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

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Abstract

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
Volume73
Issue number6-7
DOIs
Publication statusPublished - jún. 2008

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Point groups
Crystal symmetry

ASJC Scopus subject areas

  • Chemistry(all)

Cite this

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title = "A note on the symmetry properties of L{\"o}wdin's orthogonalization schemes",
abstract = "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 L{\"o}wdin orthogonalized vectors preserve symmetry relation of the original vectors.",
keywords = "Canonical orthogonalization, Slater-koster theorem, Symmetric orthogonalization",
author = "T. Rokob and A. Szabados and P. Surj{\'a}n",
year = "2008",
month = "6",
doi = "10.1135/cccc20080937",
language = "English",
volume = "73",
pages = "937--944",
journal = "ChemPlusChem",
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publisher = "Wiley-VCH Verlag",
number = "6-7",

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T1 - A note on the symmetry properties of Löwdin's orthogonalization schemes

AU - Rokob, T.

AU - Szabados, A.

AU - Surján, P.

PY - 2008/6

Y1 - 2008/6

N2 - 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.

AB - 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.

KW - Canonical orthogonalization

KW - Slater-koster theorem

KW - Symmetric orthogonalization

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U2 - 10.1135/cccc20080937

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JF - ChemPlusChem

SN - 2192-6506

IS - 6-7

ER -