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Journal of Molecular Modeling

, 25:323 | Cite as

Hylleraas’ variational method with orthogonality restrictions

  • V. N. Glushkov
  • X. AssfeldEmail author
Original Paper
  • 38 Downloads

Abstract

In this paper, we suggest a new computational technique for the minimization of Hylleraas’ functional with additional orthogonality restrictions imposed on the desired vectors. It is shown how Hylleraas’ constrained problem can be reduced to an unconstrained one by minimal computational efforts. The asymptotic projection (AP) method proposed earlier to minimize Rayleigh’s quotient subject to some orthogonality restrictions is applied to construct a modified Hylleraas’ functional whose solution fulfills the required constraints automatically. Specifically, equivalence between the original problem and the one for the modified Hamilton operator is derived. It is shown that the AP methodology allows additional restrictions to be treated in a unified approach for both Rayleigh’s quotient and Hylleraas’ functional. Specific features of the method are demonstrated on the electronic parallel polarizability of H2+. Some emphasis is put on the choice of specific distributed basis set adapted for polarizability computation. A comparison with other methods, considered exact or extremely accurate, is also given.

Keywords

Hylleraas’ functional Orthogonality restrictions Asymptotic projection method Minimization 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of ChemistryOles Honchar Dnipropetrovsk National UniversityDnipropetrovskUkraine
  2. 2.Laboratoire de Physique et Chimie ThéoriquesUMR 7019, CNRS & Université de LorraineVandoeuvre-les-Nancy CedexFrance

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