The formulation of a self-consistent constricted variational density functional theory for the description of excited states

• Published in: Chemical physics 2011-11, Vol.391 (1), p.11-18
• Main Authors: Cullen, John, Krykunov, Mykhaylo, Ziegler, Tom
• Format: Article
• Language: English
• Subjects: Charge transfer transitions; Constricted variational density functional theory; Time dependent density functional theory
• ISSN: 0301-0104
• DOI: 10.1016/j.chemphys.2011.05.021

In constricted variational density functional theory suggested here we perform a unitary transformation (Part A) among the occupied ϕ occ and virtual ϕ vir ground state orbitals to any order in the variational parameter matrix U to obtain the new occupied ϕ occ ′ and virtual ϕ vir ′ exited state orbitals. From ϕ occ ′ we calculate the excited state energy E(U) and optimize it with respect to U under the constraint (Part B) that one electron is transferred from the occupied orbital space to the virtual orbital space. [Display omitted] ► We outline a self-consistent density functional approach to the calculation of transition energies. ► The approach is an improvement over a previous scheme [Ziegler et al. Chem. Phys. 130, 154102 (2009)]. ► We describe how our method is related to other schemes based on density functional theory. We outline here a self-consistent approach to the calculation of transition energies within density functional theory. The method is based on constricted variational theory (CV-DFT). It constitutes in the first place an improvement over a previous scheme [T. Ziegler, M. Seth, M. Krykunov, J. Autschbach, F. Wang, Chem. Phys. 130 (2009) 154102] in that it includes terms in the variational parameters to any desired order n including n = ∞. For n = 2, CV( n)-DFT is similar to TD-DFT. Adiabatic TD-DFT becomes identical to CV(2)-DFT after the Tamm–Dancoff approximation is applied to both theories. We have termed the new scheme CV( n)-DFT. In the second place, the scheme can be implemented self-consistently, SCF-CV( n)-DFT. The procedure outlined here could also be used to formulate a SCF-CV( n) Hartree–Fock theory. The approach is further kindred to the ΔSCF-DFT procedures predating TD-DFT and we describe how adiabatic TD-DFT and ΔSCF-DFT are related through different approximations to SCF-CV( n)-DFT.