Exact molecular direct, cavity, and bridge functions in water system.

The exact molecular bridge function of the extended simple point charge model of liquid water at room temperature is extracted from Monte Carlo (MC) simulation data. The projections gμνmnl(r) onto rotational invariants of the highly directional pair distribution function g(r,Ω) are accumulated during simulation performed with N = 512 molecules (cubic box size L ≈ 25 Å). Making intensive use of anisotropic integral equation techniques, the molecular Ornstein-Zernike equation fed with the MC data available at short distances and completed beyond L/2 with the hypernetted chain closure valid at long distances is then inverted in order to derive on the whole r range the direct correlation function cμνmnl(r), the cavity function yμνmnl(r), the negative excess potential of mean force lnyμνmnl(r), and, finally, the holy grail in such liquid state theory, the bridge function bμνmnl(r) projections. For completeness, the short distance domain inside the soft core can be reached, thanks to the use of a specially designed anisotropic finite potential which replaces the true one between a single pair of molecules in the simulation. The final bridge function b(r,Ω) of bulk water presents strong, non-universal directional features and can now serve as a reference for approximated bridge functions or functionals in liquid physics of aqueous solvents and solutions.