Cluster pair correlation function of simple fluids: energetic connectivity criteria

TL;DR

This paper investigates the clustering behavior of Lennard-Jones particles using an energetic connectivity criterion based on relative kinetic and potential energies, solving integral equations and comparing with molecular dynamics simulations.

Contribution

It introduces and applies an integral equation approach to analyze particle clustering with Hill's energetic criterion, including velocity dependence, and compares results with simulations.

Findings

Integral equation solutions match molecular dynamics results

Velocity-dependent criterion affects clustering predictions

Comparison with velocity-averaged models highlights energetic effects

Abstract

We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by T.L. Hill [J. Chem. Phys. 32, 617 (1955)] for the bond between pairs of particles. The criterion establishes that two particles are bonded (directly connected) if their relative kinetic energy is less than minus their relative potential energy. Thus, in general, it depends on the direction as well as on the magnitude of the velocities and positions of the particles. An integral equation for the pair connectedness function, proposed by two of the authors [Phys Rev. E 61, R6067 (2000)], is solved for this criterion and the results are compared with those obtained from molecular dynamics simulations and from a connectedness Percus-Yevick like integral equation for a velocity-averaged version of Hill's energetic criterion.