ISSN:
0020-7608
Keywords:
Computational Chemistry and Molecular Modeling
;
Atomic, Molecular and Optical Physics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
Klein has pointed out that des Cloizeaux's orthonormalization is just another formulation of Löwdin's symmetric orthonormalization. We demonstrate that des Cloizeaux's formulation is convenient for theoretical discussions and that it is intimately connected with polar decomposition--which is a generalization to operators of the fact that any complex number z can be written r exp (iθ) where r is positive and θ real. We generalize two other properties for z and find an interpretation of the Carlson-Keller theorem. Recently Lathouwers found that Löwdin's canonical orthonormalization leads to the eigenvectors of a positive operator. This operator is des Cloizeaux's. We discuss some variational theorems on this background and find the Courant-Hilbert-Löwdin “measure of linear independence” from a simple least squares consideration, closely related to Lathouwers' results.An orthonormalization due to Schweinler and Wigner (1970) is observed to be Löwdin's canonical. The Schweinler-Wigner maximum characterization is referred to a simple general theorem, which also implies a new maximum characterization.In Sections 6 and 7 we consider transformation to an effective Hamiltonian from the point of view of polar decomposition and symmetric orthonormalization. It turns out that the polar part of Bloch's transformation is des Cloizeaux's. The characterizations of this by both Klein and Jørgensen are visualized in a simple way.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/qua.560120215
