Semi-classical path integral non-adiabatic dynamics: a partial linearized classical mapping Hamiltonian approach

A new partially linearized approximate approach to non-adiabatic quantum dynamics is derived based on linearizing the path difference for nuclear degrees of freedom (DOF) in the classical mapping Hamiltonian while keeping quantum interference effects inherent in the forward and backward propagators for the electronic DOF. With this new approach, the non-adiabatic force that acts on the nuclear DOF is a mean force rather than a state dependent force as found in some alternative approaches. Various benchmark examples are explored to test the accuracy of this new approach, and compare its performance with other approaches for a wide range of physical phenomena including: non-adiabatic scattering, excited state conical intersection dynamics, excited state photoisomerization, and excitation energy transfer in realistic condensed phase model systems. Results indicate that, even though the method is based on a "mean trajectory"-like scheme, it can accurately capture electronic population branching through multiple avoided crossing regions and that the approach offers a robust and reliable way to treat quantum dynamical phenomena in a wide range of condensed phase applications.