On the proof by reductio ad absurdum of the Hohenberg-Kohn theorem for ensembles of fractionally occupied states of Coulomb systems

摘要

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 and colleagues is self-contradictory, since the to-be-refuted assumption (negation) regarding the ensemble one-electron densities and the assumption regarding the external potentials are logically incompatible to each other due to the Kato electron-nuclear cusp theorem. It is proved, however, that the Kato theorem itself provides a satisfactory proof of this theorem. (c) 2006 Wiley Periodicals, Inc.