Continuous degeneracy of sets of localized orbitals

• Published in: International journal of quantum chemistry Vol. 76; no. 3; pp. 428 - 433
• Main Authors: Scheurer, P., Schwarz, W. H. E.
• Format: Journal Article
• Language: English
• Published: New York John Wiley & Sons, Inc 2000
• Subjects: degeneracy; localized orbitals
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/(SICI)1097-461X(2000)76:3<428::AID-QUA11>3.0.CO;2-Y

Continuous degeneracy of sets of localized Hartree–Fock orbitals (LMOs) can occur only if an occupied set of degenerate canonical orbitals (CMOs) is mixed with other orbitals by the unitary localization transformation. Accordingly, at the nonrelativistic level, systems with electronic charge distribution of the following symmetries will not qualify: C1; Cs, Ci, C2; C2h, C2v, D2; D2h. Among the remaining systems, continuous degeneracy of LMO sets will occur if some (linear combinations of) integrals vanish: this will also not be the case for systems of C3; C3v, D3 symmetry; for systems of higher symmetry, it will depend on which ones of the different degenerate and nondegenerate CMO species are occupied. If the number of atomic or bond density maxima matches the number of occupied orbitals, then the LMOs are uniquely fixed and do not show continuous degeneracy. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 428–433, 2000