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

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