Connectivity of hydrogen bonds in liquid water

We report on a molecular dynamics (MD) study of the connectivity of hydrogen bond networks in liquid water, focusing primarily on the microscopic distribution functions giving the weight fraction of molecules belonging to a ‘‘net’’ of M molecules (M=1,2,3,...). The MD data compare favorably—using no adjustable parameters—with predictions of random bond percolation theory. We also study the connectivity of those molecules with four intact hydrogen bonds, and compare the corresponding distribution functions with correlated-site percolation theory. Our analysis supports the proposal that when looking at the bond connectivity, water appears as a macroscopic space-filling network—as expected from continuum models of water. When looking at the correlated site percolation problem defined by the four-bonded molecules, water appears as a myriad of tiny ramified low-density patches, somewhat reminiscent of mixture theories and cluster models. In Appendix A, we find a strong correlation between the number of molecules within a sphere of radius rc around a given molecule and the total interaction energy of that molecule with its neighbors residing in that sphere; for most choices of rc, the energy becomes less negative when more molecules are in the sphere, in contrast to the behavior of a normal fluid. This result supports the finding of Geiger and Stanley that regions of high bond connectivity are correlated with regions of low density. In Appendix B we describe in detail how we adapt conventional percolation theory to the calculation of cluster size distribution functions for hydrogen bond networks in water.