Electronic transitions for a fully polarizable QM/MM approach based on fluctuating charges and fluctuating dipoles: Linear and corrected linear response regimes

The fully polarizable Quantum Mechanics/Molecular Mechanics (QM/MM) approach based on fluctuating charges and fluctuating dipoles, named QM/FQFμ [T. Giovannini et al., J. Chem. Theory Comput. 15, 2233 (2019)], is extended to the calculation of vertical excitation energies of solvated molecular systems. Excitation energies are defined within two different solvation regimes, i.e., linear response (LR), where the response of the MM portion is adjusted to the QM transition density, and corrected-Linear Response (cLR) in which the MM response is adjusted to the relaxed QM density, thus being able to account for charge equilibration in the excited state. The model, which is specified in terms of three physical parameters (electronegativity, chemical hardness, and polarizability) is applied to vacuo-to-water solvatochromic shifts of aqueous solutions of para-nitroaniline, pyridine, and pyrimidine. The results show a good agreement with their experimental counterparts, thus highlighting the potentialities of this approach.