# Some corrected integral equations and their results for the square-well fluid

## Abstract

Extensions of the hypernetted chain (HNC), Percus-Yevick (PY), and mean spherical approximation (MSA) integral equations which incorporate corrections to part of the usual closure relations between h(r) and c(r) are derived. These are evaluated numerically in the case of a square-well fluid with a well width of 0.5σ, where σ is the hard-core diameter. The corrected HNC and PY equations are shown to be related to the usual HNC and PY theories in the same way that the optimized cluster theory is related to the MSA. These equations were originally derived by Lado some time ago using Fourier transform techniques. An advantage of our formulation is that we are also able to make contact with the recent PY, MS, and HNC perturbation equations of Henderson and colleagues and of Madden and Fitts. The numerically determined equations of state and radial distribution functions are compared with the computer simulation results and with previously reported integral equation results. The corrected HNC equation is found to give results superior to any of the other approximations. © 1978 American Institute of Physics.