Role of Triplet Correlations in Tetrahedral Ordering of Liquid Water: A DFT-RISM Study with Bridge Functions

Abstract

We present a classical density functional theory (DFT) study of liquid water in which bridge functions arising from triplet correlations are explicitly incorporated beyond the hypernetted-chain (HNC) approximation. Starting from a third-order density expansion of the Helmholtz free energy functional, we construct a tractable DFT–RISM (reference interaction site model) framework in which three-body direct correlations are included through a physically motivated factorization scheme. Particular attention is paid to the oxygen–oxygen (O–O) radial distribution function, whose second peak at around 4.5 A is a hallmark of local tetrahedral ordering. We show that this structural feature can be generated within an integral equation framework by introducing an effective bridge function with appropriate inter-particle correlation contributions. Comparison with molecular dynamics data demonstrates that the inclusion of triplet correlations significantly improves the description of the O–O correlations beyond the HNC level, while maintaining reasonable agreement for O–H and H–H correlations. These results provide a physically transparent route to understanding the origin of tetrahedral ordering in liquid water and highlight the essential role of three-body correlations in molecular liquids, particularly in hydrogen-bonded systems.