Experimental Benchmark Data and Systematic Evaluation of Two <i>a Posteriori</i>, Polarizable-Continuum Corrections for Vertical Excitation Energies in Solution

We report the implementation and evaluation of a perturbative, density-based correction scheme for vertical excitation energies calculated in the framework of a polarizable continuum model (PCM). Because the proposed first-order correction terms depend solely on the zeroth-order excited-state density, a transfer of the approach to any configuration interaction-type excited-state method is straightforward. Employing the algebraic-diagrammatic construction (ADC) scheme of up to third order as well as time-dependent density-functional theory (TD-DFT), we demonstrate and evaluate the approach. For this purpose, we assembled a set of experimental benchmark data for solvatochromism in molecules (xBDSM) containing 44 gas-phase to solvent shifts for 17 molecules. These data are compared to solvent shifts calculated at the ADC(1), ADC(2), ADC­(3/2), and TD-DFT/LRC-ωPBE levels of theory in combination with state-specific as well as linear-response type PCM-based correction schemes. Some unexpected trends and differences between TD-DFT, the levels of ADC, and variants of the PCM are observed and discussed. The most accurate combinations reproduce experimental solvent shifts resulting from the bulk electrostatic interaction with maximum errors in the order of 50 meV and a mean absolute deviation of 20–30 meV for the xBDSM set