b) The manuscript has been accepted by J. Chem. Phys.

Based on the recently developed unified theoretical framework [J. Liu, J. Chem. Phys. 145(20), 204105 (2016)], we propose a new perspective for studying nonadiabatic dynamics with classical mapping models (CMMs) of the coupled multistate Hamiltonian onto the Cartesian phase space. CMMs treat the underlying electronic state degrees of freedom classically with a simple physical population constraint while employing the linearized semiclassical initial value representation to describe the nuclear degrees of freedom. We have tested various benchmark condensed phase models where numerically exact results are available, which range from finite temperature to more challenging zero temperature, from adiabatic to nonadiabatic domains, and from weak to strong system-bath coupling regions. CMMs demonstrate overall reasonably accurate dynamics behaviors in comparison to exact results even in the asymptotic long time limit for various spin-boson models and site-exciton models. Further investigation of the strategy used in CMMs may lead to practically useful approaches to study nonadiabatic processes in realistic molecular systems in the condensed phase.

A simple model is presented for treating local imaginary frequencies that are important in the study of quantum effects in chemical reactions and various dynamical processes in molecular liquids. It significantly extends the range of accuracy of conventional local harmonic approximations (LHAs) used in the linearized semiclassical initial value representation/classical Wigner approximation for real time correlation functions. The key idea is realizing that a local Gaussian approximation (LGA) for the momentum distribution (from the Wigner function involving the Boltzmann operator) can be a good approximation even when a LHA for the potential energy surface fails. The model is applied here to two examples where imaginary frequencies play a significant role: the chemical reaction rate for a linear model of the H+H(2) reaction and an analogous asymmetric barrier--a case where the imaginary frequency of the barrier dominates the process--and for momentum autocorrelation functions in liquid para-hydrogen at two thermal state points (25 and 14 K under nearly zero external pressure). We also generalize the LGA model to the Feynman-Kleinert approximation.