Invariant Expansion. II. The Ornstein-Zernike Equation for Nonspherical Molecules and an Extended Solution to the Mean Spherical Model

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Abstract
The Ornstein‐Zernike equation for fluids with nonspherical molecules obtained in a former publication [L. Blum and A. J. Torruella, J. Chem. Phys. 56, 303 (1972)] is written in coordinate space as a convolution matrix equation. A rather simple property of the angular coupling coefficients of our former work allows us to write the Ornstein‐Zernike equation in irreducible form, as a set of uncoupled matrix equations, of rather small size. A generalization of Baxter's form of the Ornstein‐Zernike equation to matrices allows us to write a formal solution to the mean spherical model of neutral hard spheres with almost arbitrary electrostatic multipoles. This is an extension of Wertheim's solution for dipoles [J. Chem. Phys. 55, 4291 (1971)]. The formal solution consists in showing that the direct correlation function inside the hard core is a polynomial in the interatomic distance r. The coefficients of the polynomials are obtained by solving a set of quadratic matrix equations. The class of potentials that admit this kind of a solution is larger than the electrostatic multipole interaction but does not include some cross interactions like the dipole‐quadrupole interaction.