Static Dielectric Permittivity of Ice from First Principles

The static permittivity of ice is computed from first principles as a function of the electric field, together with the generalized Kirkwood factor. The molecular dipole in ice is unambiguously obtained by an original method combining a slab approach and Berry phase calculations, and the fluctuations of the polarization are sampled by Monte Carlo runs using first-principles model Hamiltonians for different proton configurations. Common approximations in the exchange-correlation functionals overestimate the dielectric permittivity and enhance ferroelectric configurations and the Kirkwood factor, whereas dielectric saturation effects compare well with experiment.

Figure 1

Orthorhombic unit cell of ice Ih containing eight water molecules (adapted with permission from Ref. [38]).

Figure 2

Longitudinal view of ice slab (top) and of electrostatic potential profile averaged in $xy$ plane (bottom). The profile is shown for two different values of the displacement field $|D_1|<|D_2|$, and the resulting electric field inside the slab is obtained in each case as the slope of the dotted line.

Figure 3

Electric field inside the slab vs displacement field.

Figure 4

Static permittivity of ice Ih vs electric field from PBE model Hamiltonians using unweighed Bernal-Fowler configurations (“isoenergetic”) or Boltzmann sampling of the same (“nonisoenergetic”).

Figure 5

Double-layer capacitance from experiment [60] and static permittivity from Eq. (5) of the present model (both are normalized to maximum values) vs potential bias. By convention, $U=0$ at the potential of zero charge.