Non-adiabatic Ring Polymer Molecular Dynamics in the Phase Space of the SU(N) Lie Group

TL;DR

This paper introduces the spin mapping non-adiabatic RPMD (SM-NRPMD), a novel method for simulating electronic non-adiabatic dynamics using SU(N) Lie Group phase space, improving accuracy and preserving system symmetry.

Contribution

The paper develops the SM-NRPMD approach based on spin mapping and ring polymer path integrals, offering numerical advantages over previous methods and better symmetry preservation.

Findings

SM-NRPMD accurately computes correlation functions in three-state systems.

The method outperforms the MMST-based NRPMD in numerical tests.

SM-NRPMD effectively captures nuclear quantum effects and electronic dynamics.

Abstract

We derive the non-adiabatic ring polymer molecular dynamics (RPMD) approach in the phase space of the SU(N) Lie Group. This method, which we refer to as the spin mapping non-adiabatic RPMD (SM-NRPMD), is based on the spin-mapping formalism for the electronic degrees of freedom (DOFs) and ring polymer path-integral description for the nuclear DOFs. Using the Stratonovich-Weyl transform for the electronic DOFs, and the Wigner transform for the nuclear DOFs, we derived an exact expression of the Kubo-transformed time-correlation function (TCF). We further derive the spin mapping non-adiabatic Matsubara dynamics using the Matsubara approximation that removes the high frequency nuclear normal modes in the TCF and derive the SM-NRPMD approach from the non-adiabatic Matsubara dynamics by discarding the imaginary part of the Liouvillian. The SM-NRPMD method has numerical advantages compared to the original NRPMD method based on the MMST mapping formalism, due to a more natural mapping using the SU(N) Lie Group that preserves the symmetry of the original system. We numerically compute the Kubo-transformed position auto-correlation function and electronic population correlation function for three-state model systems. The numerical results demonstrate the accuracy of the SM-NRPMD method, which outperforms the original MMST-based NRPMD. We envision that the SM-NRPMD method will be a powerful approach to simulate electronic non-adiabatic dynamics and nuclear quantum effects accurately.