A consistent dielectric response model for water ice over the whole energy–momentum plane

We have developed, for the first time, a consistent analytic model for the complex dielectric response function, ε, of amorphous and hexagonal ice over the complete energy–momentum plane. The energy dependence at the optical limit is based on a parametrization of all dielectric data representations, namely Im(ε), Re(ε) and Im(−1/ε), using a linear combination of Drude-type functions associated with the various interband transitions. The “fitting” procedure is forced to self-consistency by the fulfillment (to within 1%) of the f-sum-rules for Im(ε) and Im(−1/ε). The momentum dependence is provided by appropriate dispersion relationships for the Drude coefficients obtained from our recent analysis of the experimental Bethe ridge of liquid water. Time-dependent density functional theory (TDDFT) calculations of the optical oscillator strength (up to 20 eV) of H2O clusters are also presented for comparison. It is expected that the present development will permit accurate calculations of inelastic scattering probabilities and associated quantities (e.g. stopping forces) of swift charges in solid water.