Multidimensional Effects in Nonadiabatic Statistical Theories of Spin-Forbidden Kinetics: A Case Study of (3)O + CO → CO2.

The appropriateness of treating crossing seams of electronic states of different spins as nonadiabatic transition states in statistical calculations of spin-forbidden reaction rates is considered. We show that the spin-forbidden reaction coordinate, the nuclear coordinate perpendicular to the crossing seam, is coupled to the remaining nuclear degrees of freedom. This coupling gives rise to multidimensional effects that are not typically included in statistical treatments of spin-forbidden kinetics. Three qualitative categories of multidimensional effects may be identified: static multidimensional effects due to the geometry-dependence of the local shape of the crossing seam and of the spin-orbit coupling, dynamical multidimensional effects due to energy exchange with the reaction coordinate during the seam crossing, and nonlocal (history-dependent) multidimensional effects due to interference of the electronic variables at second, third, and later seam crossings. Nonlocal multidimensional effects are intimately related to electronic decoherence, where electronic dephasing acts to erase the history of the system. A semiclassical model based on short-time full-dimensional trajectories that includes all three multidimensional effects as well as a model for electronic decoherence is presented. The results of this multidimensional nonadiabatic statistical theory (MNST) for the (3)O + CO → CO2 reaction are compared with the results of statistical theories employing one-dimensional (Landau-Zener and weak coupling) models for the transition probability and with those calculated previously using multistate trajectories. The MNST method is shown to accurately reproduce the multistate decay-of-mixing trajectory results, so long as consistent thresholds are used. The MNST approach has several advantages over multistate trajectory approaches and is more suitable in chemical kinetics calculations at low temperatures and for complex systems. The error in statistical calculations that neglect multidimensional effects is shown to be as large as a factor of 2 for this system, with static multidimensional effects identified as the largest source of error.