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Externally localized molecular orbitals: A numerical investigation of localization degeneracy
Author(s) -
Scheurer P.,
Schwarz W. H. E.
Publication year - 2000
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(2000)76:3<420::aid-qua10>3.0.co;2-8
Subject(s) - degeneracy (biology) , symmetry (geometry) , atomic orbital , physics , basis set , localized molecular orbitals , statistical physics , molecule , quantum mechanics , mathematics , linear combination of atomic orbitals , geometry , bioinformatics , biology , electron
An algorithm of unitarily transforming a set of occupied molecular orbitals into a set of localized orbitals (LMOs), which optimally resembles a set of guess LMOs, is applied to investigate degeneracy among LMO sets. It is shown that (1) systems of D 4 h symmetry (e.g., cyclobutadienedianion) can exhibit continuous degeneracy of LMOs, although this was excluded by a symmetry theorem in the literature; (2) systems of D 3 h symmetry (e.g., Kekule benzene, borazine) do not exhibit continuous LMO degeneracy, although this was to be expected on the basis of the above‐mentioned theorem; and (3) some systems of D 6 h symmetry (e.g., benzene) exhibit continuous LMO degeneracy while others of the same symmetry (e.g., coronene) do not. For small molecules and clusters, there are rather few cases of discrete degeneracy of LMO sets and even less cases of discrete near degeneracy. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 420–427, 2000