First-order mean spherical approximation for inhomogeneous fluids

The first-order mean-spherical approximation (FMSA) [Y. Tang, J. Chem. Phys., 118, 4140 (2003)] is extended to the studies of inhomogeneous fluids by combining with Rosenfeld's perturbative method [Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993)]. In the extension, the key input-direct correlation function of FMSA-is applied to constructing the free energy density functional. Preserving its high fidelity at the bulk limit, the FMSA shows satisfactory performance for Yukawa fluids near hard and attractive walls. The results are better than or comparable to several other theories reported before for the geometry. The FMSA is found, in particular, more satisfactory than the traditional mean-field theory for predicting density profiles around hard walls. The FMSA is also compared with the full MSA for inhomogeneous fluids, showing no appreciable differences. The inhomogeneous FMSA goes successfully through the self-consistency test for reproducing the radial distribution function of the bulk Yukawa fluid. As far as the computation is concerned, the FMSA can be executed much faster than any nonmean-field theories, and the speed is virtually identical to that of the mean-field theory.