Embedding potentials for excited states of embedded species

Abstract

Frozen-Density-Embedding Theory (FDET) is a formalism to obtain the upper bound of the groundstate energy of the total system and the corresponding embedded wavefunction by means of EulerLagrange equations [T. A. Wesolowski, Phys. Rev. A 77(1), 012504 (2008)]. FDET provides the expression for the embedding potential as a functional of the electron density of the embedded species, electron density of the environment, and the field generated by other charges in the environment. Under certain conditions, FDET leads to the exact ground-state energy and density of the whole system. Following Perdew-Levy theorem on stationary states of the ground-state energy functional, the other-than-ground-state stationary states of the FDET energy functional correspond to excited states. In the present work, we analyze such use of other-than-ground-state embedded wavefunctions obtained in practical calculations, i.e., when the FDET embedding potential is approximated. Three computational approaches based on FDET, that assure self-consistent excitation energy and embedded wavefunction dealing with the issue of orthogonality of embedded wavefunctions for different states in a different manner, are proposed and discussed.

Orthogonality of embedded wave functions for different states in frozen-density embedding theory

“…7 and the present section provides a summary of the key equations. The tilde in the equations given in the present section (such as inẼ nad xct [ρ A , ρ B ], for instance) indicates that the respective functional is approximated.…”

“…The consistency can easily be restored without additional computational cost using the method proposed in Ref. 7 (labeled as "method B" there and "linearized FDET" in the present work).…”

“…The linearized version of FDET proposed in Ref. 7 for excited states is given in Section III. We present details of our calculations in Section IV.…”

“…In Ref. 7, we proposed the approximate formulation of FDET in which the orthogonality of embedded wave functions is assured by construction. We will refer to this formulation as linearized FDET.…”

Multi-state extrapolation of UV/Vis absorption spectra with QM/QM hybrid methods

“…[10][11][12][13][14][15][16] The use of QM/QM methods has also been extended in recent times to excited state calculations. [17][18][19][20][21][22][23][24] One of the most successful hybrid methods is ONIOM (Our own N-layered Integrated molecular Orbital molecular Mechanics), [25][26][27][28][29][30] which is briefly described in Sec. II.…”