Search

A new differential equation for the pair correlation function of a uniform liquid is derived from density functional theory. Its utility is probed by studying various regimes analytically, since the numerical solution is complicated by the fact that the coefficients depend on the unkown. It is shown that the behavior of the solution at large interparticle separation agrees with the Ornstein–Zernike differential equation and generalizes the equation obtained by Fisher et al. for the asymptotic behavior of the Yvon–Born–Green equation. Correct behavior is also obtained near the limit of zero separation, at least at low density. At higher densities, this limit of the equation is probed through computer simulation data. Extension beyond the square-gradient approximation leads to a result in agreement with that originally predicted by Hart. [ABSTRACT FROM AUTHOR]