Polarizable Continuum Models and Green's Function $\bf{GW}$ Formalism: On the Dynamics of the Solvent Electrons

TL;DR

This paper investigates the impact of simplifying the solvent dielectric response in $GW$ calculations for water, showing that a static approximation introduces minimal errors and proposing a single-pole model for efficient, accurate dynamical simulations.

Contribution

It introduces a single-pole model to accurately mimic the full frequency-dependent dielectric response of water in $GW$ calculations, enabling efficient dynamical solvent effects modeling.

Findings

Static dielectric approximation causes less than a few percent error in energy shifts.

Single-pole model accurately reproduces the full dielectric response in the visible-UV range.

Method enables fully dynamical $GW$ calculations with minimal computational effort.

Abstract

The many-body $GW$ 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 $(\epsilon_\infty)$ 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 $GW$ calculation with the only knowledge of the cavity reaction field calculated for the $\epsilon_\infty$ optical dielectric constant.