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.