Invariant expansion III: The general solution of the mean spherical model for neutral spheres with electostatic interactions

Abstract

The partial solution for the mean spherical model of neutral spheres with electrostatic interactions obtained in a previous communication [L. Blum, J. Chem. Phys. 57, 1862 (1972).] is extended to the general case, in which the electrostatic interactions of odd parity, like the dipole-quadrupole interaction, are included. The solution is given in terms of a linear transform of the direct correlation function, which is shown to be a polynomial in r inside the hard core diameter. The coefficients of this polynomial are determined from a sufficient number of boundary conditions. The method of solution employs the so-called second Baxter form of the Ornstein-Zernike equation [Australian J. Phys. 21, 563 (1968).] which is derived for this particular case. Also, alternative forms of the Ornstein-Zernike equation in coordinate space are obtained. The case of molecules with linear dipole and quadrupole moments is summarily illustrated.