Comment on the calculation of forces for multibody interatomic potentials

TL;DR

This paper examines how different force definitions in multibody interatomic potentials affect stress tensor calculations, highlighting discrepancies depending on the force partitioning method and localization function.

Contribution

It compares two force definitions for multibody potentials and analyzes their impact on stress tensor computation, emphasizing the importance of force partitioning choices.

Findings

Forces coincide only for pair or embedded-atom potentials.

Hardy's stress tensor varies with localization function radius.

Force definition choice significantly influences stress tensor results.

Abstract

The system of particles interacting via multibody interatomic potential of general form is considered. Possible variants of partition of the total force acting on a single particle into pair contributions are discussed. Two definitions for the force acting between a pair of particles are compared. The forces coincide only if the particles interact via pair or embedded-atom potentials. However in literature both definitions are used in order to determine Cauchy stress tensor. A simplest example of the linear pure shear of perfect square lattice is analyzed. It is shown that, Hardy's definition for the stress tensor gives different results depending on the radius of localization function. The differences strongly depend on the way of the force definition.