A note on the symmetry properties of Löwdin's orthogonalization schemes

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We point out that the well-known symmetry properties of the symmetrically and canonically orthogonalized vectors hold only under certain conditions on the overlapping vectors. In particular, the matrix of the transformation induced by the symmetry operator must be unitary. This requirement is not fulfilled if Cartesian d or f functions are used in the basis set. If such functions are present, canonically orthogonalized orbitals do not transform according to representations of the molecular point group; nor do Löwdin orthogonalized vectors preserve symmetry relation of the original vectors.

Original languageEnglish
Pages (from-to)937-944
Number of pages8
JournalCollection of Czechoslovak Chemical Communications
Issue number6-7
Publication statusPublished - Jun 1 2008



  • Canonical orthogonalization
  • Slater-koster theorem
  • Symmetric orthogonalization

ASJC Scopus subject areas

  • Chemistry(all)

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