Chapter 13. Elimination Techniques
Published Online: 22 JUN 2009
DOI: 10.1002/9783527627486.ch13
Copyright © 2009 Wiley-VCH Verlag GmbH & Co. KGaA
Book Title
Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science
Additional Information
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
Publication History
- Published Online: 22 JUN 2009
- Published Print: 14 JAN 2009
ISBN Information
Print ISBN: 9783527312924
Online ISBN: 9783527627486
- Summary
- Chapter
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.