Chapter 9. Many-Electron Atoms
Published Online: 22 JUN 2009
DOI: 10.1002/9783527627486.ch9
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) Many-Electron Atoms, in Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527627486.ch9
Publication History
- Published Online: 22 JUN 2009
- Published Print: 14 JAN 2009
ISBN Information
Print ISBN: 9783527312924
Online ISBN: 9783527627486
- Summary
- Chapter
Keywords:
- Many-Electron Atoms;
- transformation;
- many-electron Hamiltonian coordinates;
- polar coordinates;
- atomic many-electron wave function;
- one-electron integrals;
- two-electron integrals;
- spherical symmetry;
- self-consistent-field equations;
- atomic spinors;
- radial functions;
- numerical discretization;
- solution techniques
Summary
The spherical symmetry of the attractive nuclear potential of atoms in the absence of additional fields allows one to formulate the many-electron problem in the radial coordinate only. It is instructive to study the difference between these many-electron equations and the single-electron Dirac hydrogen atom from chapter 6. In addition, analytical results can be obtained for the unkown atomic spinors in the short- and long-range limit that also serve well for spherical averages in the case of molecules. Last but not least, atomic spinors are also a good starting point for establishing approximations to molecular spinors discussed in the following chapter.