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 mol ecular interactions, surprisingly simple and accurate theories (The Variati onal Mean Spherical Scaling Approximation, VMSSA) [(Velazquez, Blum J. Chem . Phys. 110 (1990) 10931, Blum, Velazquez, J: Quantum Chem (Theochem), in p ress)] can be obtained. The basic idea is that if the interactions can be e xpressed in a rapidly converging sum of(complex) exponentials, then the Orn stein-Zernike equation (OZ) has an analytical solution. This analytical sol ution is used to construct a robust interpolation scheme, the variation mea n 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 m atrix Gamma. Both the excess energy Delta E(Gamma) and the excess entropy D elta 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. Ph ys. 96 (1999) 821) and three-exponential closures of the OZ equation (Blum, J. Stat. Phys., submitted for publication). In this paper we extend this t o M Yukawas, a complete basis set: We obtain a solution for the one-compone nt 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 reser ved.