Variational Theory of the Radial Distribution Function

A variational approach to the calculation of the radial distribution function is presented. The approximations consist in the neglect of fourth-order correlation in the entropy and the use of a constant third-order correlation chosen to satisfy the third-order normalization condition. The average interaction energy, containing only pair terms, does not involve correlations higher than second order. Finally, one obtains approximate expression for the excess Helmholtz free energy as a function of the radial distribution function (r.d.f.) and macroscopic parameters. This free energy, when minimized with respect to the r.d.f. at constant temperature and density, yields an integral equation for the r.d.f. This theory has a simpler structure and yields thermodynamic functions in a more direct way than earlier theories. The theory has not yet been adequately tested; however, the author speculates that it will give good results for short-range forces but poor results for long-range forces.