Solution of the Ornstein-Zernike equation for spheres with octupolar surface adhesion: Toward a simple model of water

An analytic solution of the molecular Ornstein-Zernike equation for spheres with octupolar sticky potentials is given explicitly. In its most general form the closure of the direct correlation function is of the form of the mean spherical approximation for arbitrary multipolar interactions, and the total correlation function contains terms that arise in the Percus-Yevick approximation for spheres with anisotropic surface adhesion. In addition to generalizing several earlier analyses of special cases of this closure, the solution presented here contains new simplifying insights that reduce the complexity of the resulting algebraic equations. The tetrahedral octupole case can be explicitly solved in terms of the inverses of two 3 by 3 matrices. We give explicit solution for a model that has, the nearest-neighbor geometry of water and show that the atom-atom pair correlation functions are in rather fair agreement with the neutron scattering experiments, considering the shortcomings of the sticky potential.