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.

Acknowledgement

For the financial support of this research, the authors are grateful to the US Department of Energy (DE-FG02-06ER46296). This work utilizes supercomputers from the National Energy Research Scientific Computing Center (NERSC). S.L. Zhao also acknowledges detailed discussion with Daniel Borgis at Ecole Normale Supérieure, Paris, on direct sampling of the structure factor from simulation.

Notes

1. For systems with dipole–dipole interactions, Equation (12) would include a non-analytic term. Such a term is not relevant for SPC/E water.