Variational extensions of the mean spherical approximation

In a previous work we have proposed a method to study complex systems with objects of arbitrary size. For certain specific forms of the atomic and molecular interactions, surprisingly simple and accurate theories (The Variational Mean Spherical Scaling Approximation, VMSSA) [(Velazquez, Blum J. Chem. Phys. 110 (1990) 10931, Blum, Velazquez, J: Quantum Chem (Theochem), in press)] can be obtained. The basic idea is that if the interactions can be expressed in a rapidly converging sum of(complex) exponentials, then the Ornstein-Zernike equation (OZ) has an analytical solution. This analytical solution is used to construct a robust interpolation scheme, the variation mean spherical scaling approximation (VMSSA). The Helmholtz excess free energy Delta 4 = Delta E - T Delta S is then written as a function of a scaling matrix Gamma. Both the excess energy Delta E(Gamma) and the excess entropy Delta S(Gamma) will be functionals of Gamma. in previous work of this series the form of this functional was found for the two- (Blum, Herrera, Mel. Phys. 96 (1999) 821) and three-exponential closures of the OZ equation (Blum, J. Stat. Phys., submitted for publication). In this paper we extend this to M Yukawas, a complete basis set: We obtain a solution for the one-component case and give a closed-form expression for the MSA excess entropy, which is also the VMSSA entropy. (C) 2000 Elsevier Science B.V. All rights reserved.