Structure in liquid water: A study of spatial distribution functions

Abstract

Despite the fact that an enormous literature has now accumulated on the structure in liquid water, the focus has been primarily limited to the average radial distributions of particles; local (atomic) pair-density maps which span both the radial and the angular coordinates of the separation vector have remained largely unexplored. In this work, we have obtained the spatial distribution functions gOO(r,Ω) and gOH(r,Ω) for liquid water and have applied them to an analysis of the equilibrium structure. Molecular dynamics simulations of SPC/E water have been carried out at temperatures of −10, 25, and 100 °C and the local liquid structure examined. It is found that the unfolded O...O distribution demonstrates, in addition to peaks consistent with a continuous tetrahedral network pattern, a distinct maximum in the local atomic pair density at ‘‘interstitial’’ separations of about 3.5 Å. This local maximum is lost in the spatially folded radial distribution function gOO(r) due to averaging over the entire angular space. By examining the peaks in gOO(r,Ω) due to nearest neighbors, we have shown that the tetrahedral network coordination number in liquid SPC/E water equals 4.0 and does not depend on temperature. The average number of molecules in additional nontetrahedral coordination, which is found to vary with temperature, has also been extracted, enabling us to establish full average coordination numbers of 4.8–5.0 in the temperature range of −10–100 °C. In addition, we have determined and analyzed statistical distributions for the pair energies and H-bond angles for different water fractions as identified from gOO(r,Ω) and gOH(r,Ω).