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Explicitly Correlated Wave Functions in Chemistry and Physics pp 275–329Cite as

Direct Perturbation Theory of Relativistic Effects

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Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 13))

Abstract

The direct perturbation theory (DPT) of relativistic effects is outlined. It is free from the singularities that plague approaches based on the Foldy­Wouthuysen transformation. The nonrelativistic limit (nrl) of the Dirac equation consistent with DPT is the Lévy-Leblond equation. If one can­not solve the latter or the inhomogeneous differential equations of DPT exactly, the method of choice is stationary direct perturbation theory. The leading correction to the wave function is then obtained by mak­ing the Hylleraas-Rutkowski functional stationary. This functional has a nice minimax property. If one cares for a regular approximation (the exact relativistic corrections to the wave function have lnr-type singu­larities near a nucleus) it is important to regularize the upper and the lower component of the bispinor consistently. Quasidegenerate DPT is the generalization to the case where a degeneracy or near-degeneracy in the nrl is split by relativity. The last part of this chapter is devoted to many-electron systems, both at the Hartree-Fock level and with inclu­sion of electron correlation. DPT is free from variational collapse and unaffected by the Brown-Ravenhall disease.

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Author information

Authors and Affiliations

  1. Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780, Bochum, Germany

    Werner Kutzelnigg

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  1. Werner Kutzelnigg
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Editors and Affiliations

  1. Institute of Bioorganic Chemistry PAN, Adam Mickiewicz University in Poznań, Poznań, Poland

    Jacek Rychlewski

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Kutzelnigg, W. (2003). Direct Perturbation Theory of Relativistic Effects. In: Rychlewski, J. (eds) Explicitly Correlated Wave Functions in Chemistry and Physics. Progress in Theoretical Chemistry and Physics, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0313-0_6

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  • DOI: https://doi.org/10.1007/978-94-017-0313-0_6

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  • Print ISBN: 978-90-481-6448-6

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