Non-Adiabatic Ring Polymer Molecular Dynamics with Spin Mapping Variables

TL;DR

This paper introduces a novel non-adiabatic ring polymer molecular dynamics method using spin mapping variables, enabling efficient quantum statistical sampling and accurate dynamical simulations of non-adiabatic systems.

Contribution

The paper develops the spin-mapping NRPMD approach, deriving a new Hamiltonian and demonstrating improved numerical stability and accuracy over traditional harmonic oscillator mappings.

Findings

SM-NRPMD agrees well with exact results for model systems.

Spin mapping variables yield nearly time-independent expectation values.

The method preserves invariant dynamics under different potential partitionings.

Abstract

We present a new non-adiabatic ring polymer molecular dynamics (NRPMD) method based on the spin mapping formalism, which we refer to as the spin-mapping NRPMD (SM-NRPMD) approach. We derive the path-integral partition function expression using the spin coherent state basis for the electronic states and the ring polymer formalism for the nuclear degrees of freedom (DOFs). This partition function provides an efficient sampling of the quantum statistics. Using the basic property of the Stratonovich-Weyl transformation, we derive a Hamiltonian which we propose for the dynamical propagation of the coupled spin mapping variables and the nuclear ring polymer. The accuracy of the SM-NRPMD method is numerically demonstrated by computing nuclear position and population auto-correlation functions of non-adiabatic model systems. The results from SM-NRPMD agree very well with the numerically exact results. The main advantage of using the spin mapping variables over the harmonic oscillator mapping variables is numerically demonstrated, where the former provides nearly time-independent expectation values of physical observables for systems under thermal equilibrium, the latter can not preserve the initial quantum Boltzmann distribution. We also explicitly demonstrate that SM-NRPMD provides invariant dynamics upon various ways of partitioning the state-dependent and state-independent potentials.