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Title: Quantal density-functional theory of excited states: The state arbitrariness of the model noninteracting system

Abstract

The quantal density-functional theory (Q-DFT) of nondegenerate excited-states 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 correlation-kinetic 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 Q-DFT 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 » the atom, with the highest occupied eigenvalues being the negative of the ionization potential. From these results we determine the corresponding Kohn-Sham density-functional theory (KS-DFT) 'exchange-correlation' potential energy for the two S systems. Further, based on the results of the model calculations, suggestions for the KS-DFT of excited states are made.« less

Authors:
 [1]; ;  [2];  [2];  [3]
  1. Sacred Heart University, 5151 Park Avenue, Fairfield, Connecticut 06825 (United States)
  2. Graduate School, City University of New York, 365 Fifth Avenue, New York, New York 10016 (United States)
  3. (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 density-functional 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 density-functional 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 density-functional 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 density-functional 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 density-functional theory (Q-DFT) of nondegenerate excited-states 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 correlation-kinetic 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 Q-DFT 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 Kohn-Sham density-functional theory (KS-DFT) 'exchange-correlation' potential energy for the two S systems. Further, based on the results of the model calculations, suggestions for the KS-DFT 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.
  • A formally exact expression for the interaction density response function {chi}(r,r{sup '},{omega}) exists in terms of (i) its noninteracting counterpart {chi}{sub 0}(r,r{sup '},{omega}) and (ii) an exchange (x)-correlation (c) kernel f{sub xc}(r,r{sup '},{omega}). In the absence of a first-principles theory for the {omega} dependence of f{sub xc}, the adiabatic approximation is most frequently made in this term, to construct a workable time-dependent density-functional theory. In the present study, a proposal is put forward to avoid the adiabatic approximation by working in the exchange-only limit in which f{sub xc} is set equal to f{sub x}(r,r{sup '},{omega}). We then refer to amore » result for the exchange energy given by Pines and Nozieres to motivate the assumption that f{sub x}=f{sub x}[Im {chi}{sub 0}(r,r{sup '},{omega})]. The essential proposal here is therefore that the integral equation to be solved for the interacting density response function {chi} is in the exchange-only case characterized entirely by the noninteracting response function {chi}{sub 0}.« less
  • It is investigated, whether the number of excited (pseudo)states can be truncated in the sum-over-states expression for indirect spin-spin coupling constants (SSCCs), which is used in the Contributions from Localized Orbitals within the Polarization Propagator Approach and Inner Projections of the Polarization Propagator (IPPP-CLOPPA) approach to analyzing SSCCs in terms of localized orbitals. As a test set we have studied the nine simple compounds, CH{sub 4}, NH{sub 3}, H{sub 2}O, SiH{sub 4}, PH{sub 3}, SH{sub 2}, C{sub 2}H{sub 2}, C{sub 2}H{sub 4}, and C{sub 2}H{sub 6}. The excited (pseudo)states were obtained from time-dependent density functional theory (TD-DFT) calculations with themore » B3LYP exchange-correlation functional and the specialized core-property basis set, aug-cc-pVTZ-J. We investigated both how the calculated coupling constants depend on the number of (pseudo)states included in the summation and whether the summation can be truncated in a systematic way at a smaller number of states and extrapolated to the total number of (pseudo)states for the given one-electron basis set. We find that this is possible and that for some of the couplings it is sufficient to include only about 30% of the excited (pseudo)states.« less
  • We generalize the quantal density-functional theory (QDFT) of electrons in the presence of an external electrostatic field E(r)=-{nabla}v(r) to include an external magnetostatic field B(r)={nabla}xA(r), where (v(r),A(r)) are the respective scalar and vector potentials. The generalized QDFT, valid for nondegenerate ground and excited states, is the mapping from the interacting system of electrons to a model of noninteracting fermions with the same density {rho}(r) and physical current density j(r), and from which the total energy can be obtained. The properties ({rho}(r),j(r)) constitute the basic quantum-mechanical variables because, as proved previously, for a nondegenerate ground state they uniquely determine the potentialsmore » (v(r),A(r)). The mapping to the noninteracting system is arbitrary in that the model fermions may be either in their ground or excited state. The theory is explicated by application to a ground state of the exactly solvable (two-dimensional) Hooke's atom in a magnetic field, with the mapping being to a model system also in its ground state. The majority of properties of the model are obtained in closed analytical or semianalytical form. A comparison with the corresponding mapping from a ground state of the (three-dimensional) Hooke's atom in the absence of a magnetic field is also made.« less
  • In this work we present a study of the excitation energies of adenine, cytosine, guanine, thymine and the adenine-thymine (AT) and guanine-cytosine (GC) base pairs using long-range corrected (LC) density functional theory. We compare three recent LC-functionals, BNL, CAM-B3LYP and LC-PBE0 with B3LYP and coupled cluster results from the literature. We find that the best overall performance is for the BNL functional based on LDA. However, in order to achieve this good agreement a smaller attenuation parameter was needed which leads to non-optimum performance for ground state properties. B3LYP, on the other hand, severely underestimates the charge transfer (CT) transitionsmore » in the base pairs. Surprisingly we also find that the CAM-B3LYP functional also underestimates the CT excitation energy for the GC base pair, but correctly describes the AT base pair. This illustrates the importance of retaining the full long-range exact exchange even at distances as short as that of the DNA base pairs. The worst overall performance was obtained with the LC-PBE0 functional which overestimates the excitations for the individual bases as well as the base pairs. It is therefore crucial to strike a good balance between the amount of local and long-range exact exchange.« less