PM3 and ab initio Studies on the C8H8 Potential Energy Surface. Thermal Isomerism of syn- and anti- Tricyclo[,5]octa-3,7-dienes

Carlota Conesa and Henry S. Rzepa*

Department of Chemistry. Imperial College of Science, Technology and Medicine, London, SW7 2AY. UK

Summary We have identified for the first time symmetry allowed pathways for rearrangement of both the syn (1) and anti (2) isomers of cyclobutadiene dimer in the closed shell potential energy surface for the isomerisation to cyclo-octatetraene. At the B3LYP/6-31G(d) level of theory, the calculated activation energy for the reaction of 1 is 3.2 kcal.mol-1 lower than that for 2, in good agreement with the experimental difference of 3.6 kcal mol-1. The possible influence of the s strain on the synchrony of the pericyclic reactions of the systems is discussed.

Introduction The thermal interconversions of C8H8 isomers have been the subject of many reports1 since the synthesis of cyclooctatetraene in 19112. This is certainly due to the fact that cyclooctatetraene (COT) lacks the stabilization of other annulenes and therefore interconverts with its isomers relatively easily. The thermal isomerisation of the syn and anti isomers of cyclobutadiene3 dimmer (1 and 2 respectively) to COT 4 (Scheme 1) were discovered in 1964 by Nenitzescu4 and has been further studied independently by the Dewar5 and the Frey6 groups. Early MINDO/3 calculations5 by Dewar suggested that the activation energy for the forbidden p2s+p2s cycloelimination to give 4 was likely to be very large, and that forbidden disrotatory ring opening of 1 to bicyclo[4.2.0]octa-2,4,7-triene (BOT) 3 might be higher than that of the anti isomer 2, contrary to experiment (a discrimination of 3.6 Kcal.mol-15 in favour of 1 is found). These results led to the prediction5 of a crossover to the triplet surface to give triplet 4. On the other hand, Frey et al. discarded a major triplet pathway and suggested a biradical mechanism in which the triplet component of the reaction would depend on the relative rates of intersystem crossing and the rate of conversion of the biradical to BOT.

Our own interest in this system originates in our search for model systems for studying the relationship between the aromaticity and geometry of pericyclic transition states and the strain in the s framework. We had previously identified a system7 where severe s strain induced gross asynchronicity for the two forming bonds in a p2s+p4s cycloaddition. Shaik in a series of articles has recently suggested that the six-fold symmetry of benzene itself is induced by the s framework rather than by the p aromaticity8.This model of geometrical symmetry induced not by aromaticity but by the s framework has not hitherto been evaluated for transition states, and particularly for those such as pericyclic reactions where both synchronous and asynchronous behaviour can be manifested. We report here new results on the potential energy surface connecting 1 and 2 to 4 which investigates these aspects, and which for the first time establish that formally allowed singlet pathways for the interconversion of 1 and 2 to 4 can exist.

Computational Procedure. Initial estimates of the stationary point geometries were obtained by molecular mechanics minimization using the MM2 forcefield in a Tektronix CAChe workstation system. These approximate geometries were then re-optimized at the PM3 level using the MOPAC V6.0 program9 implemented on CAChe workstations. The transition states structures were located by using the saddle option within MOPAC10 or the eigenvector following routine (TS) and higher order saddle points were located by minimizing the sum of the squared gradients (NLLSQ). This was followed by calculation of the force constant matrix and normal coordinate analysis to characterize the stationary point, and an intrinsic reaction coordinate calculation along the first normal mode direction to verify the identity of the reactants and products deriving from the transition state. Final values of the gradient norms were < 0.01 Kcal.mol-1-1 unless indicated. Ab initio calculations were performed on PM3 geometries using the GAUSSIAN94 program system11, transition states being located by using the Berny algorithm12 or the synchronous transit-guided quasi-Newton (STQN) methods implemented by Schlegel13. Molecular coordinates in the form of Gaussian or Mopac files for located stationary points are integreted into this article together with animations of all important imaginary modes showing the form of the eigenvectors.

Results and Discussion The first part of the investigation was to establish if possible pathways existed involving either two concurrent or two consecutive allowed conrotatory 4p-electrocyclic ring openings to give the isomeric chair-cyclooctatetraene structures 8 and 13 respectively (Scheme2) which could be intermediates on the pathway to 4. The second part of the investigation requires finding a hitherto unstudied pathway from 8 to the tube-COT 4. An analogous pathway connecting 13 to tube-COT 4 at the MNDO and MINDO/3 levels has been reported14 previously to involve low energy barriers.

