RELAXATION PATHS FROM A CONICAL INTERSECTION - THE MECHANISM OF PRODUCT FORMATION IN THE CYCLOHEXADIENE HEXATRIENE PHOTOCHEMICAL INTERCONVERSION/

An algorithm for the computation of initial relaxation directions (IRD ) from; the tip of a conical intersection is discussed. The steepest d escent paths that can be computed starting from these IRD provide a de scription of the ground state relaxation of the ''cold'' excited state species that occur in organic photochemistry where slow motion and/or thermal equilibration is possible (such as in cool jet, in matrices, and in solution). Under such conditions we show that the central concl usions drawn from a search for IRD and those obtained from semiclassic al trajectory computations are the same. In this paper, IRD computatio ns are used to investigate the mechanism of photoproduct formation and distribution in the photolysis of cyclohexadiene (CHD) and cZc-hexatr iene (cZc-HT). A systematic search for the IRD in the region of the 2A (1)/1A(1) conical intersection (see Celani, P.; Ottani, S.; Olivucci, M.; Bernardi, F.; Robb, M. A. J. Am. Chem. Sec. 1994, 116, 10141-10151 ) located on the 2A(1) potential energy surface of these systems yield s three relaxation paths. The first two paths, which start in the stri ct vicinity of the intersection, are nearly equivalent energetically a nd lead to production of CHD and cZc-HT, respectively. The third path, which begins at a much larger distance, lies higher in energy and end s at a methylenecyclopentene diradical (MCPD) minimum. Further, while the first two paths define directions that form a 60 degrees angle wit h the excited state entry channel(i.e. the direction along where the c onical intersection region is entered), the third path is orthogonal. It is shown that these findings are consistent with the experimental o bservations which show nearly equivalent quantum yields for CHD and cZ c-HT and no production of MCPD. The results of the IRD computations ha ve been validated by investigating the decay dynamics of trajectories starting from a ''circle'' of points around the conical intersection, with the initial kinetic energy distributed in randomly sampled vibrat ional modes. These computations have been carried out using a trajecto ry-surface-hopping (TSH) method and a hybrid molecular mechanics valen ce bond (MM-VB) force field to model the ab initio potentials.