What can x-ray scattering tell us about the radial distribution functions of water?

We present an analysis of the Advanced Light Source (ALS) x-ray scattering experiment on pure liquid water at ambient temperature and pressure described in the preceding article. The present study discusses the extraction of radial distribution functions from the x-ray scattering of molecular fluids. It is proposed that the atomic scattering factors used to model water be modified to include the changes in the intramolecular electron distribution caused by chemical bonding effects. Based on this analysis we present a $g_{\mathrm{OO}}\mathrm{(r)}$ for water consistent with our recent experimental data gathered at the ALS, which differs in some aspects from the $g_{\mathrm{OO}}\mathrm{(r)}$ reported by other x-ray and neutron scattering experiments. Our $g_{\mathrm{OO}}\mathrm{(r)}$ exhibits a taller and sharper first peak, and systematic shifts in all peak positions to smaller r. Based on experimental uncertainties, we discuss what features of $g_{\mathrm{OO}}\mathrm{(r)}$ should be reproduced by classical simulations of nonpolarizable and polarizable water models, as well as ab initio simulations of water, at ambient conditions. We directly compare many water models and simulations to the present data, and discuss possible improvements in both classical and ab initio simulation approaches in the future.