond effects can be significantly modulated by altering the number of intervening a bonds between the interac­tion sites l4 . For example, a biradical separated by a propano-bridge would be expected to have a symmet­ric HOMO. In this system, the through- space and through-bond effects act in concert. Through-bond destabilization due to filled (J bonds of the propano­bridge would be more effective for the antisymmetric combination in this system (Figure 4). These effects have been elegantly established for the 1t MO energies of non-conjugated dienes by means of PE spectros-

1718 INDIAN J. CHEM., SEC B, JULY 2003

I I I

CJ,-CJ2 : I I I I

-----{ CJ,+CJ2\

n1+n2 I~ I .,. ,

,: + \, : n1-n2 '- n1-n2 I ,

: '- n1+n2 I r--I I I I I I

I I I I I I I I I I I I I I I

, I , I , I , I , I

'?t+CJj

0)

¢ cd

Figure 3 - Through-bond interac tions between the hybrid orbi ­ta ls at the radical sites of 2 via the intervening C-C (J bonds

I

c:G I I

~

, , r-:-

" a* I

";~\I'

n1-n 2................. \ " - ,I

~ ~ I, n1+n2........... ... " \

, I, '----' , n1+n2 '. , ,

, I I

~

, I , ~

Figure 4- Through-bond interac tion between the hybrid orbitals at the radical sites via the intervening propano bridge

copy'S. The same electronic factors should be equally valid for the biradical MO energies as well.

As a general rule, even number of intervening (J-bonds lead to opposing through-space and through­bond effects. In the corresponding biradicaloids, the HOMO is expected to be antisymmetric combination n,-n2. In contrast, odd number of intervening (J bonds lead to co-operative through-space and through-bond effects resulting in the stabilization of S-type orbital combination. In order to examine the consequences of the switch in orbital symmetry of the HOMO in the corresponding systems, we have examined the PE surfaces of cyclisation processes leading to biradi­caloids in diynes separated by different number of C-C (J bonds.

Systems Examined \

As discussed above, the HOMO of a biradicaloid species is likely to be the symmetric type orbital n, + n2 if the radical centers are connected by methyl­ene or a propano bridge. It would be of interest to ex­amine the PE surface for the formation of these bi­radicals through ring closure from the corresponding acyclic diynes. Therefore, we have chosen 1,4-pentadiyne 3 and 1,6-heptadiyne 4 for a detailed ex­amination (Scheme II). The corresponding diradi­caloid products in Bergman type cydization are 1,4-dehydro-l ,3- cyclopentadiene 5 and 1 ,4-dehydro- L ,3-cycloheptadiene 6, respectively . We have also chosen the prototype (Z)-hexa-l ,5-diyn-3-ene 1 to find out the energy profile for Bergman cyc1ization .

Computational Details Semiempirical AM 1'6 methodology has been em­

ployed to determine the potential energy surface at the RHF level for the Bergman type cycliztaion of 3 and

<: J ~ 9 3 5

G --~ c) 4 6

Scheme 11- Bergman cycl ization of 3 and 4

KUNDU et al. : THE ROLE OF ORBITAL SYMMETRY IN BERGMAN CYCLIZATION 1719

4. In this process the newly formed C-C bond distance between the two reacting 7t bonds was chosen as the reaction co-ordinate.The highest energy structure on the minimum energy reaction pathway (MERP) with the assumed reaction co-ordinate was refined by minimizing the gradient norm. The nature of the reac­tants, transition states and products was characterized by the number of imaginary frequencies (NIMAG). In order to obtain more realistic energetics estimates, single point calculations have been carried out using the singles and pair excitation configuration interac­tion (PECI=8)17 in case of the prototype Bergman cy­c1ization with I .The biradical nature of the products 5 and 6 (Scheme II) was tested by doing the calcula­tions with the key ward BlRADICAL.

Results and Discussion Reaction pror.Ie for (Z)-hexa-I,5-diyn-3-ene I

The energy profile of Bergman cyclization for the unsubstituted enediyne molecule 1 computed at the RHFI AM 1 level corresponds to a single step process (Figure 5), as in previous semiempirical8 and ab ini­tio9 studies. The transition state smoothly connects the reactant 1 and the 1,4-biradical product 2. The transi­tion state (C2V) and 1,4-dehydrobenzene (D2h) have the expected Hessian index of 1 and 0, respectively. The separation between the terminal carbon. atoms of the diyne 1 is very large in the reactant, 4.40A. This distance is brought down quite substantially in the transition state. In fact, the newly formed C-C bond distance(1.73A), in the transition state is close to that in the product 2 (1.47 A). The product like geometry of the transition state is consistent with the endother­micity of the reaction and Hammond postulatel 8

. The RHF/AMI computed heat of formation of the transi­tion state is 172.1 kcal/mol, which reduces to 152.0 kcal/mol on inclusion of configuration interaction at the PECI=8 level. This variation indicates that the transition state is a biradicaloid species. The product 2 also shows a similar energy pattern, consistent with its expected biradical character.

