To account for solvent screening, we replace χ 0 in Eq. 3 with χ solv = χ 0 + χ lq , where χ lq is the independent-particle susceptibility of the liquid using an implicit solvation model. This approach is labeled GW@GGA+SaLSA+χ lq below. Note that χ lq is also a response to the total Coulomb potential, analogous to χ 0 for the electrons, which is necessary for this additivity. Most implicit solvation models incorporate a local dielectric response with a spatially-dependent relative permittivity ϵ lq (r), leading to χlq being a differential operator defined by χlq ϕ(r) = 1 4π ∇ • (ϵ lq (r) -1)∇ϕ(r), where ϕ(r) is the electrostatic potential. This χ lq which can be directly combined with χ 0 to account for solvent screening. However, for these local models χ lq GG ′ ∝ G•G ′ in a planewave basis, which then requires a large plane-wave cutoff to properly account for the solvation effects in the dielectric matrices and thus complicate convergence of the GW calculation.