Family of Oxygen-Oxygen Radial Distribution Functions for Water

In a typical X-ray diffraction experiment, the elastically scattered intensity, I(Q), is the experimental observable. I(Q) contains contributions from both intramolecular as well as intermolecular correlations embodied in the scattering factors, H-OO(Q) and H-OH(Q), with negligible contributions from H-HH(Q). Thus, to accurately define the oxygen-oxygen radial distribution function, g(OO)(r), a model of the electron density is required to accurately weigh the H-OO(Q) component relative to the intramolecular and oxygen-hydrogen correlations from the total intensity observable. In this work, we carefully define the electron density model and its underlying assumptions and more explicitly utilize two restraints on the allowable g(OO)(r) functions, which must conform to both very low experimental errors at high Q and the need to satisfy the isothermal compressibility at low Q Although highly restrained by these conditions, the underdetermined nature of the problem is such that we present a family of g(OO)(r) values that provide equally good agreement with the high-Q intensity and compressibility restraints and with physically correct behavior at small r.