About the computation of finite temperatureensemble averages of hybrid quantum-classicalsystems with Molecular Dynamics

TL;DR

This paper explores methods for calculating finite temperature ensemble averages in hybrid quantum-classical systems using molecular dynamics, addressing both classical ions and quantum electrons at thermal equilibrium.

Contribution

It introduces new formulas and discusses existing approaches for finite temperature calculations in hybrid quantum-classical molecular dynamics.

Findings

Provides formulas for finite temperature ensemble averages

Analyzes previous approaches in the literature

Addresses both classical and quantum subsystems at finite temperature

Abstract

Molecular or condensed matter systems are often well approximated by hybrid quantum-classical models: the electrons retain their quantum character, whereas the ions are considered to be classical particles. We discuss various alternative approaches for the computation of equilibrium (canonical) ensemble averages for observables of these hybrid quantum-classical systems through the use of molecular dynamics (MD), i.e. by performing dynamics in the presence of a thermostat and computing time averages over the trajectories. Often, in classical or ab initio MD, the temperature of the electrons is ignored and they are assumed to remain at the instantaneous ground state given by each ionic configuration during the evolution. Here, however, we discuss the general case that considers both classical and quantum subsystems at finite temperature canonical equilibrium. Inspired by a recent formal derivation for the canonical ensemble for quantum classical hybrids, we discuss previous approaches found in the literature, and provide some new formulas.