Statistical theory of nonadiabatic transitions

Based on results of the preceding paper, and assuming fast equilibration in phase space to the temperature of the surrounding media compared to the time scale of a reaction, we formulate a statistical theory of intramolecular nonadiabatic transitions. A classical mechanics description of phase space dynamics allows for an ab initio treatment of multidimensional reaction coordinates and easy combination with any standard molecular dynamics (MD) method. The presented approach has several features that distinguishes it from existing methodologies. First, the applicability limits of the approach are well defined. Second, the nonadiabatic transitions are treated dynamically, with full account of detailed balance, including zero-point energy, quantum coherence effects, arbitrarily long memory, and change of the free energy of the bath. Compared to popular trajectory surface hopping schemes, our MD-based algorithm is more efficient computationally, and does not use artificial ad hoc constructions like a "fewest switching" algorithm, and rescaling of velocities to conserve total energy. The enhanced capabilities of the new method are demonstrated considering a model of two coupled harmonic oscillators. We show that in the rate regime and at moderate friction the approach precisely reproduces the free-energy-gap law. It also predicts a general trend of the reaction dynamics in the low friction limit, and is valid beyond the rate regime.