A phase-space theory and Monte Carlo sampling method for studying nonadiabatic unimolecular reactions

A statistical method for calculating nonadiabatic unimolecular rate constants is developed. The rate constant is considered as a weighted flux through a ‘‘transition-state,’’ represented by the locus of intersection of two diabatic potential energy surfaces. Phase-space points close to the transition-state contribute to the rate constant, with a weight given by a transition probability (e.g., the Landau–Zener transition probability). The resulting expressions are approximated using a Monte Carlo technique. The statistical model is general and applicable to large polyatomic systems. Application is made to N2O predissociation, and the results are compared with those of classical trajectory surface-hopping calculations. A comparison is also made to the phase-space theory developed by Zahr et al. [G. E. Zahr, R. K. Preston, and W. H. Miller, J. Chem. Phys. 62, 1127 (1975)]. The Monte Carlo calculations are in good agreement with the trajectory results.