Molecular dynamics simulations of liquid water: Voronoi polyhedra and network topology

We have carried out various runs at different temperatures simulating liquid water via the TIP4P model, a well tested and widely used 4-site intermolecular potential. Voronoi polyhedra have been constructed and the distributions of various quantities analyzed. The higher the temperature, the more the distributions are similar to those of a normal liquid: as a reference for a corresponding liquid without hydrogen bonds, we have examined hydrogen sulphide. The typical shape of the Voronoi polyhedra is not too far from the polyhedra of a perfect ice I_h crystal, although the numbers of vertices and faces are almost doubled. Indeed the actual number of vertices increases rapidly toward the liquid value as the crystal is perturbed by thermal motions. It is remarkable that the total surface and volume are always found closely correlated. It denotes a quasi-constant shape, i.e. the various shapes are not dependent on the volume. Indeed a direct analysis shows that there is no correlation between volume and shape. A quantitative characterization of the Voronoi polyhedra shape is proposed, through an “asphericity” parameter, whose distribution is found to be greatly affected by temperature: a net shift of the centre of the curve toward the value for the ice is found as the temperature is lowered. Finally it is found that there is a positive correlation between the potential energy of a molecule and the local volume, thus indicating that the hypothesis that the four-bonded molecules have a local density lower than average is incorrect.