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On Löwdin orthogonalization

✍ Scribed by John G. Aiken; John A. Erdos; Jerome A. Goldstein

Book ID
104580058
Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
367 KB
Volume
18
Category
Article
ISSN
0020-7608

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✦ Synopsis

Abstract

It is shown that the Löwdin orthogonalization gives the unique minimum for the functional ϕ measuring the least squares distance between the given orbitals and the orthogonalized orbitals. Furthermore a much stronger result is obtained, namely that ϕ has only one local minimum, which is attained at the Löwdin orthogonalization and which is global. This justifies certain computer programs that compute Löwdin orthogonalization via minimization procedures. Finally there is a discussion of replacing the least squares metric by other metrics. The Löwdin orthogonalization turns out to be optimal with respect to all the commonly encountered norms.

📜 SIMILAR VOLUMES

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## Abstract By use of the pseudo‐inverse matrix technique the generalization of the Löwdin orthogonalization, given by Kashiwagi and Sasaki, is shown to be valid in a case of singular metric matrices for two basis sets of functions. The application of the same idea to the inverse vibrational proble

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## Abstract A quadratically convergent process using a continued fraction method for finding the square root of the overlap matrix used in Löwdin orthogonalization is presented. The continued fraction method is compared to several other methods for finding the square root of a matrix. The method is