  In this report the radial distribution functions (RDFs) of liquid water are
calculated on the basis of the classical density functional theory combined
with the reference interaction site model for molecular liquids. The bridge
functions, which are neglected in the hypernetted-chain (HNC) approximation,
are taken into account through the density expansion for the Helmholtz free
energy functional up to the third order. A factorization approximation to the
ternary direct correlation functions in terms of the site-site pair correlation
functions is then employed in the expression of the bridge functions, thus
leading to a closed set of integral equations for the determination of the
RDFs. It is confirmed through numerical calculations that incorporation of the
oxygen-oxygen bridge function substantially improves the poor descriptions by
the HNC approximation at room temperature, e.g., for the second peak of the
oxygen-oxygen RDF.
