A path integral methodology for obtaining thermodynamic properties of nonadiabatic systems using Gaussian mixture distributions

TL;DR

This paper presents a novel path integral Monte Carlo method for calculating thermodynamic properties of nonadiabatic systems, utilizing Gaussian mixture models to reduce stochastic error and improve computational efficiency.

Contribution

It introduces a new path integral formulation without mapping schemes and employs Gaussian mixtures to efficiently evaluate the partition function in nonadiabatic systems.

Findings

Gaussian mixture models reduce stochastic error in Monte Carlo estimations.

Choice of sampling distribution significantly impacts method efficiency.

The approach achieves lower computational cost with improved sampling strategies.

Abstract

We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition function in a product basis of continuous nuclear and discrete electronic degrees of freedom without the use of any mapping schemes. We separate our Hamiltonian into a harmonic portion and a coupling portion; the partition function can then be calculated as the product of a Monte Carlo estimator (of the coupling contribution to the partition function) and a normalization factor (that is evaluated analytically). A Gaussian mixture model is used to evaluate the Monte Carlo estimator in a computationally efficient manner. Using two model systems, we demonstrate our approach to reduce the stochastic error associated with the Monte Carlo estimator. We show that the selection of the harmonic oscillators comprising the sampling distribution directly affects the efficiency of the method. Our results demonstrate that our path integral Monte Carlo method's deviation from exact Trotter calculations is dominated by the choice of the sampling distribution. By improving the sampling distribution, we can drastically reduce the stochastic error leading to lower computational cost.