Collect. Czech. Chem. Commun. 2008, 73, 937-944

A Note on the Symmetry Properties of Löwdin's Orthogonalization Schemes

András T. Rokoba, Ágnes Szabadosb and Peter R. Surjánb,*

a Chemical Research Center, Hungarian Academy of Sciences, H-1525 Budapest, P.O. Box 17, Hungary
b Eötvös University, Laboratory of Theoretical Chemistry, H-1518 Budapest 112, P.O. Box 32, Hungary


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.

Keywords: Canonical orthogonalization; Symmetric orthogonalization; Slater-Koster theorem.

References: 11 live references.