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

摘要

The Ornsteinhyphen;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 Ornsteinhyphen;Zernike equation in irreducible form, as a set of uncoupled matrix equations, of rather small size. A generalization of Baxter's form of the Ornsteinhyphen;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 distancer. 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 dipolehyphen;quadrupole interaction.