Soft representation of the square-well and square-shoulder potentials to be used in Brownian and molecular dynamics simulations

Abstract

The discrete hard-sphere (HS), square-well (SW), and square-shoulder (SS) potentials have become the battle horse of molecular and complex fluids because they contain the basic elements to describe the thermodynamic, structural, and transport properties of both types of fluids. The mathematical simplicity of these discrete potentials allows us to obtain some analytical results despite the nature and complexity of the modeled systems. However, the divergent forces arising at the potential discontinuities may lead to severe issues when discrete potentials are used in computer simulations with uniform time steps. One of the few routes to avoid these technical problems is to replace the discrete potentials with continuous and differentiable forms built under strict physical criteria to capture the correct phenomenology. The match of the second virial coefficient between the discrete and the soft potentials has recently been successfully used to construct a continuous representation that mimics some physical properties of HSs (Báez et al 2018 J. Chem. Phys. 149 164907). In this paper, we report an extension of this idea to construct soft representations of the discrete SW and SS potentials. We assess the accuracy of the resulting soft potential by studying structural and thermodynamic properties of the modeled systems by using extensive Brownian and molecular dynamics computer simulations. Besides, Monte Carlo results for the original discrete potentials are used as benchmark. We have also implemented the discrete interaction models and their soft counterparts within the integral equations theory of liquids, finding that the most widely used approximations predict almost identical results for both potentials.