As an example, the authors studied solvatochromic shifts of the first ionization potential (HOMO energy) for the four nucleobases adenine, cytosine, thymine, and uracil upon embedding in water represented by a polarizable continuum model. They pointed out the importance of carefully choosing the appropriate value of the dielectric constant for the embedding region, corresponding to fast and slow screening processes. The high dielectric constant of water (ϵ r = 78.35 ) results as a combination of relaxation processes of electronic (fast) and nuclear (slow) degrees of freedom. The authors argue that while for the ground state, screening from both is appropriate, only the fast, electronic, processes can react to the excitation (ionization) process, and therefore one should use the optical dielectric constant ϵ ∞ = 1.78 in the embedded calculation, yielding in the end to an additional contribution to the solvatochromic shift: first, the ground-state is calculated based on DFT with PCM using the high ϵ r , then a GW embedding calculation is performed starting from the molecular orbitals of this ϵ r -embedded ground state, however using ϵ ∞ in the reaction field calculation. In Table , we reprint the results from this socalled non-equilibrium approach as reported in Ref. , obtained with the direct use of the static approximation in the determination of the embedded quasiparticle calculations (here labeled ∆GW ) and the ∆COHSEX variants, respectively. One can see that both approaches give very similar shifts in the non-equilibrium calculation with deviations less than 0.05 eV. In an equilibrium calculation, that is, if ϵ r is also used in the embedded GW step, the overall shifts are larger (due to the much larger polarization effect) as are the differences between ∆GW and ∆COHSEX.