On the quantum mechanical potential of mean force. I. A path integral perspective

TL;DR

This paper develops and validates two path integral estimators for the quantum mechanical potential of mean force, enabling accurate computation of PMF derivatives and values in quantum systems through Monte Carlo simulations.

Contribution

It introduces two novel path integral estimators for the quantum PMF derivative, validated on model systems, advancing computational methods in quantum thermodynamics.

Findings

Estimators accurately reproduce PMF and its derivative for harmonic oscillator and Lennard-Jones systems.

Validated estimators against reference results at multiple temperatures.

Establishes a foundation for applying these estimators to more complex systems in future work.

Abstract

We derive two path integral estimators for the derivative of the quantum mechanical potential of mean force (PMF), which may be numerically integrated to yield the PMF. For the first estimator, we perform the differentiation on the exact path integral, and for the second, we perform the differentiation on the path integral after discretization. These estimators are successfully validated against reference results for the harmonic oscillator and Lennard-Jones dimer systems using constrained path integral Monte Carlo (PIMC) simulations. Specifically, the estimators reproduce both the derivative of the PMF, as well as the PMF itself, for the model systems at multiple temperatures. In Paper II, these estimators are implemented alongside path integral molecular dynamics (PIMD) with a constrained path integral Langevin equation thermostat for use with more general systems and potentials.