Hohenberg-Kohn theorem including electron spin
نویسندگان
چکیده
منابع مشابه
Lack of Hohenberg-Kohn theorem for excited states.
For a given excited state there exist densities that arise from more than one external potential. This is due to a qualitatively different energy-density relationship from that of the ground state and is related to positive eigenvalues in the nonlocal susceptibility for excited states. Resulting problems with the generalization of the density functional methodology to excited states are discussed.
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It is shown that, for isolated many-electron Coulomb systems with Coulombic external potentials, the usual reductio ad absurdum proof of the Hohenberg-Kohn theorem is unsatisfactory since the to-be-refuted assumption made about the one-electron densities and the assumption about the external potentials are not compatible with the Kato cusp condition. The theorem is, however, provable by more so...
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Proof I : Assume that there exist two potentials V (1) ext (~r) and V (2) ext (~r) differing by more than a constant and giving rise to the same ground state density, n(~r). Obviously, V (1) ext (~r) and V (2) ext (~r) belong to distinct Hamiltonians Ĥ (1) ext(~r) and Ĥ (2) ext(~r), which give rise to distinct wavefunctions Ψ (1) ext(~r) and Ψ (2) ext(~r). Because of the variational principle, ...
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We show that under well-defined conditions the Hohenberg-Kohn theorem (HKT) that provides the foundation of ground-state density functional theory (DFT) can be extended to the lowest-energy resonance of unbound electronic systems. The extended version of the HKT provides an adequate framework to carry out DFT calculations of negative electron affinities.
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ژورنال
عنوان ژورنال: Physical Review A
سال: 2012
ISSN: 1050-2947,1094-1622
DOI: 10.1103/physreva.86.042502