Theoretical Chemistry Accounts

, 131:1109 | Cite as

Mayer’s orthogonalization: relation to the Gram-Schmidt and Löwdin’s symmetrical scheme

  • Péter R. Nagy
  • Péter R. Surján
  • Ágnes SzabadosEmail author
Regular Article


A method introduced by Mayer (Theor Chem Acc 104:163, 2000) for generating an orthogonal set of basis vectors, perpendicular to an arbitrary start vector, is examined. The procedure provides the complementary vectors in closed form, expressed with the components of the start vector. Mayer’s method belongs to the family of orthogonalization schemes, which keep an arbitrary vector intact without introducing any non-physical sequence-dependence. It is shown that Mayer’s orthogonalization is recovered by performing a two-step combination of the Gram-Schmidt and Löwdin’s symmetrical orthogonalization. Processor time requirement of constructing Mayer’s orthonormal set is proportional to ∼N 2, in contrast to the rough ∼N 3 CPU requirement of performing either a full Gram-Schmidt or Löwdin’s symmetrical orthogonalization. Utility of Mayer’s orthogonalization is demonstrated on an electronic structure application using perturbation theory to improve multiconfigurational wavefunctions.


Orthogonalization Mayer vectors 



The authors are indebted to Professor I. Mayer (Budapest) for a detailed inspection and instructive critical remarks on the present study. This work has been supported by the Hungarian National Research Fund (OTKA), grant numbers K-81588 and K-81590. The European Union and the European Social Fund have also provided financial support to the project under the grant agreements TÁMOP 4.2.1./B-09/1/KMR-2010-0003 and 4.2.2./B-10/1-2010-0030.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Péter R. Nagy
    • 1
  • Péter R. Surján
    • 1
  • Ágnes Szabados
    • 1
    Email author
  1. 1.Laboratory of Theoretical ChemistryEötvös UniversityBudapestHungary

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