Minimal Modification to Nos\'e-Hoover Barostat Enables Correct NPT Sampling

TL;DR

This paper introduces a minimal and simple modification to the Nosé-Hoover barostat that corrects NPT sampling issues, ensuring proper ergodic behavior with less complexity than previous methods.

Contribution

A straightforward constant addition to the Nosé-Hoover equations corrects NPT sampling, simplifying previous complex modifications and improving ergodic sampling accuracy.

Findings

Corrects NPT sampling with minimal modification

Simplifies previous approaches to Nosé-Hoover adjustments

Ensures proper ergodic sampling in simulations

Abstract

The Nos\'e-Hoover dynamics for isothermal-isobaric (NPT) computer simulations do not generate the appropriate partition function for ergodic systems. The present paper points out that this can be corrected with a simple addition of a constant term to only one of the equations of motion. The solution proposed is much simpler than previous modifications done towards the same goal. The present modification is motivated by the work virial theorem, which has been derived for the special case of an infinitely periodic system in the first part of this paper.