Density functional theory for molecular fluids developed by Donley et al. (J. Chem. Phys. 101 (1994) 3205) is extended to include the effects of orientation-dependent bridge functions associated with the interparticle, triplet correlations. Resultant integral equations for the pair and direct correlation functions are solved for water, where the three-body direct correlation functions are approximated in terms of two-body functions. A test calculation employing a simple Gaussian form for the two-body function between the oxygen sites then provides a promising result to improve the description of the oxygen-oxygen correlations in liquid water at room temperature. (C) 2013 Elsevier B.V. All rights reserved.