Semiclassical Dynamics in Wigner Phase Space II : Non-Adiabatic Hybrid Wigner Dynamics

In this series of two articles, we present approximate semiclassical (SC) dynamic methods for adiabatic and non-adiabatic problems in Wigner phase space. Focusing on adiabatic problems, the first article introduced the Adiabatic Hybrid Wigner Dynamics (AHWD) method. It partitions the problem into a few important `system' degrees of freedom (dofs), that are treated at the Double Herman-Kluk (DHK) level, while treating the rest of the dofs (the `bath') in the classical limit. In this second article, with the use of Meyer-Miller-Stock-Thoss (MMST) mapping, an extension of Hybrid Wigner Dynamics to nonadiabatic problems, termed Nonadiabatic Hybrid Wigner Dynamics (NHWD), is introduced. Two different variants are presented differing in the choice of the quantized system. NHWD with a quantized electronic system [NHWD(E)] is shown to produce reliable results on scattering models and spin-boson models with weak coupling to nuclear modes. NHWD with a quantized vibronic system [NHWD(V)] is shown to improve on NHWD(E) for spin boson models with strong coupling to the nuclear modes. Both methods provide a rigorous avenue to systematically improve upon the widely used classical-limit SC dynamics for non-adiabatic problems.