Implementation of EC-RISM for ADC(2) and CC2 to Include Solvent Granularity Effects in Excited-State Energies and Gradients

The embedded cluster reference interaction site model (EC-RISM) employs statistical-mechanical integral equation theory to predict solvent site distributions and their interaction with a solute using quantum-mechanical electronic structure methods. In contrast to apparent surface charge models such as the polarizable continuum (PCM) or the conductor-like screening (COSMO) model, EC-RISM can account for directional solvent–solute interactions due to the description of the solvent based on conventional molecular force field models. Here we present an implementation of EC-RISM combined with correlated wave function methods for ground- and excited-state energies and, for the first time, also for ground- and excited-state energy gradients. This is achieved by self-consistent equilibrating the solvent reaction field with the solute charge density in the correlated and, possibly, electronically excited state. To account for excitonic coupling and nonequilibrium contributions to electronic transition energies, EC-RISM is further combined with COSMO. We present applications to the molecular structures and the absorption and emission energies of 4-( N, N -dimethylamino)benzonitrile (DMABN), the photobase 7-amino-4-methylcoumarin, and the photoacids phenol and 3-cyanophenol in aqueous solution. As expected, for systems without strong directional solvent interactions, such as DMABN, EC-RISM yields results similar to those obtained with COSMO whereas, for molecules or ions that form strong hydrogen bonds to the solvent (particularly the deprotonated photoacids) EC-RISM provides substantial improvements.