Preliminary calculations established that the bicyclic trans- 6-ring alkene intermediates 6 and 11 (Tables 1and 2) were genuine intermediates, but significantly higher in energy than the cyclo-octatetraenes 8 and 13, because of the significant ring strain induced within the 6-membered ring. Concurrent electrocyclic opening of both cyclobutene rings in a synchronous manner via 9 or 14 could therefore in principle avoid these high energy intermediates to give 8 or 13 directly. Such a concurrent reaction could in fact also be represented at least formally as a thermally dis-allowed p2s+ p2s cyclo-elimination. This reaction is thus formally ambiguous in the Woodward-Hoffmann sense, in either representing two concurrent but formally independent 4-electron reactions each involving a thermally allowed antara-facial component, or a single 4-electron reaction involving no antara-facial components. Formally, one is allowed, the other disallowed by the Woodward-Hoffmann rules, and so it is of some interest to see how the quantitative calculations at the SCF level model the process.

The trans-alkene strain in 6 and 11 might be counterbalanced or augmented by aromatic stabilisation/destabilisation for the synchronous geometries 9 or 14, both formally on the path leading to 8p anti-aromatic products. Schleyer and co-workers have recently reported the nucleus independent chemical shift (NICS15) method of estimating aromaticity in both stable systems and in pericyclic transition states, and have tabulated a range of typical values for both aromatic and anti-aromatic systems. We have applied this method to 9 or 14 using probes located respectively at the centres of the middle ring and the external ring (nonweighted mean of the heavy atom coordinates). The stationary point 9 has negative NICS values of -10.2 and -11.9 ppm respectively16, clearly in the range designated to be aromatic. On the same scale, benzene has a value of -11.5. The stationary point 14 shows significantly reduced aromatic character (-6.4 and -6.8 ppm). Therefore both avoidance of strained intermediates and the induced aromaticity at the symmetric geometries would appear to favour the synchronous route for this reaction, but more so for 9 than 14 based on their respective measures of aromaticity.

We next wished to establish if the stationary points 9 and 14 represent more accurately two concurrent electrocyclic ring openings, or single 2+2 cycloeliminations. Both are calculated to have two negative force constants at the PM3, and RHF and B3LYP ab initio levels (Table 1), indicating they are second order stationary points. The calculated normal mode corresponding to the most negative force constant for 9 can be approximately described as a bis-conrotatory ring opening, whilst the motions of the four atoms involved in the cycloaddition/elimination process indicate a significant degree of formally forbidden supra-supra character. The less negative force constant shows an anti-symmetric distortion leading to a true, lower energy stepwise transition state 5 (or its mirror image). In contrast, the first equivalent imaginary mode for 14 is subtly different, revealing apparent bis-disrotatory ring opening, together with supra-supra character for the central formal 2+2 elimination. Such a harmonic analysis, corresponding to a quadratic potential surface, is actually misleading. An intrinsic reaction coordinate (IRC) search using the PM3 potential and starting from 14 reveals that the route to 2 most resembles con-rotatory motions of the relevant hydrogens, whilst the route to 13 more closely resembles dis-rotatory motions. Topologically, two bis-disrotatory modes are of course equivalent to two bis-conrotatory modes (supra-supra = antara-antara). This difference between 9 and 14 may well explain the lower degree of aromaticity calculated using the NICS procedure for 14, and hence its higher relative energy. In one respect therefore 14 is remarkable, exhibiting three formally thermally forbidden pericyclic modes. The second imaginary mode in 14 is again an anti-symmetric distorsion leading to lower energy 10 (Table 1). Both 5 and 10 show only a single negative force constant, with the corresponding eigenvectors correspondng to con-rotatory ring openings.

The B3LYP level energy difference 9 - 5 of 8.7 kcal mol-1 was much smaller than 14 - 10 (22.6 kcal mol-1 ), in accord with the greater aromatic stabilisation of 9 compared with 14. This clearly indicates that in this system at least, avoidance of ring strain in the product is not sufficient to induce synchronicity in the transition state, but it does raise the intriguing possibility that appropriate substituents that might stabilise the extended aromaticity could lower the energy of the synchronous geometry to the point that it becomes a genuine transition state.

