Calculation of local and average pressure tensors in molecular simulations

Abstract

A conceptually simple method to calculate local and average pressure tensors in simulations of molecular systems with discrete particles is presented. The pressure originates from the linear momentum of the particles as well as from n-body interactions between the particles, and consists of one additive contribution for every term in the expression of the total energy. The basis for the calculation is the analysis of the velocities of the particles and of the n-body interactions between the particles at the molecular scale to obtain local pressures, and averaging of the local pressure over areas and volumes to obtain average pressures (H. Heinz, W. Paul, K. Binder, Phys. Rev. E., 72, 066704 (2005)). The explicit consideration of many-body interactions (e.g. angles, torsions, cross-terms) provides simple derivations of existing methods (method of planes, virial expression) and a straightforward extension to periodic systems. In periodic systems original particles are translated into the box in the moment of pressure calculation and the pool of n-body interactions considered is the same as in the energy expression (particle–particle and particle–image interactions). Local and average pressure tensors are augmented by interactions including particles and images, and translational symmetry to judge dissection by specified areas A α, compared to a non-periodic system. The method of planes and the virial expression, including the additional interactions in atom-based forces, are applicable without further changes in a periodic system.