A Fully Frequency-Dependent Formulation of the Open Quantum System Polarizable Continuum Model

We introduce a fully frequency-dependent formulation of the open quantum system polarizable continuum model (OQS-PCM), as derived from the non-Markovian time-dependent stochastic Schrödinger equation for a polarizable bath in the limit of averaging out the stochastic fluctuations. OQS-PCM(ω) captures the delayed coupling between solute and solvent electronic dynamics, naturally accounting for polarization, dispersion, and energy dissipation─while bridging the different solvation regimes arising from the distinct solute-solvent electronic time scales. This framework provides a transparent, physically grounded description of van der Waals interactions of a molecule with its environment, as well as the effect of fluctuations on electronic excitations. Simulation of absorption spectra in water and benzene provides insight into the role of environmental time scales in solvatochromism and energy redistribution. These results demonstrate the potential of OQS-PCM(ω) for predictive modeling of optoelectronic properties, photophysics, and the design of molecular systems strongly influenced by environmental electronic dynamics.