On material objectivity of intermolecular force in molecular dynamics

Abstract

In molecular dynamics, intermolecular forces are treated as objective constitutive quantities to be given by constitutive functions of the position and the velocity of every molecule. Following the idea in continuum mechanics, constitutive equations are required to satisfy the principle of material frame-indifference. Since the relative position is an objective vector, while the relative velocity is not, by eliminating the rigid body rotation of the system of the molecules, we can define objective relative velocities. As a consequence of the material frame-indifference requirement, the general constitutive equations in molecular dynamics must reduce to isotropic functions of relative positions and objective relative velocities of the molecules.