Site-site direct correlation functions for three popular molecular models of liquid water

Direct correlation functions (DCFs) play a pivotal role in the applications of classical density functional theory (DFT) to addressing the thermodynamic properties of inhomogeneous systems beyond the local-density or mean-field approximations. Whereas numerous studies have been dedicated to the radial distribution functions of liquid water--the most important solvent on earth, relatively little attention has been given to the site-site DCFs. The water DCFs are long-ranged and difficult to calculate directly by simulation, and the predictions from conventional liquid-state theories have been rarely calibrated. Here we report a computational procedure for accurate evaluation of the site-site DCFs of liquid water based on three popular molecular models (viz., SPC, SPC∕E, and TIP3P). The numerical results provide a benchmark for calibration of conventional liquid-state theories and fresh insights into development of new DFT methods. We show that: (1) the long-range behavior of the site-site DCFs depends on both the molecular model and the thermodynamic condition; (2) the asymptotic limit of DCFs at large distance does not follow the mean-spherical approximation (MSA); (3) individual site-site DCFs are long ranged (~40 nm) but a summation of all DCF pairs exhibits only short-range behavior (~1 nm or a few water diameters); (4) the site-site bridge correlation functions behave as the DCFs, i.e., they are also long-ranged while the summation of all bridge correlation functions is short ranged. Our analytical and numerical analyses of the DCFs provide some simple strategies for possible improvement of the numerical performance of conventional liquid-state theories.