At the RHF level, the AM 1 procedure significantly overestimates the enthalpy of activation for Bergman cyclization of 1. However, the AMIIPECI=8 calculated value of 38.4 kcal/mol is reasonably close to the ex­perimental value of 32.0 kcal/mol6. The AM IIPECI=8 calculated heat of reaction, 19.7 kcal/mol, is also slightly higher than the experimental value of 14.0 kcal/mol. Analysis of the MO's of the transition state and biradical intennediate 2, shows that both have an anti symmetric (A) HOMO and a symmetric (S)

r l'iHfO

(kcal/mol)

C':: 1.74A

~ 172.1(152.0)

"'."'33." © 1.47 A

2

",·"",,,(1 4.4O A

~ rc(A.) ~

Figure 5 -AM I Energy profile for the cyclization of 1 using RHF(PECI=8)

LUMO, fully consistent with the previous qualitative analysis. The orbital energies of antisymmetric HOMO and symmetric LUMO of the biradical intermediate, I,4-dehydrobenzene 2 were found to be -8.4 and -1.7 eV, respectively, at the AMI level. Even allowing for the usual underestimation of the energies of unfilled orbitals by SCF procedures, the calculated energy sepa­ration is fairly large. The system is best termed a bi­radicaloid rather than as a biradical.

Reaction pror.Ie for 1,4-pentadiyne 3 The potential energy profile for Bergman cycliza­

tion of the diyne 3 was examined at the AM llRHF level with the distance between the terminal carbon atoms of the two reacting 7t- bonds as the reaction co­ordinate. For each assumed value of the reaction co­ordinate, the rest of the geometry was optimized with Cs symmetry constrains. It was found that the com­puted heat of formation increased rapidly (Figure 6) as the distance was reduced from the value in the re­actant 3, 4.42 A to the distance of 1.7 A usually repre­sentative of the reaction co-ordinate parameter in Bergman cyclization transition state. For example, at distances of 3.0, 2.0 1.9 and 1.7 A between the termi­nal carbon atoms, the energies are 124.6, 188.7, 199.6 and 218.4 kcal/mol, respectively. Further, the acety­lenic units of the diyne 3 do not bend significantly from linearity (Bond angle C1-C2-C3 = 178°), while the HOMO of the species is the anti symmetric (A) com­bination of the two 7t-bonds throughout this range of geometries. The steady increase in energy along the path-way may be attributed to the strong four-electron repulsion between the in-plane 7t-bonds, without any stabilizing contribution from a new C-C IT bond.

1720 INDIAN J. CHEM., SEC B, JULY 2003

.240

i (5 E ---c

200

~ 160

0_

I <l

120

80L-~3~~--~--------~--------~2---------' 5 4 3

rc (A)

Figure 6- AM I Energy profiles along the cyclizat ion pathway of 3

An attempt was made to determine the potential energy surface in the reverse direction starting from the diradical product 5 to the reactant diyne 3. Again, the C-C CY bond being broken in diradical 5 was con­sidered as the reaction co-ordinate. Along this series of structures also, the energy increases steadi ly with increase in C-C distance. At distances of l.6, 1.7, 1.8 and 1.9A, the energies are 206.0 , 2 15.7,227.0 and 238 .2 kcal/mol, respectively. Up to the distance of 1.9A along the pathway, the symmetric (S) combina­tion of the lobes of the hybrid orbitals at the rad ical sites is doubl y filled. Beyond this va lue, there is a dis­continuity in the RHF energy surface. Partial optim i­zation of the geometry at the Rc va lue of 2.oA results in an abrupt drop in energy to 188.7 kcal/mol.

The above discontinuous energy profiles for the forwa rd and backward reactions at the AM I/RHF level are characteristic features of a symmetry forbid­den process l9 The orbita l crossing is ev ident in the computed wave functions. The surface crossing is estimated to occur at an energy of around 2 15.0 to 218 .0 kcallmol. Attempts to determine the transition

state by gradien t minimization around thi s po int were unsuccessful, obviously due to the lack of a smooth PE surface.

