An analysis of nonadiabatic ring-polymer molecular dynamics and its application to vibronic spectra

TL;DR

This paper generalizes nonadiabatic ring-polymer molecular dynamics to allow different numbers of beads for nuclear and electronic degrees of freedom, improving accuracy and enabling vibronic spectra simulations.

Contribution

It introduces a generalized approach with variable bead numbers for nuclear and electronic modes, reducing issues like negative populations and enhancing vibronic spectra modeling.

Findings

Increasing electronic mapping variables removes non-uniqueness and negative populations.

Explicit cyclic variable integration reduces the sign problem.

Promising vibronic spectra results for a model system.

Abstract

Nonadiabatic ring-polymer molecular dynamics employs the mapping approach to describe nonadiabatic effects within the ring-polymer ansatz. In this paper, it is generalized to allow for the nuclear and electronic degrees of freedom to be described by different numbers of ring-polymer beads. Analysis of the resulting method shows that as the number of electronic mapping variables increases, certain problems associated with the approach are removed, such as the non-unique choice of the mapping Hamiltonian and negative populations leading to inverted potential-energy surfaces. Explicit integration over cyclic variables reduces the sign problem for the initial distribution in the general case. A new application for the simulation of vibronic spectra is described and promising results are presented for a model system.