Quantal density functional theory of excited states: Application to an exactly solvable model

The quantal density functional theory (Q-DFT) of excited states is the desc ription of the physics of the mapping from any bound nondegenerate excited state of Schrodinger theory to that of the s-system of noninteracting Fern- Lions with equivalent density rho (k)(r), energy E-k, and ionization potent ial I-k. The s-system may either be in an excited state with the same confi guration as in Schrodinger theory or in a ground state with a consequently different configuration. The Q-DFT description of the s-system is in terms of a conservative field F-k(r), whose electron-interaction epsilon (ee)(r) and correlation-kinetic Z(tc)(r) components are separately representative o f electron correlations due to the Pauli exclusion principle and Coulomb re pulsion, and correlation-kinetic effects, respectively. The sources of thes e fields are expectations of Hermitian operators taken with respect to the system wavefunction. The local electron-interaction potential v(ee)(r) of t he s-system, representative of all the many-body correlations, is the work done to move an electron in the force of the field F-k(r). The electron int eraction E-ee and correlation-kinetic T-c components of the total energy Ek may be expressed in integral virial form in terms of their respective fiel ds. The difference between the s-system in its ground or excited state repr esentation is due entirely to correlation-kinetic effects. The highest occu pied eigenvalue of the s-system differential equation in either case is min us the ionization potential I-k. En this work we demonstrate the transforma tion of an excited state of Schrodinger theory, as represented by the first excited singlet state of the exactly solvable Hooke's atom, to that of non interacting Fern-Lions in their ground state with equivalent excited state density energy, and ionization potential. To further prove the Fern-Lions a re in a ground state, we solve the corresponding singlet s-systern differen tial equation numerically for the v(ee)(r) determined, and obtain the excit ed state density from the zero node orbitals generated. The resulting total energy is also the same. In addition, the single eigenvalue determined cor responds to minus the ionization potential of the excited state. (C) 2001 J ohn Wiley & Sons, Inc.