Impulsive correction to the elastic moduli obtained using the stress-fluctuation formalism in systems with truncated pair potential

TL;DR

This paper investigates how truncating pair potentials affects the calculation of elastic moduli using stress-fluctuation formalism, revealing impulsive corrections that are theoretically derived and numerically tested in various systems.

Contribution

It provides a theoretical framework for impulsive corrections to elastic moduli due to potential truncation and validates these corrections through numerical simulations.

Findings

Impulsive corrections significantly affect elastic moduli calculations.

Theoretical predictions match numerical results for binary mixtures and Lennard-Jones systems.

Corrections are relevant for higher derivatives of truncated potentials.

Abstract

The truncation of a pair potential at a distance r_cut is well-known to imply in general an impulsive correction to the pressure and other moments of the first derivatives of the potential. That depending on r_cut the truncation may also be of relevance to higher derivatives is shown theoretically for the Born contributions to the elastic moduli obtained using the stress-fluctuation formalism in d dimensions. Focusing on isotropic liquids for which the shear modulus G must vanish by construction, the predicted corrections are tested numerically for binary mixtures and polydisperse Lennard-Jones beads in, respectively, d=3 and d=2 dimensions.