An efficient procedure for the study of inhomogeneous liquids

Abstract

A complete description of an inhomogeneous fluid requires knowing not only its density ρ( r ) at any point r in space, but also its pair distribution function g( r ₁, r ₂). These can be found from coupled integral equations, but even in cases with homogeneity in two of the three dimensions, such solutions in direct space are cumbersome enough to have earned the task a reputation as ‘computationally intensive’. Here we propose using purpose-built basis functions that are orthogonal with weight function ρ( r ) to expedite the work. We find that these not only produce a satisfying simplification of the formalism, but also reduce the computing effort needed to something on the order of 1% of that of the earlier calculations in direct space.

Keywords:

• inhomogeneous liquids
• integral equations
• Ornstein–Zernike equation
• special orthogonal polynomials