Chapter 10. General Molecules and Molecular Aggregates

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

Published Online: 22 JUN 2009

DOI: 10.1002/9783527627486.ch10

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) General Molecules and Molecular Aggregates, in Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527627486.ch10

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



  • general molecules;
  • molecular aggregates;
  • molecular spinors;
  • Dirac–Hartree–Fock electronic energy;
  • molecular one-electron integrals;
  • molecular two-electron integrals;
  • Dirac–Hartree–Fock–Roothaan matrix equations;
  • analytic gradients;
  • post-Hartree–Fock methods


After having derived a relativistic four-component Hamiltonian operator in chapter 8 — often called a ‘fully relativistic’ Hamiltonian although fundamental requirements of special relativity have been given up (no absolute time and Lorentz covariance) — and having employed it for spherically symmetric atoms, it is now appropriate to proceed to the case of general molecules. Here, we need to introduce suitable approximations for the one-electron functions of molecular systems. Results and inventions of the historically earlier developed nonrelativistic theory are transferred to the relativistic regime. However, a couple of subtleties like variational collapse, kinetic balance and the role of the negative-energy states need to be taken care of.