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Cholesky decomposition techniques in electronic structure theory
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2011 (English)In: Linear-Scaling Techniques in Computational Chemistry and Physics: Methods and Applications / [ed] R. Zalesny, P. Mezey, M. G. Papadopoulos and J. Leszczynski, Springer, 2011, p. 301-304Chapter in book (Other academic)
Abstract [en]

We review recently developed methods to efficiently utilize the Cholesky decomposition technique in electronic structure calculations. The review starts with a brief introduction to the basics of the Cholesky decomposition technique. Subsequently, examples of applications of the technique to ab inito procedures are presented. The technique is demonstrated to be a special type of a resolution-of-identity or density-fitting scheme. This is followed by explicit examples of the Cholesky techniques used in orbital localization, computation of the exchange contributionto the Fock matrix, in MP2, gradient calculations, and so-called method specific Cholesky decomposition. Subsequently, examples of calibration of the method with respect to computed total energies, excitation energies, and auxiliary basis set pruning are presented. In particular, it is demonstrated that the Cholesky method is an unbiased method to derive auxiliary basis sets. Furthermore, details of the implementational considerations are put forward and examples from a parallel Cholesky decomposition scheme is presented. Finally, an outlook and perspectives are presented, followed by a summary and conclusions section. We are of the opinion that the Cholesky decomposition method is a technique that has been overlooked for too long. We have just recently started to understand how to efficiently incorporate the method in existing ab initio programs. The full potential of the Cholesky technique has not yet been fully explored.

Place, publisher, year, edition, pages
Springer, 2011. p. 301-304
Series
Challenges and Advances in Computational Chemistry and Physics ; 13:13
National Category
Chemical Sciences Computer and Information Sciences
Identifiers
URN: urn:nbn:se:uu:diva-145440DOI: 10.1007/978-90-481-2853-2_13ISBN: 978-90-481-2852-5 (print)OAI: oai:DiVA.org:uu-145440DiVA, id: diva2:396223
Available from: 2011-02-10 Created: 2011-02-09 Last updated: 2018-01-12Bibliographically approved

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