Dielectric constant of ices and water: a lesson about water interactions

In this paper, the dielectric constant has been evaluated for ices Ih, III, V, VI, and VII for several water models using two different methodologies. Using Monte Carlo simulations, with special moves to sample proton-disordered configurations, the dielectric constant has been rigorously evaluated. We also used an approximate route in which proton-disordered configurations satisfying the Bernal-Fowler rules were generated following the algorithm proposed by Buch et al. (Buch, V.; Sandler, P.; Sadlej, J. J. Phys. Chem. B 1998, 102, 8641), and the dielectric constant was estimated assuming that all configurations have the same statistical weight (as Pauling did when estimating the residual entropy of ice). The predictions of the Pauling model for the dielectric constant differ in general from those obtained rigorously by computer simulations because proton-disordered configurations satisfying the Bernal-Fowler rules can differ in their energies by as much as 0.10-0.30 NkT (at 243 K). These differences in energy significantly affect properties that vary from one configuration to another such as polarization, leading to different values of the dielectric constant. The Pauling predictions differ from the simulation results, especially for SPC/E and TIP5P, but yield reasonable results for TIP4P-like models. We suggest that for three charge models the polarization factor (G) in condensed phases depends on the ratio of the dipole to the quadrupole moment. The SPC/E, TIP5P, TIP4P, TIP4P/2005, TIP4P/ice models of water are unable to describe simultaneously both the experimental dielectric constants of water and ice Ih. Nonpolarizable models cannot describe the dielectric constants of the different condensed phases of water because their dipole moments (about 2.3 D) are much smaller that those estimated from first principles (of the order of 3 D). However, the predictions of TIP4P models provide an overall qualititatively correct description of the dielectric constant of the condensed phases of water, when the dipole moment of the model is scaled to the estimated value obtained from first principle calculations. Such scaling fails completely for SPC/E, TIP3P, and TIP5P as these models predict a completely different dielectric constant for ice Ih and water at the melting point, in complete disagreement with experiment. The dielectric constant of ices, as the phase diagram predictions, seems to contain interesting information about the orientational dependence of water interactions.