Stress-stress fluctuation formula for elastic constants in the NPT ensemble

TL;DR

This paper introduces a new stress-stress fluctuation formula for calculating elastic constants in the NPT ensemble, improving convergence and enabling local elastic constant determination, validated through simulations of Lennard-Jones crystals and lipid bilayers.

Contribution

A novel stress-stress fluctuation formula for the NPT ensemble that enhances convergence and allows local elastic constant calculations.

Findings

Excellent agreement between NPT and NVT ensemble results for elastic constants.

The new formula successfully applied to lipid bilayer simulations.

Improved convergence properties over existing fluctuation formulas.

Abstract

Several fluctuation formulas are available for calculating elastic constants from equilibrium correlation functions in computer simulations, but the ones available for simulations at constant pressure exhibit slow convergence properties and cannot be used for the determination of local elastic constants. To overcome these drawbacks, we derive a stress-stress fluctuation formula in the $NPT$ ensemble based on known expressions in the $NVT$ ensemble. We validate the formula in the $NPT$ ensemble by calculating elastic constants for the simple nearest-neighbor Lennard-Jones crystal and by comparing the results with those obtained in the $NVT$ ensemble. For both local and bulk elastic constants we find an excellent agreement between the simulated data in the two ensembles. To demonstrate the usefulness of the new formula, we apply it to determine the elastic constants of a simulated lipid bilayer.