Chapter 9. Many-Electron Atoms

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

Published Online: 22 JUN 2009

DOI: 10.1002/9783527627486.ch9

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) 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

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:

  • 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.