Premium
The Weizsäcker functional: Some rigorous results
Author(s) -
Romera E.,
Dehesa J. S.,
Yañez R. J.
Publication year - 1995
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.560560518
Subject(s) - density functional theory , kinetic energy , fermi–dirac statistics , boltzmann constant , energy functional , physics , fermi gamma ray space telescope , thomas–fermi model , quantum mechanics , statistical physics , mathematics , electron
Abstract The Weizsäcker functional T W is a necessary element to explain basic physical and chemical phenomena of atomic and molecular systems in the general density functional theory initiated by Hohenberg and Kohn. Here, rigorous inequalities which involve the functional T W and two arbitrary power‐type density functionals ωα ≔ ∫ ρ α ( r ) d r are found by the successive applications of Sobolev and Hölder inequalities. Particular cases of these inequalities give lower bounds to the Weizsacker functional of an N ‐electron system in terms of a fundamental and/or experimentally measurable quantity such as, e.g., the Thomas–Fermi kinetic energy T 0 , the Dirac–Slater exchange energy K 0 and the average electronic density 〈ρ〉 in doing so, some known relationships appear. A numerical Hartree–Fock study of the accuracy of some resulting lower bounds is carried out. Finally, rigorous relationships between the Weizsäcker functional and the Boltzmann–Shannon information entropy of the system under consideration are given. © 1995 John Wiley & Sons, Inc.