| Abstract
| - An algorithm for the computation of initial relaxation directions(IRD) from the tip of a conical intersectionis discussed. The steepest descent paths that can be computedstarting from these IRD provide a descriptionof the ground state relaxation of the “cold” excited state speciesthat occur in organic photochemistry whereslow motion and/or thermal equilibration is possible (such as in cooljet, in matrices, and in solution). Undersuch conditions we show that the central conclusions drawn from asearch for IRD and those obtained fromsemiclassical trajectory computations are the same. In this paper,IRD computations are used to investigatethe mechanism of photoproduct formation and distribution in thephotolysis of cyclohexadiene (CHD) andcZc-hexatriene (cZc-HT). A systematic searchfor the IRD in the region of the 2A1/1A1conical intersection(see Celani, P.; Ottani, S.; Olivucci, M.; Bernardi, F.; Robb, M. A.J. Am. Chem. Soc. 1994, 116, 10141−10151) located on the 2A1 potential energy surface of thesesystems yields three relaxation paths. The firsttwo paths, which start in the strict vicinity of the intersection, arenearly equivalent energetically and lead toproduction of CHD and cZc-HT, respectively. The thirdpath, which begins at a much larger distance, lieshigher in energy and ends at a methylenecyclopentene diradical (MCPD)minimum. Further, while the firsttwo paths define directions that form a 60° angle with the excitedstate entry channel (i.e. the direction alongwhere the conical intersection region is entered), the third path isorthogonal. It is shown that these findingsare consistent with the experimental observations which show nearlyequivalent quantum yields for CHDand cZc-HT and no production of MCPD. The results ofthe IRD computations have been validated byinvestigating the decay dynamics of trajectories starting from a“circle” of points around the conical intersection,with the initial kinetic energy distributed in randomly sampledvibrational modes. These computations havebeen carried out using a trajectory-surface-hopping (TSH) method and ahybrid molecular mechanics valencebond (MM−VB) force field to model the ab initiopotentials.
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