Quantal Density Functional Theory of Excited States

Abstract

We explain by quantal density functional theory the physics of mapping from any bound nondegenerate excited state of Schrödinger theory to an S system of noninteracting fermions with equivalent density and energy. The S system may be in a ground or excited state. In either case, the highest occupied eigenvalue is the negative of the ionization potential. We demonstrate this physics with examples. The theory further provides a new framework for calculations of atomic excited states including multiplet structure.

Analysis of Floquet formulation of time-dependent density-functional theory

“…On the other hand for the ground-state, occupation is uniquely defined and so is the potential. More examples of this kind exist in the literature [7,8,9,10,11]. Exactly in the same manner as in stationary-state theory, in Floquet theory of TDDFT also the "ground-state" gives the potential uniquely but for "excited-states" more than one potential can be found.…”

“…Finally, one may raise a question if Floquet theory of TDDFT is applicable only to "ground-states". The answer is that even for steady-state "excited-states", a theory similar to the stationary-state excited-state DFT [4,5,6,7,8,9,10,11] can be developed but that is not our main concern here. In this appendix, we show that if one confines the quasienergies to a range such that they go to their unperturbed counterpart when the time-periodic potential is turned off, then there is a well defined ground-state quasienergy satisfying the minimum variational principle.…”

“…For our discussion, we show that even in the stationary-state theory, we can generate a given excited-state density by two different potentials [7,8,9,10,11]. Again consider two electrons in a one-dimensional harmonic oscillator potential.…”

Quantal density functional theory of the hydrogen molecule

“…The in principle exact framework of Q-DFT for ground and excited states, both nondegenerate and degenerate, has been demonstrated by application to exactly solvable model atomic systems [3,5,6,7,8] as well as by the use of essentially exact atomic correlated wave functions [2,4,9]. In its approximate form, Q-DFT has been applied to atoms, atomic ions, atoms in excited states, and positron binding, as well as to the many-electron inhomogeneity at metallic surfaces and metallic clusters.…”

“…In this paper we analyze the Hydrogen molecule (H 2 ) in its ground-state electronic configuration (σ g 1s) 2 from the perspective of time-independent Quantal density functional theory (Q-DFT) [1,2,3,4,5,6,7,8]. The in principle exact framework of Q-DFT for ground and excited states, both nondegenerate and degenerate, has been demonstrated by application to exactly solvable model atomic systems [3,5,6,7,8] as well as by the use of essentially exact atomic correlated wave functions [2,4,9].…”