Comment on On the original proof by reductio ad absurdum of the Hohenberg-Kohn theorem for many-electron

Comment on “On the Original Proof byReductio Ad Absurdum of theHohenberg–Kohn Theorem for Many-Electron Coulomb Systems”1,2 1 1W. SZCZEPANIK, M. DULAK, T. A. WESOLOWSKI1Department of Physical Chemistry, University of Geneva, 30, quai Ernest-Ansermet,CH-1211 Geneva 4, Switzerland2Department of Theoretical Chemistry, Jagiellonian University, ul. Ingardena 3,30-060 Cracow, PolandReceived 23 March 2006; accepted 24 April 2006Published online 13 September 2006 in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/qua.21102ABSTRACT: We argue with Kryachko’s criticism [Int J Quantum Chem 2005, 103,818] of the original proof of the second Hohenberg-Kohn theorem. The Kato cuspcondition can be used to refute a “to-be-refuted” statement as an alternative to theoriginal proof by Hohenberg and Kohn applicable for Coulombic systems. Sincealternative ways to prove falseness of the “to-be-refuted” statement in a reduction adabsurdum proof do not exclude each other, Kryachko’s criticism is not justified.© 2006 Wiley Periodicals, Inc. Int J Quantum Chem 107: 762–763, 2007Key words: Hohenberg-Kohn theorems; reductio ad absurdum; Kato cusp condition;Coulombic systemsn the recent article [1], the original proof of external potential can be uniquely reconstructedI the first Hohenberg–Kohn theorem [2] was from the information contained in the electroncriticized “the usual reductio ad absurdum proof density for a Coulomb system (see also the rele-of the theorem is ...