Chapter 13. Elimination Techniques

  1. Prof. Dr. Markus Reiher and
  2. Dr. Alexander Wolf

Published Online: 22 JUN 2009

DOI: 10.1002/9783527627486.ch13

Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science

Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science

How to Cite

Reiher, M. and Wolf, A. (2009) Elimination Techniques, in Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527627486.ch13

Author Information

  1. ETH Zuerich, Laboratory for Physical Chemistry, Hoenggerberg Campus, Wolfgang-Pauli-Strasse 10, 8093 Zuerich, Switzerland

Publication History

  1. Published Online: 22 JUN 2009
  2. Published Print: 14 JAN 2009

ISBN Information

Print ISBN: 9783527312924

Online ISBN: 9783527627486

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Keywords:

  • elimination techniques;
  • Pauli elimination;
  • Breit–Pauli theory;
  • Cowan–Griffin approach;
  • Wood–Boring approach;
  • elimination of Dirac matrices;
  • regular approximations

Summary

A straightforward and easy reduction of the four-component one-electron equations to two-component form is the elimination of the two small components. This is achieved by expressing the small component through the large component via rearrangement of the lower two coupled (integro-)differential equations and substituting the result into the remaining upper two equations. Main issues to be considered are then from which formulation of the four-component one-electron equation one should start and how the arising energy and potential in the kinetic operator of the Hamiltonian — leading to equations which are no longer eigenvalue equations — should be treated.