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 the description of the solvent based on conventional molecular force field models. Here we present an implementation of EC-RISM combined with correlated wavefunction 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-consistently equilibrating the solvent reaction field with the solute charge density in the correlated and/or electronically excited state. To account for excitonic coupling and non-equilibrium 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 a substantially quantitative improvements.