# Chapter 8. First-Quantized Dirac-Based Many-Electron Theory

Published Online: 22 JUN 2009

DOI: 10.1002/9783527627486.ch8

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) First-Quantized Dirac-Based Many-Electron Theory, in Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527627486.ch8

#### Publication History

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

#### ISBN Information

Print ISBN: 9783527312924

Online ISBN: 9783527627486

- Summary
- Chapter

### Keywords:

- first-quantized Dirac-based many-electron theory;
- two-electron systems;
- Breit equation;
- quasi-relativistic many-particle Hamiltonians;
- Born–Oppenheimer approximation;
- tensor structure;
- approximations;
- many-electron wave function;
- second quantization;
- many-electron Hamiltonian;
- effective one-particle equations;
- relativistic density functional theory;
- coupled-cluster expansion

### Summary

In the preceding chapter quantum electrodynamics was established as the well-defined and exact theory for matter subject to electromagnetic interactions. However, we noted that the second-quantized formalism with variable particle numbers is not necessarily the most appropriate one for the molecular sciences. Pair-creation processes cannot occur in the energy range relevant to molecular systems and hence have not to be taken into account if we can benefit from their neglect. And in fact, a consistent and numerically reliable many-electron theory can be developed starting from a first-quantized picture of fixed particle numbers and neglecting the quantization of electromagnetic fields. This chapter presents the basic framework to be further detailed in the subsequent chapters.