Choosing a good representation of the quantum state wave functions for semiclassical surface hopping calculations

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Abstract

Simple curve crossing problems have shown that the probability of transition between quantum states for the fast degrees of freedom becomes small at low energies, if the adiabatic representation is employed for the quantum state wave functions. Conversely, the transition probability approaches unity at high energies in the adiabatic representation, but it is small if the diabatic representation is employed. Methods are developed and numerically tested for choosing a representation, which is intermediate between the adiabatic and diabatic representations, so as to approximately minimize the interstate coupling in semiclassical surface hopping methods. The reduction in the coupling should diminish the importance of multihop trajectories in surface hopping procedures, resulting in a corresponding reduction in the computational effort required for accurate calculations.

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