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On the Proof by Reductio ad Absurdum of the Hohenberg-Kohn Theorem for Ensembles of Fractionally Occupied States of Coulomb Systems

E. S. Kryachko
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Abstract

It is demonstrated that the original reductio ad absurdum proof of the generalization of the Hohenberg-Kohn theorem for ensembles of fractionally occupied states for isolated many-electron Coulomb systems with Coulomb-type external potentials by Gross et al. [Phys. Rev. A 37, 2809 (1988)] is self-contradictory since the to-be-refuted assumption (negation) regarding the ensemble one-electron densities and the assumption about the external potentials are logically incompatible to each other due to the Kato electron-nuclear cusp theorem. It is however proved that the Kato theorem itself provides a satisfactory proof of this theorem.

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E. S. Kryachko. 2006-02-06. On the Proof by Reductio ad Absurdum of the Hohenberg-Kohn Theorem for Ensembles of Fractionally Occupied States of Coulomb Systems. https://doi.org/10.1002/qua.20970

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