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Maximum principles in DFT from reciprocal variational problem
Author(s) -
TkaczŚmiech Katarzyna,
Ptak W. S.
Publication year - 1997
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/(sici)1097-461x(1997)65:5<499::aid-qua14>3.0.co;2-z
Subject(s) - reciprocal , calculus of variations , formalism (music) , density functional theory , maximum entropy method , variational principle , principle of maximum entropy , mathematics , first variation , electron , calculus (dental) , theoretical physics , quantum mechanics , physics , statistical physics , mathematical analysis , medicine , art , musical , philosophy , linguistics , statistics , dentistry , visual arts
Formalism of density‐functional theory (DFT) is based on the calculus of variation. In the Hohenberg and Kohn theorem, a variational equation minimizing electronic energy with respect to an electron density is constructed. The calculus of variation allows one to formulate a problem which is reciprocal to an original one. Also, we may consider the problem of finding the electron density determining a given energy E = E [ρ] for a maximum number N = N [ρ] of the electrons forming the system. In this work, the reciprocal variational problem is discussed. Mathematical considerations are followed by a presentation of an application of the reciprocal problem (maximum entropy principle). Other possibilities of the applications are sketched. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 499–501, 1997