Surface hopping method

The goal of this chapter is twofold. First we wish to critically compare—from both a conceptional and a practical point of view—various classical and mixed quantum-classical strategies to describe non-Born-Oppenheimer dynamics. To this end. Section II introduces five multidimensional model problems, each representing a specific challenge for a classical description. Allowing for exact quantum-mechanical reference calculations, aU models have been used as benchmark problems to study approximate descriptions. In what follows, Section III describes in some detail the mean-field trajectory method and also discusses its connection to time-dependent self-consistent-field schemes. The surface-hopping method is considered in Section IV, which discusses various motivations of the ansatz as well as several variants of the implementation. Section V gives a brief account on the quantum-classical Liouville description and considers the possibility of an exact stochastic realization of its equation of motion. 

The approximation (58) resembles the usual momentum-jump ansatz employed in various surface-hopping methods [55, 57, 58, 61, 66, 67, 82]. In order to determine the momentum shift of a trajectory, however, the latter formulations typically require the conservation of nuclear energy ... 

SEMICLASSICAL SURFACE HOPPING METHODS FORNONADIABATIC TRANSITIONS IN CONDENSED PHASES... 

II. SEMICLASSICAL SURFACE-HOPPING METHODS FOR NONADIABATIC PROBLEMS... 

C. Surface Hopping Method for Time Dependent Transition Probabilities... 

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