Hydrogen Bonds and van der Waals Forces in Ice at Ambient and High Pressures

The first principles methods, density-functional theory and quantum Monte Carlo, have been used to examine the balance between van der Waals (vdW) forces and hydrogen bonding in ambient and high-pressure phases of ice. At higher pressure, the contribution to the lattice energy from vdW increases and that from hydrogen bonding decreases, leading vdW to have a substantial effect on the transition pressures between the crystalline ice phases. An important consequence, likely to be of relevance to molecular crystals in general, is that transition pressures obtained from density-functional theory exchange-correlation functionals which neglect vdW forces are greatly overestimated.

Figure 1

(a) Relative lattice energies ($\Delta U_0$) and (b) volumes ($\Delta V_0$) of the high-pressure ice phases with respect to the lattice energy of ice $\mathrm{I}h$ obtained with the methods indicated. (c) Transition pressures ($P_{\mathrm{tr}}$) from ice $\mathrm{I}h$ to the various high-pressure phases.

Figure 2

(a) H bond strength index [38] and (b) vdW energy contributions plotted as a function of the experimental densities of the ice phases at zero pressure. Experimental values are taken from 39, 40, 41.

Figure 3

(a) O-O radial distribution functions [$g(r)$] of ice $\mathrm{I}h$, ice II, and ice VIII. (b) Integrated number of neighbors [$N(r)$] and (c) vdW contributions (obtained from the TS scheme) as a function of O-O distance for the same three phases.