Including rigorous numerical bounds in quantum chemistry calculations: Gaussian integral evaluation

Pete P. Janes, Alistair P. Rendell

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

Large scale quantum chemistry calculations often involve evaluating and processing millions of Gaussian integrals. Whereas literature in this field, like other areas of scientific computing, has focused on devising more efficient algorithms for evaluating these integrals, relatively little has been done to fathom the effects numerical errors may have on their accuracy. In this work we present several methods for computing rigorous bounds on the incomplete gamma function, known in this context as Fm(T), which is a core quantity used in Gaussian integral evaluation. Based on a computational paradigm called interval arithmetic, these bounds are guaranteed to contain the true numerical result of Fm(T), notwithstanding the presence of rounding and truncation errors. Experimental results are analysed to determine the best numerical approaches for ensuring that the bounds are not only rigorous, but also sufficiently precise. A worst-case error analysis of existing numerical techniques is also presented as a consequence of this work.

Original languageEnglish
Title of host publicationProceedings - 2008 IEEE 11th International Conference on Computational Science and Engineering, CSE 2008
Pages75-82
Number of pages8
DOIs
Publication statusPublished - 22 Sep 2008
Externally publishedYes
Event2008 IEEE 11th International Conference on Computational Science and Engineering, CSE 2008 - Sao Paulo, SP, Brazil
Duration: 16 Jul 200818 Jul 2008

Publication series

NameProceedings - 2008 IEEE 11th International Conference on Computational Science and Engineering, CSE 2008

Conference

Conference2008 IEEE 11th International Conference on Computational Science and Engineering, CSE 2008
CountryBrazil
CitySao Paulo, SP
Period16/07/0818/07/08

Keywords

  • interval arithmetic
  • Error analysis
  • Chemistry

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