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Are the unconventional density variations really unconventional?
Author(s) -
Zhang Yu Adam,
Wang Yan Alexander
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.22330
Subject(s) - fock space , ground state , hilbert space , quantum , electron density , space (punctuation) , quantum mechanics , discontinuity (linguistics) , physics , order (exchange) , electron , chemistry , mathematics , mathematical analysis , philosophy , linguistics , finance , economics
Based on numerical evidence and theoretical arguments, we demonstrate that the unconventional density variations are not really unconventional and should be included in the density variational domain of any ground‐state density. As a result, Lieb's Theorem 3.10 (Lieb, Int J Quantum Chem 1983, 24, 243) is reconfirmed. More specifically, the energy variation δ E v is of order higher than linear order of the density variation δ n (r) about the ground‐state density n 0 (r) of a system with a fixed number of electrons in Hilbert space, whereas δ E v is of linear order of δ n (r) about the ground‐state density of a system with a varied number of electrons in Fock space. The unconventional density variations are not the cause for the linear‐order behavior of δ E v in Fock space and the derivative discontinuity of the total energy. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009