Analysis of variants of non-adiabatic ring polymer molecular dynamics for calculating excited state dynamics

The non-adiabatic ring polymer molecular dynamics (NRPMD) method, which combines the path-integral ring polymer molecular dynamics framework for the nuclei with the Meyer-Miller-Stock-Thoss mapping of the electronic states, is a powerful tool for simulating non-adiabatic dynamics including nuclear quantum effects. However, challenges arise in utilizing NRPMD associated with zero-point energy leakage between the electronic and nuclear degrees of freedom and ambiguities in how to apply the method under non-equilibrium conditions. Here, we explore several variants of NRPMD and compare their performance using a set of benchmark systems for excited-state electronic population dynamics. Within this context, we adopt an idea from recent work on the linearized semi-classical initial value representation and derive a new NRPMD correlation function for the population of the electronic states in terms of a trace-less operator and the identity operator. The in-depth analysis of the different choices when utilizing NRPMD provides new insight into the practical implementation of the method and related techniques.