An efficient method for accurate evaluation of the site–site direct correlation functions of molecular fluids

Abstract

The direct correlation function (DCF) plays an important role in liquid integral-equation theories and non-mean-field applications of the classical density functional theory (DFT). While for a simple fluid the DCF can easily be calculated from the radial distribution function via the Fourier transform and/or, for special cases, can be derived from analytical solutions of the Ornstein–Zernike equation, computation of the site–site DCFs of a molecular fluid is more challenging because of numerical issues associated with solving the matrix integral equations. This paper describes a new theoretical method for accurate evaluation of the site–site DCFs of molecular fluids by combination of molecular simulation and analytical asymptotic analysis. The computational procedure entails four steps: (1) molecular simulation is used to calculate the site–site total correlation functions (TCFs) in real space; (2) the reference-interaction-site model (RISM) is used to calculate the site–site DCFs in Fourier space at large wavenumbers; (3) asymptotic expressions are derived for the TCFs and DCFs in the limit of small wavenumbers; and (4) site–site DCFs over the entire range are obtained by interpolation of the asymptotic results. The numerical procedure has been illustrated by application to bulk SPC/E water. Accurate evaluation of the site–site DCFs for water lays a foundation for future applications of the DFT to aqueous systems with atomic details.