A corrected-linear response formalism for the calculation of electronic excitation energies of solvated molecules with the CCSD-PCM method

In this work, we present an efficient approximation to compute excitation energies in solution when coupled cluster (CC) methods are combined with a polarizable solvation model. Two formalisms exist to compute excited state energies with polarizable solvation models: state-specific (SS) and linear-response (LR). The former more accurately describes the solute–solvent polarization in the excited state, but is computationally intensive. The LR formalism is efficient, but lacks proper relaxation effects. An approximate method, called corrected-LR (cLR), was originally formulated in the context of time-dependent density functional theory and the polarizable continuum model of solvation (PCM), and was shown to be able to recover most of the relaxation contributions of the SS formalism at a cost similar to LR. We have expanded the cLR idea to CC theory, and introduced an extra approximation that further reduces the computational effort with negligible loss of accuracy. The test cases reported in this contribution clearly show that the cLR-CC-PCM method is able to estimate transition energies in very close agreement with the SS formalism at a cost that is similar (in fact, slightly smaller) than the LR formalism. The average SS–LR difference is of the order of 0.10–0.20 eV for nonequilibrium calculations, and 0.30–0.55 eV for equilibrium calculations. The SS–cLR average difference is, on the other hand, 0.01–0.02 eV for nonequilibrium calculations, and 0.05–0.15 eV for equilibrium calculations. Therefore, the cLR approach is a promising alternative for computing excited state energies in solution with computationally intensive CC methods.