It is qui te likely that geometry optimization with inclusion of CI would lead to a cont inuous energy profile with a well defined transition state. However, the o rbital crossi ng would manifest itself in an inevi­tab le barrier, of the order of the energy required to reach the surface crossing point mentioned above. This implies a reverse acti vation barrier of about 15 .0 kcal/mol, making the enthalpy of acti vation for cycli­zation very large indeed . I SCF sing le point calcul a­tion was carried out on the RHF/AMI optimized ge­ometry of the product 5 with the keyward BIRADI­CAL. There was a reduction of heat of formation ( 178.0 kcal/mol ) by nearly 22 .0 kacllmol compared to the RHFI AM I computed heat of formation (200.3 kcal/mol), indicating the biradical nature of the spe­ci es , I ,4-dehydro- l ,3-cyclopentadiene S.

Reaction profile for 1,6-heptadiyne 4 The cycl ization profile for 1,6-heptadiyne 4 wa

KUNDU el al.: THE ROLE OF ORBITAL SYMMETRY IN BERGMAN CYCLIZATION 1721

examined using the same strategy used for 1,4-pentadiyne 3 . Again it was found that the energy in­

creases steadily (Figure 7) as the two 1t-bonds come closer, without any evidence of the presence of a tran­sition state structure. The HOMO of the reacting spe­cies was found to be the antisymmetric (A) combina­

tion of the two 1t-bonds along this path-way . The ace­tylenic units remain essentially linear (Bond angle C 1-Cr C3 = 178°) in spite of bringing them close to each other. There is no bonding interaction between the terminal carbon atoms.

The energy profile for the reverse reaction, viz . the ring opening of 1 ,4-dehydro-1 ,3-cycloheptadiene 6 was examined at the AM l/RHF level using the bond being broken as the reaction co-ordinate. Instead of the rapidly increasing energy profile with a surface crossing as found in the case of l,4-pentadiyne, a different surface was obtained. As the C-C distance was marginally increased from the value found in the biradical 6, a transition state structure was located. The structure 7 , was computed to be only 2.3 kcallmol higher in energy than 6 at the AMlIRHF level (Figure 7). Interestingly , the transition structure does not correspond to Bergman type cyclization from 4 . Further increase in the C-C bond distance results in a steeply downhill reaction pathway leading to the bicyclic product, bicyclo[3 .2.0]-1 ,3-heptadiene 8. Computed Hessians confirm the ttansition state nature of 7 for the one-step cyclization of the biradicaloid 6 to 8. This process is a direct consequence of the nature of the HOMO in 6. In view of its sy mmetric nature, cyclization to form a new C-C bond in the bicyclic structure is a favoured process.

From the above AM1/RHF results, it is evident that the symmetric nature of the HOMO of the biradicaloid 6 leads to two interesting consequences. First, the or­bital symmetry is responsible for the lack of a smooth pathway for Bergman type cyclization of the diyne 4 leading to 6. Second, the nature of the HOMO of the biradical is also manifest in the alternative pathway with a negligible barrier available for the species to cyclize to yield a bicyclic closed shell derivative 8. Thus, orbital symmetry fundamentally alters the nature of the PE surfaces in these systems. The biradical na-

, ture of the product 6 was confirmed by doing single point 1SCF calculation on the RHF/AM1 optimized geometry with the keyward BIRADICAL, as we have done in case of the biradical product 5. A characteristic reduction of heat of formation by nearly 21.0 kcallmole was observed compared to the RHFI AM 1 computed heat of formation (166.2 kcallmol) .

7

I 6

110.6

"'HfO co (kcal/mol)

8 884

(i 4 03 A

4

rc(A)-

Figure 7 - AM I Energy profiles for the cyc1ization of 4

The electronic structures of the cyclized biradi­caloids derived from 3 and 4 computed at ab initio level with the 6-31 G* basis set20 confirm the above results. In contrast to 2 , the biradicaloids 5 and 6 have a sy mmetric HOMO (frontier orbital gap of 9.0 and 8.6 eV at the HF/6-31 G * level ). Hence, cyclization of diynes 3 and 4 to the biradicals 5 and 6 , respectivel y, are electronically forbidden. On the other hand, the antisymmetric combination nl-n2 of the hybrid orbi­tals at the radical s ites in 1,4-dehydrobenzene, is the HOMO, due to through-bond interactions. As a result, Bergman cyclization is a thermally sy mmetry-a llowed process (Scheme I ).

In summary, Berg man cyclization is to be consid­ered as an important addition to the class of biradi­caloid process in which orbital sy mmetry plays a key role21

. Through-bond interactions and orbital symme­try should not be overlooked while designing syn­thetic analogues of enediyne type DNA cleaving molecules .

Acknowledgement The authors are thankful to Prof. J Chandrasekhar

for helpful discuss ions. Authors are also grateful to the UGC, New Delhi and the University of Calcutta for providing financial support.

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1722 INDIA N J. CHEM., SEC B, JUL Y 2003

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