Nonuniform Continuum Model for Solvatochromism Based on Frozen‐Density Embedding Theory

AbstractFrozen‐density embedding theory (FDET) provides the formal framework for multilevel numerical simulations, such that a selected subsystem is described at the quantum mechanical level, whereas its environment is described by means of the electron density (frozen density; ${\rho _{\rm{B}} (\vec r)}$). The frozen density ${\rho _{\rm{B}} (\vec r)}$ is usually obtained from some lower‐level quantum mechanical methods applied to the environment, but FDET is not limited to such choices for ${\rho _{\rm{B}} (\vec r)}$. The present work concerns the application of FDET, in which ${\rho _{\rm{B}} (\vec r)}$ is the statistically averaged electron density of the solvent ${\left\langle {\rho _{\rm{B}} (\vec r)} \right\rangle }$. The specific solute–solvent interactions are represented in a statistical manner in ${\left\langle {\rho _{\rm{B}} (\vec r)} \right\rangle }$. A full self‐consistent treatment of solvated chromophore, thus involves a single geometry of the chromophore in a given state and the corresponding ${\left\langle {\rho _{\rm{B}} (\vec r)} \right\rangle }$. We show that the coupling between the two descriptors might be made in an approximate manner that is applicable for both absorption and emission. The proposed protocol leads to accurate (error in the range of 0.05 eV) descriptions of the solvatochromic shifts in both absorption and emission.