Polarizable Continuum Models and Green’s Function <i>GW</i> Formalism: On the Dynamics of the Solvent Electrons

The many-body <i>GW</i> formalism, for the calculation of ionization potentials or electronic affinities, relies on the frequency-dependent dielectric function built from the electronic degrees of freedom. Considering the case of water as a solvent treated within the polarizable continuum model, we explore the impact of restricting the full frequency-dependence of the solvent electronic dielectric response to a frequency-independent (ϵ_∞) optical dielectric constant. For solutes presenting small to large highest-occupied to lowest-unoccupied molecular orbital energy gaps, we show that such a restriction induces errors no larger than a few percent on the energy level shifts from the gas to the solvated phase. We further introduce a remarkably accurate single-pole model for mimicking the effect of the full frequency dependence of the water dielectric function in the visible-UV range. This allows a fully dynamical embedded <i>GW</i> calculation with the only knowledge of the cavity reaction field calculated for the ϵ_∞ optical dielectric constant.