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Relationship between orthogonalization and orbital localization procedures
Author(s) -
Lévy B.,
Berthier G.
Publication year - 1977
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.560120316
Subject(s) - orthogonalization , equivalence (formal languages) , atomic orbital , operator (biology) , matrix (chemical analysis) , molecular orbital , mathematics , computational chemistry , physics , quantum mechanics , chemistry , pure mathematics , algorithm , molecule , biochemistry , repressor , chromatography , transcription factor , gene , electron
A condition for the equivalence of the Löwdin orthogonalization method and various localization methods is derived, taking the matrix elements of the localizing operator into consideration. In the example of the π atomic orbitals of benzene, it is shown that the “ultralocalized” functions defined in the Anderson fashion with help of the Boys minimum‐fluctuation criterion do not fulfill this condition, in contrast with a Ruedenberg‐type localization.