How to choose the frozen density in Frozen-Density Embedding Theory-based numerical simulations of local excitations?

According to Frozen-Density Embedding Theory, any observable evaluated for the embedded species is a functional of the frozen density (rho (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 rho (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 rho (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.