Spin-mapping approach for nonadiabatic molecular dynamics

Abstract

We propose a trajectory-based method for simulating nonadiabatic dynamics in molecular systems with two coupled electronic states. Employing a quantum-mechanically exact mapping of the two-level problem to a spin-12 coherent state, we use the Stratonovich-Weyl transform to construct a classical phase space of a spin vector constrained to a spherical surface whose radius is consistent with the quantum magnitude of the spin. In contrast with the singly excited harmonic oscillator basis used in Meyer-Miller-Stock-Thoss (MMST) mapping, the theory requires no additional projection operators onto the space of physical states. When treated under a quasiclassical approximation, we show that the resulting dynamics are equivalent to those generated by the MMST Hamiltonian. What differs is the value of the zero-point energy parameter as well as the initial distribution and the measurement operators used in constructing correlation functions. For various spin-boson models, the results of the method are seen to be a significant improvement compared to both standard Ehrenfest dynamics and linearized semiclassical MMST mapping, without adding any computational complexity.