Evolutionary optimization of the Verlet closure relation for the hard-sphere and square-well fluids

TL;DR

This paper uses evolutionary algorithms to optimize the Verlet closure relation in solving the Ornstein-Zernike equation for hard-sphere and square-well fluids, improving thermodynamic consistency and agreement with simulations.

Contribution

It introduces an evolutionary optimization approach to refine the Verlet closure parameters, enhancing the accuracy of fluid structure predictions.

Findings

Good agreement with simulations at low and high densities

Deviations near the freezing transition for hard-sphere fluids

Potential for further improvement with additional thermodynamic criteria

Abstract

The Ornstein-Zernike equation is solved for the hard-sphere and square-well fluids using a diverse selection of closure relations; the attraction range of the square-well is chosen to be $\lambda=1.5.$ In particular, for both fluids we mainly focus on the solution based on a three-parameter version of the Verlet closure relation [Mol. Phys. 42, 1291-1302 (1981)]. To find the free parameters of the latter, an unconstrained optimization problem is defined as a condition of thermodynamic consistency based on the compressibility and solved using Evolutionary Algorithms. For the hard-sphere fluid, the results show good agreement when compared with mean-field equations of state and accurate computer simulation results; at high densities, i.e., close to the freezing transition, expected (small) deviations are seen. In the case of the square-well fluid, a good agreement is observed at low and high densities when compared with event-driven molecular dynamics computer simulations. For intermediate densities, the explored closure relations vary in terms of accuracy. Our findings suggest that a modification of the optimization problem to include, for example, additional thermodynamic consistency criteria could improve the results for the type of fluids here explored.