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Locality of exchange matrices for common Gaussian basis sets

✍ Scribed by John E. Harriman; Douglas E. Hoch

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 159 KB
Volume: 63
Category: Article
ISSN: 0020-7608
DOI: 10.1002/(sici)1097-461x(1997)63:1<111::aid-qua15>3.0.co;2-f

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✦ Synopsis

This article investigates a new approach to local approximations to exchange. When a finite basis set is introduced, any operator may be regarded as equivalent to a local operator if its matrix can be reproduced as the matrix of a multiplicative function operator. The expectation values of such operators can be determined from the electron density. Any matrix can be divided into local and nonlocal components, in a way dependent on linear dependencies among basis-set products. A measure of locality is provided by the ratio of the norm of the local component to that of the whole matrix. The local contribution to an expectation value can also be compared with the total. The self-consistent field exchange matrices and their expectation values for atoms Li through Ne and for LiH and HF with several Cartesian Gaussian basis sets were investigated in this way, and for the atoms, the exchange supermatrix was also examined. It has been found in all cases that the matrices and expectation values are more than 92% local; most are more than 99% local.

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