### 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 language | English |
---|---|

Pages (from-to) | 937-944 |

Number of pages | 8 |

Journal | Collection of Czechoslovak Chemical Communications |

Volume | 73 |

Issue number | 6-7 |

DOIs | |

Publication status | Published - jún. 2008 |

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### ASJC Scopus subject areas

- Chemistry(all)

### Cite this

**A note on the symmetry properties of Löwdin's orthogonalization schemes.** / Rokob, T.; Szabados, A.; Surján, P.

Research output: Article

}

TY - JOUR

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

UR - http://www.scopus.com/inward/record.url?scp=55949097693&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=55949097693&partnerID=8YFLogxK

U2 - 10.1135/cccc20080937

DO - 10.1135/cccc20080937

M3 - Article

VL - 73

SP - 937

EP - 944

JO - ChemPlusChem

JF - ChemPlusChem

SN - 2192-6506

IS - 6-7

ER -