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Novel orthogonalization and biorthogonalization algorithms

Towards multistate multiconfiguration perturbation theory

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Abstract

Orthogonalization with the prerequisite of kee** several vectors fixed is examined. Explicit formulae are derived both for orthogonal and biorthogonal vector sets. Calculation of the inverse or square root of the entire overlap matrix is eliminated, allowing computational time reduction. In this special situation, it is found sufficient to evaluate the functions of matrices of the dimension matching the number of fixed vectors. The (bi)orthogonal sets find direct application in extending multiconfigurational perturbation theory to deal with multiple reference vectors.

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Notes

  1. Orthonormality of vectors \(\mathbf{c}^i\) is assumed since orthonormalizing m vectors is relatively cheap for \(m \ll N\).

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Acknowledgments

The authors are indebted to a Referee who helped to significantly improve the manuscript. The work presented here is a direct continuation of the research being followed in the laboratory of Péter Surján. It is a delight for the authors—all of them students of prof. Surján for some time in their life—to congratulate him on the occasion of reaching 60 and express their gratitude to the outstanding scholar.

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Authors and Affiliations

  1. Laboratory of Theoretical Chemistry, Eötvös University, POB 32, Budapest, 1518, Hungary

    Zsuzsanna Tóth, Péter Jeszenszki & Ágnes Szabados

  2. MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, POB 91, Budapest, 1521, Hungary

    Péter R. Nagy

Authors
  1. Zsuzsanna Tóth
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  2. Péter R. Nagy
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  3. Péter Jeszenszki
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  4. Ágnes Szabados
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Corresponding author

Correspondence to Ágnes Szabados.

Additional information

Published as part of the special collection of articles “Festschrift in honour of P. R. Surjan.”

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Tóth, Z., Nagy, P.R., Jeszenszki, P. et al. Novel orthogonalization and biorthogonalization algorithms. Theor Chem Acc 134, 100 (2015). https://doi.org/10.1007/s00214-015-1703-x

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  • DOI: https://doi.org/10.1007/s00214-015-1703-x

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