Fundamental measure theory of inhomogeneous two-body correlation functions

TL;DR

This paper develops analytical formulas within fundamental measure theory to efficiently compute inhomogeneous two-body correlation functions in three-dimensional hard-sphere systems, aiding understanding of packing structures and perturbation theories.

Contribution

It provides explicit functional formulas for the inhomogeneous two-body direct correlation function in symmetric cases, enabling rapid real-space correlation calculations.

Findings

Analytic formulas for Hankel and Legendre transforms of correlation functions.

Facilitates quick computation of inhomogeneous density correlations.

Supports development of perturbation theories for realistic models.

Abstract

For the three-dimensional hard-sphere model we investigate the inhomogeneous two-body correlations predicted by Rosenfeld's fundamental measure theory. For the special cases in which the density has either planar or spherical symmetry we provide analytic formulae for the Hankel and Legendre transforms, respectively, of the inhomogeneous two-body direct correlation function as explicit functionals of the density. When combined with the Ornstein-Zernike relation our analytical results allow for rapid calculation of inhomogeneous hard-sphere density correlations in real-space. These provide not only information about the packing structures of the hard-sphere system, but also form an essential building-block for constructing perturbation theories of more realistic models.