Quantal densityfunctional theory of excited states: The state arbitrariness of the model noninteracting system
Abstract
The quantal densityfunctional theory (QDFT) of nondegenerate excitedstates maps the pure state of the Schroedinger equation to one of noninteracting fermions such that the equivalent excited state density, energy, and ionization potential are obtained. The state of the model S system is arbitrary in that it may be in a ground or excited state. The potential energy of the model fermions differs as a function of this state. The contribution of correlations due to the Pauli exclusion principle and Coulomb repulsion to the potential and total energy of these fermions is independent of the state of the S system. The differences are solely a consequence of correlationkinetic effects. Irrespective of the state of the S system, the highest occupied eigenvalue of the model fermions is the negative of the ionization potential. In this paper we demonstrate the state arbitrariness of the model system by application of QDFT to the first excited singlet state of the exactly solvable Hookean atom. We construct two model S systems: one in a singlet ground state (1s{sup 2}), and the other in a singlet first excited state (1s2s). In each case, the density and energy determined are equivalent to those of the excited state ofmore »
 Authors:
 Sacred Heart University, 5151 Park Avenue, Fairfield, Connecticut 06825 (United States)
 Graduate School, City University of New York, 365 Fifth Avenue, New York, New York 10016 (United States)
 (United States)
 Publication Date:
 OSTI Identifier:
 20640322
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 68; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.68.042504; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; CORRELATIONS; COULOMB FIELD; DENSITY FUNCTIONAL METHOD; EIGENFUNCTIONS; EIGENVALUES; ENERGY DENSITY; EXACT SOLUTIONS; EXCITED STATES; FERMIONS; GROUND STATES; IONIZATION POTENTIAL; PAULI PRINCIPLE; POTENTIAL ENERGY; POTENTIALS; SCHROEDINGER EQUATION
Citation Formats
Slamet, Marlina, Singh, Ranbir, Sahni, Viraht, Massa, Lou, and Crest Center for Mesoscopic Modeling and Simulation, City University of New York, New York, New York 10016. Quantal densityfunctional theory of excited states: The state arbitrariness of the model noninteracting system. United States: N. p., 2003.
Web. doi:10.1103/PhysRevA.68.042504.
Slamet, Marlina, Singh, Ranbir, Sahni, Viraht, Massa, Lou, & Crest Center for Mesoscopic Modeling and Simulation, City University of New York, New York, New York 10016. Quantal densityfunctional theory of excited states: The state arbitrariness of the model noninteracting system. United States. doi:10.1103/PhysRevA.68.042504.
Slamet, Marlina, Singh, Ranbir, Sahni, Viraht, Massa, Lou, and Crest Center for Mesoscopic Modeling and Simulation, City University of New York, New York, New York 10016. 2003.
"Quantal densityfunctional theory of excited states: The state arbitrariness of the model noninteracting system". United States.
doi:10.1103/PhysRevA.68.042504.
@article{osti_20640322,
title = {Quantal densityfunctional theory of excited states: The state arbitrariness of the model noninteracting system},
author = {Slamet, Marlina and Singh, Ranbir and Sahni, Viraht and Massa, Lou and Crest Center for Mesoscopic Modeling and Simulation, City University of New York, New York, New York 10016},
abstractNote = {The quantal densityfunctional theory (QDFT) of nondegenerate excitedstates maps the pure state of the Schroedinger equation to one of noninteracting fermions such that the equivalent excited state density, energy, and ionization potential are obtained. The state of the model S system is arbitrary in that it may be in a ground or excited state. The potential energy of the model fermions differs as a function of this state. The contribution of correlations due to the Pauli exclusion principle and Coulomb repulsion to the potential and total energy of these fermions is independent of the state of the S system. The differences are solely a consequence of correlationkinetic effects. Irrespective of the state of the S system, the highest occupied eigenvalue of the model fermions is the negative of the ionization potential. In this paper we demonstrate the state arbitrariness of the model system by application of QDFT to the first excited singlet state of the exactly solvable Hookean atom. We construct two model S systems: one in a singlet ground state (1s{sup 2}), and the other in a singlet first excited state (1s2s). In each case, the density and energy determined are equivalent to those of the excited state of the atom, with the highest occupied eigenvalues being the negative of the ionization potential. From these results we determine the corresponding KohnSham densityfunctional theory (KSDFT) 'exchangecorrelation' potential energy for the two S systems. Further, based on the results of the model calculations, suggestions for the KSDFT of excited states are made.},
doi = {10.1103/PhysRevA.68.042504},
journal = {Physical Review. A},
number = 4,
volume = 68,
place = {United States},
year = 2003,
month =
}

We explain by quantal density functional theory the physics of mapping from any bound nondegenerate excited state of Schroedinger 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.

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