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A smooth l1-norm sparseness function for orbital based linear scaling total energy minimization


Weber, V; Hutter, J (2008). A smooth l1-norm sparseness function for orbital based linear scaling total energy minimization. Journal of Chemical Physics, 128(6):064107.

Abstract

A smooth l(1)-norm based function to obtain a sparse representation of the orbital coefficients is introduced. This sparseness function is further parametrized with respect to unitary transformations among the occupied orbitals. Thus the function can be straightforwardly included in an optimization scheme or used on the fly during self-consistent field iterations to induce or maintain the sparsity of the orbital coefficients. As practical examples, we induce sparsity in the orbital coefficients of liquid water and bulk silicon. We also report the sparsity of the orbital coefficients of 1024 water molecules along a short Born-Oppenheimer molecular dynamics trajectory. It is observed that, after a stabilization period, the sparsity of the orbitals can be kept stable along the dynamics with small additional computational effort.

A smooth l(1)-norm based function to obtain a sparse representation of the orbital coefficients is introduced. This sparseness function is further parametrized with respect to unitary transformations among the occupied orbitals. Thus the function can be straightforwardly included in an optimization scheme or used on the fly during self-consistent field iterations to induce or maintain the sparsity of the orbital coefficients. As practical examples, we induce sparsity in the orbital coefficients of liquid water and bulk silicon. We also report the sparsity of the orbital coefficients of 1024 water molecules along a short Born-Oppenheimer molecular dynamics trajectory. It is observed that, after a stabilization period, the sparsity of the orbitals can be kept stable along the dynamics with small additional computational effort.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Department of Chemistry
Dewey Decimal Classification:540 Chemistry
Language:English
Date:2008
Deposited On:08 Sep 2008 09:09
Last Modified:01 Jun 2016 12:57
Publisher:American Institute of Physics
ISSN:0021-9606
Additional Information:Copyright 2008 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Chemical Physics 2008, 128(6):064107 and may be found at http://link.aip.org/link/?JCPSA6/128/064107/1.
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:10.1063/1.2828507
Official URL:http://link.aip.org/link/?JCPSA6/128/064107/1
Permanent URL: http://doi.org/10.5167/uzh-3158

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