Dispersion Interactions and Vibrational Effects in Ice as a Function of Pressure: A First Principles Study

We present a first principles theoretical framework that accurately accounts for several properties of ice, over a wide pressure range. In particular, we show that, by using a recently developed nonlocal van der Waals functional and by taking into account hydrogen zero point motion, one can properly describe the zero temperature equation of state, the vibrational spectra, and the dielectric properties of ice at low pressure and of ice VIII, a stable phase between 2 and 60 GPa. While semilocal density functionals yield a transition pressure from ice XI to VIII that is overestimated by almost an order of magnitude, we find good agreement with experiments when dispersion forces are taken into account. Zero point energy contributions do not alter the computed transition pressure, but they affect structural properties, including equilibrium volumes and bulk moduli.

Figure 1

The change in electronic density in cubic ice and ice VIII with respect to a free water molecule as calculated with semilocal (PBE) and van der Waals (vdW-DF2) functionals. Pink and blue isosurfaces (all chosen at the same value) show regions where the density is increased and decreased, respectively. Oxygen and hydrogen atoms are indicated as red and cyan balls, respectively.

Figure 2

The phonon density of states for ice XI (red solid line) and VIII (blue dashed line) calculated by using (a) PBE and (b) vdW-DF2 functionals (see the text). Calculations for $I_c$ agree closely with those of ice XI and are omitted. $\times$ and $+$ symbols indicate experimentally measured peaks for hexagonal ice and ice VIII, respectively.