Excitation Energies of Embedded Chromophores from Frozen-Density Embedding Theory Using State-Specific Electron Densities of the Environment

Starting
from the Perdew–Levy theorem on extrema
of the
Hohenberg–Kohn functional, the expression for the vertical
excitation energy is derived within the formal framework of Frozen-Density
Embedding Theory (FDET) that makes it possible to use state-specific
electron densities of the environment (ρB) of an embedded species. The derived general expression involves
the embedded wave functions for ground and excited states that are
orthogonal and is exact up to quadratic terms in the appropriate density
expansion. It can be applied in practice using various methods differing
in the treatment of the electron–electron correlation for embedded
electrons, the method to evaluate different contributions to the excitation
energy, the method to generate state-specific ρB, and the approximation used for the non-electrostatic
component of the FDET embedding potential. The derived expression
is applied for 47 local excitations in 10 embedded organic chromophores.
The explicit treatment of the differential polarization of ρB improves indeed the accuracy of the excitation
energy as compared to the implicit treatment in which the same ρB is used for all states of embedded chromophore.
For 47 local excitations in 10 embedded organic chromophores, the
average absolute errors in excitation energies drop from 0.04 to 0.03
eV and their standard deviations from 0.032 to 0.025 eV, respectively.
The maximal errors show similar trends.