Path Integral Molecular Dynamics for Exact Quantum Statistics of Multi-Electronic-State Systems

TL;DR

This paper introduces an exact path integral molecular dynamics method for calculating quantum statistical properties of multi-electronic-state systems, extending previous single-surface approaches to more complex systems.

Contribution

The authors develop a new MES-PIMD approach with an effective potential and estimators, enabling accurate quantum statistics for complex multi-electronic systems beyond common approximations.

Findings

Successfully applied to 1D and multi-dimensional models

Provides a practical tool for complex MES systems

Works in both diabatic and adiabatic representations

Abstract

An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD) [J. Chem. Phys. 145, 024103 (2016); 147, 034109 (2017)] for quantum statistical mechanics when a single potential energy surface is involved. We first define an effective potential function that is numerically favorable for MES-PIMD, and then derive corresponding estimators in MES-PIMD for evaluating various physical properties. Its application to several representative one-dimensional and multi-dimensional models demonstrates that MES-PIMD in principle offers a practical tool in either of the diabatic and adiabatic representations for studying exact quantum statistics of complex/large MES systems when the Born-Oppenheimer approximation, Condon approximation, and harmonic bath approximation are broken.