1. Introduction  2. Frozen-Density Embedding Theory  3. Extensions and Formalisms Related to FDET  4. Approximations in FDET for Multilevel Simulations  5. Numerical Simulations Using Approximated FDET Embedding Potentials  6. Concluding Remarks

Recent application of the Frozen-Density Embedding Theory based continuum model of the solvent, which is used for calculating solvatochromic shifts in the UV/Vis range, are reviewed. In this model, the solvent is represented as a non-uniform continuum taking into account both the statistical nature of the solvent and specific solute–solvent interactions. It offers, therefore, a computationally attractive alternative to methods in which the solvent is described at atomistic level. The evaluation of the solvatochromic shift involves only two calculations of excitation energy instead of at least hundreds needed to account for inhomogeneous broadening. The present review provides a detailed graphical analysis of the key quantities of this model: the average charge density of the solvent (<�_B>) and the corresponding Frozen-Density Embedding Theory derived embedding potential for coumarin 153.

Frozen-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; �_B( r →) ) The frozen density �B( r →) is usually obtained from some lower-level quantum mechanical methods applied to the environment, but FDET is not limited to such choices for �B( r →). The present work concerns the application of FDET, in which �B( r →) is the statistically averaged electron density of the solvent <�B( r →)> . The specific solute–solvent interactions are represented in a statistical manner in <�B( r →)>. A full self-consistent treatment of solvated chromophore, thus involves a single geometry of the chromophore in a given state and the corresponding <�B( r →)>. 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.

According to Frozen-Density Embedding Theory, any observable evaluated for the embedded species is a functional of the frozen density (�_B —the density associated with the environment). The environment-induced shifts in the energies of local excitations in organic chromophores embedded in hydrogen-bonded environments are analyzed. The excitation energies obtained for �_B , which is derived from ground-state calculations for the whole environment applying medium quality basis sets (STO–DZP) or larger, vary in a narrow range (about 0.02 eV which is at least one order of magnitude less than the magnitude of the shift). At the same time, the ground-state dipole moment of the environment varies significantly. The lack of correlation between the calculated shift and the dipole moment of the environment reflects the fact that, in Frozen-Density Embedding Theory, the partitioning of the total density is not unique. As a consequence, such concepts as “environment polarization� are not well defined within Frozen-Density Embedding Theory. Other strategies to generate �_B (superposition of densities of atoms/molecules in the environment) are shown to be less robust for simulating excitation energy shifts for chromophores in environments comprising hydrogen-bonded molecules.