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Novel orthogonalization and biorthogonalization algorithms

Towards multistate multiconfiguration perturbation theory
  • Zsuzsanna Tóth
  • Péter R. Nagy
  • Péter Jeszenszki
  • Ágnes SzabadosEmail author
Chapter
Part of the Highlights in Theoretical Chemistry book series (HITC, volume 12)

Abstract

Orthogonalization with the prerequisite of keeping 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.

Keywords

Overlap Orthogonalization Biorthogonal sets Multiconfiguration perturbation theory Multistate theory 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Zsuzsanna Tóth
    • 1
  • Péter R. Nagy
    • 2
  • Péter Jeszenszki
    • 1
  • Ágnes Szabados
    • 1
    Email author
  1. 1.Laboratory of Theoretical ChemistryEötvös UniversityBudapestHungary
  2. 2.MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials ScienceBudapest University of Technology and EconomicsBudapestHungary

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