Vertical excitation energies of embedded systems: The vertical excitation model (VEM) within polarizable QM/MM

Polarizable quantum mechanics/molecular mechanics (QM/MM) approaches based on fluctuating charges and dipoles [QM/FQ(Fμ)] are formulated within the state-specific vertical excitation model (VEM) to compute vertical excitation energies of solvated systems. This methodology overcomes the limitations of the widely used linear response (LR) approach. While LR can capture the dynamic response of the solvent to the QM transition density, it neglects the solvent reorganization that follows solute relaxation upon electronic excitation. In contrast, the VEM framework explicitly accounts for this effect. Benchmark calculations of vertical excitation energies using QM/FQ(Fμ) are reported for a representative set of solutes-acrolein, acetone, caffeine, p-nitroaniline, coumarin 153, doxorubicin, and betaine-30-comparing VEM with LR, corrected LR (cLR), and cLR2 schemes. The results reveal notable variations in solvent response, depending on the character of the electronic transition, and demonstrate that optimal accuracy can be achieved by selecting the most appropriate model for each specific system and excitation.