# Chapter 11. Decoupling the Negative-Energy States

Published Online: 22 JUN 2009

DOI: 10.1002/9783527627486.ch11

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) Decoupling the Negative-Energy States, in Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527627486.ch11

#### Publication History

- Published Online: 22 JUN 2009
- Published Print: 14 JAN 2009

#### ISBN Information

Print ISBN: 9783527312924

Online ISBN: 9783527627486

- Summary
- Chapter

### Keywords:

- decoupling negative-energy states;
- one-electron equations;
- closed-form unitary transformation;
- Dirac Hamiltonian;
- free-particle Foldy–Wouthuysen transformation;
- Foldy–Wouthuysen expansion;
- infinite-order two-component one-step protocol;
- well-defined analytic block-diagonal Hamiltonians

### Summary

In the preceding chapters we set out from fundamental physical theory to arrive at a suitable theory for calculations on atoms and molecules, which still features four-component one-particle states. However, we noted that not only for small nuclear charges the contribution of the lower components of these spinors are small indeed. Hence, attempts were made to find Hamiltonians which do not require lower components in the corresponding one-particle functions and which thus are more convenient from a conceptual and — if possible — from a computational point of view. The principal options for such an elimination of small components are now introduced.