Bond-Valence Constraints on Liquid Water Structure

The recent controversy about the structure of liquid water pits a new model involving water molecules in relatively stable "rings-and-chains" structures against the standard model that posits water molecules in distorted tetrahedral coordination. Molecular dynamics (MD) simulations, both classical and ab initio, almost uniformly support the standard model, but because none of them can yet reproduce all of the anomalous properties of water, they leave room for doubt. We argue that it is possible to evaluate these simulations by testing them against their adherence to the bond-valence model, a well-known and quantitatively accurate empirical summary of the behavior of atoms in the bonded networks of inorganic solids. Here we use the results of ab initio MD simulations of ice, water, and several solvated aqueous species to show that the valence sum rule (the first axiom of the bond-valence model) is followed in both solid and liquid bond networks. We then test MD simulations of water, employing several popular potential models against this criterion and the experimental O-O RDF. It appears that most of those tested cannot satisfy both criteria well, except TIP4P, TIP4P/2005, and TIP5P. If the valence sum rule really can be applied to simulated liquid structures, then it follows that the bonding behaviors of atoms in liquids are in some ways identical to those in solids. We support this interpretation by showing that the simulations produce O-H...O geometries that are completely consistent with the range of geometries available in solids, and the distributions of instantaneous valence sums reaching the atoms in both the ice and liquid water simulations are essentially identical. Furthermore, we show that none of the extant asymmetric water potentials that produce "rings-and-chains" structures can satisfy our geometric criteria. Taken together, this is powerful evidence in favor of the standard distorted tetrahedral model of liquid water structure.