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Polarized atomic orbitals for linear scaling methods


Berghold, G; Parrinello, M; Hutter, J (2002). Polarized atomic orbitals for linear scaling methods. Journal of Chemical Physics, 116(5):1800-1810.

Abstract

We present a modified version of the polarized atomic orbital (PAO) method [M. S. Lee and M. Head-Gordon, J. Chem. Phys. 107, 9085 (1997)] to construct minimal basis sets optimized in the molecular environment. The minimal basis set derives its flexibility from the fact that it is formed as a linear combination of a larger set of atomic orbitals. This approach significantly reduces the number of independent variables to be determined during a calculation, while retaining most of the essential chemistry resulting from the admixture of higher angular momentum functions. Furthermore, we combine the PAO method with linear scaling algorithms. We use the Chebyshev polynomial expansion method, the conjugate gradient density matrix search, and the canonical purification of the density matrix. The combined scheme overcomes one of the major drawbacks of standard approaches for large nonorthogonal basis sets, namely numerical instabilities resulting from ill-conditioned overlap matrices. We find that the condition number of the PAO overlap matrix is independent from the condition number of the underlying extended basis set, and consequently no numerical instabilities are encountered. Various applications are shown to confirm this conclusion and to compare the performance of the PAO method with extended basis-set calculations.

We present a modified version of the polarized atomic orbital (PAO) method [M. S. Lee and M. Head-Gordon, J. Chem. Phys. 107, 9085 (1997)] to construct minimal basis sets optimized in the molecular environment. The minimal basis set derives its flexibility from the fact that it is formed as a linear combination of a larger set of atomic orbitals. This approach significantly reduces the number of independent variables to be determined during a calculation, while retaining most of the essential chemistry resulting from the admixture of higher angular momentum functions. Furthermore, we combine the PAO method with linear scaling algorithms. We use the Chebyshev polynomial expansion method, the conjugate gradient density matrix search, and the canonical purification of the density matrix. The combined scheme overcomes one of the major drawbacks of standard approaches for large nonorthogonal basis sets, namely numerical instabilities resulting from ill-conditioned overlap matrices. We find that the condition number of the PAO overlap matrix is independent from the condition number of the underlying extended basis set, and consequently no numerical instabilities are encountered. Various applications are shown to confirm this conclusion and to compare the performance of the PAO method with extended basis-set calculations.

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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:1 February 2002
Deposited On:09 Oct 2008 09:57
Last Modified:01 Jun 2016 13:01
Publisher:American Institute of Physics
ISSN:0021-9606
Additional Information:Copyright 2002 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 2002, 116(5), 1800-1810 and may be found at http://link.aip.org/link/?JCPSA6/116/1800/1.
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:10.1063/1.1431270
Official URL:http://link.aip.org/link/?JCPSA6/116/1800/1
Permanent URL: http://doi.org/10.5167/uzh-3196

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