Some simple calculations of the density profile of inhomogeneous hard spheres using the Lovett-Mou-Buff-Wertheim equation with the bulk direct correlation function

The Lovett-Mou-Buff-Wertheim (LMBW) equation relating pair direct correlation functions with singlet density profiles is considered. If the direct correlation function is approximated by its bulk value, the LMBW equation becomes the hypernetted chain (HNC) approximation or, if linearized, the Percus-Yevick (PY) approximation. For a system of particles near a hard wall, substitution of the contact value theorem into the LMBW equation leads to a modified HNC equation or, with linearization, a modified PY equation. Numerical results for hard spheres indicate that the modified HNC equation is an improvement but that the modified PY equation is not. © 1989 American Chemical Society.