Vertical Excitation Energies in Solution via a Two-Time-Scale Solvation Model Coupled to Pair-Density Functional Theory

Accurately describing electronically excited states in solution requires both a multiconfigurational treatment of the solute and an efficient account of solvent effects. Multiconfiguration pair-density functional theory (MC-PDFT) and its multi-state, linearized extension (L-PDFT) can recover correlation beyond state-averaged complete active space self-consistent field theory (SA-CASSCF) at a fraction of the cost of multireference perturbation theory (e.g. CASPT2) or multireference configuration interaction. Here we combine MC-PDFT and L-PDFT with a nonequilibrium-treatment of the electrostatic solvation effect using the solvation model based on density (SMD). The resulting models are called MC-NSCRF-PDFT and L-NSCRF-PDFT, where NSCRF denotes the key state-specific excited-state nonequilibrium self-consistent reaction field step. We apply the new models to the solvatochromic shifts of the lowest valence excitations of formaldehyde, acetone, acrolein, and methylenecyclopropene and to the aqueous shifts of the lowest π → π∗ and n → π∗ transitions of cytosine. For vertical excitation energies in solution, MC-NSCRF-PDFT and L-NSCRF-PDFT give results that are in agreement with the far-more-expensive NSCRF model based on multistate CASPT2. These results establish MC-NSCRF-PDFT and L-NSCRF-PDFT as accurate and computationally efficient tools for electronic excitation energies in the condensed phase.