An Open Quantum System Theory for Polarizable Continuum Models

Abstract: The problem of a solute described by Quantum Chemistry within a solvent represented as a polarizable continuum model (PCM) is here reformulated in terms of the open quantum systems (OQS) theory. Using its stochastic Schr\"{o}dinger Equation formulation, we are able to provide a more comprehensive picture of the electronic energies and of the coupling between solute and solvent electronic dynamics. In particular, OQS-PCM proves to be a unifying theoretical framework naturally including polarization and dispersion interactions, the effect of solvent fluctuations, and the non-Markovian solvent response. As such, the OQS-PCM describes the interplay between the solute and the solvent typical electronic dynamical times, and yields both the standard PCM and the so-called Born Oppenheimer solvation regime, where the solvent electronic response is considered faster than any electronic dynamics taking place in the solute. In analyzing the OQS-PCM, we obtained an expression for the solute-solvent dispersion (van der Waals) interactions that is very transparent in terms of a physical interpretation based on fluctuations and response functions. Finally, we present various numerical tests that support the theoretical findings