We next have to establish that 5 and 10 represent the rate limiting transition states in the surface, and that closed shell pathways to 4 can be found. Firstly, we note that both 6 and 11 can convert to 8 and 13 respectively via transition states 7 and 12. These both exhibit the conrotatory imaginary modes expected from thermal opening of a cyclobutene rather than the disrotatory mode expected for opening of a cyclohexadiene. In this, both 7 and 12 represent examples of a formally dis-allowed 6p thermal process, but in fact avoid this by having one of the spectator alkene bonds essentially orthogonal to the remaining p system.The existence of chair-COT 13 has been the object of previous speculation 14 . The studies reported a tendency of isomerisation to the more stable tube-COT 4 according to the reaction in Scheme 3. Table 2 shows the comparison between the previous MNDO and MINDO/314 results and those obtained at the PM3, RHF/6-31G(d) and B3LYP/6-31G(d) levels. No transition state for the analogous transformation (chair-COT 8 to tube-COT 4) could be located, and the isomerisation of 8 to 13 by rotating along two single bonds was of high energy at the PM3 level (166.91 Kcal.mol-1). However, a transition state which connects chair-COT 8 and semibulvalene 18 could be found (Scheme4). Since the interconnection between semibulvalene 18 and tube-COT 4 has been described17 this seemed to be a suitable pathway for the isomerisation of 8 to 4. However, both PM3 and ab initio calculations predict a large barrier energy for the transformation 18->4(Table1).

Next, we considered the possibility of an allowed 6p- disrotatory ring opening of the intermediates 6 and 11 to give via transition states 20 and 23 the trans cyclooctatetraene 21. The latter compound is known to be obtained at room temperature18 but could undergo further isomerisation to tube-COT 4 at the conditions under discussion (Scheme 5). The ring opening would be formally identical to the valence isomerisation of BOT->COT. The energies of 20, 22 and 23 are lower than the initial transition state 5 and 10 (Tables 1 and 2), establishing the latter as the rate-limiting species.

Compound 11 could undergo a 4p ring opening (Scheme 2) to 13 via transition state 12 or a formal 6p ring opening (Scheme 5) to 21 via transition state 23. The imaginary mode for 23 is unusual in resembling neither dis nor con-rotation, one hydrogen rotating and the other not. Perhaps such a mode avoids the contradiction that either dis or con-rotatory openings would violate the Woodward-Hoffmann rules. The route via 23 is slightly favoured energetically over 12, and the intermediate 21 could in turn readily evolve to tube-COT 4 through p-bond shifting. This latter seems to be the pathway of lowest overall energy (Figures 2, 4 and 6). The bond shifting transition state for the transformation 21->4 would not be planar and therefore of lower symmetry than the reported19 transition state for the bond shifting in tube-COT . For compound 6, at PM3 and RHF/6-31G(d) levels, a 4p- ring opening to 8 Scheme 2 would have a lower barrier energy than the 6p ring opening to 21 (Scheme 5) but the pathway through 8 would imply the formation of 18 and the high energetic transformation 18->4 (Figures 1 and 3). The DFT (B3LYP / 6-31G(d)) results are in favor of the 6p ring opening 6->21 (Scheme 5, figure 5) and in this case all the subsequent energy barriers would be accessible.

On the basis that 5 and 10 represent the genuine transition for the overall reactions, the activation energies obtained on this basis at the DFT level (DH# 32.3 and 35.5 kcal.mol-1 for 1->5->4 and 2->10->4 respectively) are in good agreement with those obtained experimentally (Ea=28.8-30.5 and 32.4-32.6 kcal.mol-1 respectively5,6). Figure 7 shows the geometry of both transition state structures (5 and 10) that determine the activation energies. Finally we note that the activation energy for reaction of 1 3.2 kcal.mol-1 lower than for 2, in good agreement with the experimental measurement of 3.6 kcal mol-15.

Conclusions.According to DFT ab initio calculations, the thermal isomerisation of the syn- and anti- dimers of cyclobutadiene 1 and 2 to cyclooctatetraene 4 can take place without the involvement of triplet states,contrary to a previous report. The newly proposed pathway consists of a symmetry allowed 4p- conrotatory ring opening giving high strained bicyclo[4.2.0]octa-2c,4t,6c-trienes 4 and 6 as the rate determining step. The pathway involving synchronous breaking of two s-bonds is not promoted by avoidance of these strained intermediates, but there is some evidence that the relative aromaticity of the synchronous stationary point 9 does in part offset the ring strain in 6. Intermediates 6 and 11 could readily undergo a further symmetry allowed 6p- disrotatory ring opening to 1c,3c,5c,7t-cyclooctatetraene 21, and the latter could isomerise through a p-bond shifting to the more stable 1c,3c,5c,7c-cyclooctatetraene 3.

Acknowledgments We thank Mr Christopher S. Page for the technical support and Mr Omer Casher for providing us with the IRIX Explorer module EyeWriteXYZ; employed to generate the xyz files used in the animations that are contained in the supplementary material. We also thank the Ministerio de Spanish Educación y Cultura for a postdoctoral fellowship (to C.C.).