Direct correlation functions for three-site and four-site water models
Direct correlation functions (DCFs) play a pivotal role in modern liquid-state theories and are virtually indispensable for non-mean-field implementation of the classical density functional theory (cDFT). Whereas analytical expressions have been derived for the DCFs of simple fluids and electrolytes, DCFs for molecular systems are attainable only through numerical solution of the integral-equation theories in combination with molecular simulation or an approximate closure. Unlike radial distribution functions, DCFs reflect the variational of the local chemical potential of individual atoms/interaction sites with the density-profile fluctuations, which are difficult to be sampled from the simulation trajectory. This article presents an improved numerical procedure to calculate the DCFs of three-site (SPC/E and TIP3P) and four-site (TIP4P-Ew) water models based on the reference interaction site model and molecular dynamics simulations. In combination with the modified fundamental measure theory for the bridge functionals, the DCFs have been utilised to predict the hydration free energies of 504 small organic molecules. The theoretical predictions yield an average unsigned error of 0.66 kcal/mol in comparison with the simulation data, better than that (∼1 kcal/mol) reported in previous cDFT calculations.