Continuous degeneracy of sets of localized orbitals

✍ Scribed by P. Scheurer; W. H. E. Schwarz

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 160 KB
• Volume: 76
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(2000)76:3<428::aid-qua11>3.0.co;2-y

✦ Synopsis

Continuous degeneracy of sets of localized Hartree᎐Fock orbitals LMOs

Ž

. 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: C ; C , C , C ; C , C , D ; D . Among the remaining systems, continuous

Ž . degeneracy of LMO sets will occur if some linear combinations of integrals vanish: this will also not be the case for systems of C ; C , D symmetry; for systems of higher 3 3v 3 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.