Relativistic Molecular Physics Ph.D. Course

FQM 711
2 Credits
32 hours
Professor Kenneth G. Dyall

The basis of the relativistic quantum theory for atoms and molecules will be reviewed. The course will cover the following topics:

  • Basic special relativity, electromagnetism, gauges
  • The Dirac equation and its nonrelativistic limit
  • The Dirac energy spectrum
  • Very basic field theory and QED.
  • Atomic solutions of the Dirac equation and their properties. Nuclear models.
  • Mean-field theory and the minimax principle.
  • Basis set expansions for the Dirac equation, kinetic balance, types of basis sets
  • Review of group theory, atomic symmetry, double groups, spinor symmetries
  • Time-reversal symmetry, operators and integrals under time reversal.
  • Electron correlation, with time-reversal and double-group symmetry.
  • Properties and relativistic property operators
  • Spin separation in the Dirac equation, spin-free and spin-orbit Hamiltonians
  • Foldy-Wouthuysen transformation, Pauli and Breit-Pauli Hamiltonians
  • Direct perturbation theory
  • Douglas-Kroll-Hess and related approximations
  • Regular approximations: ZORA, IORA.
  • Matrix methods: X2C and approximations.
  • Relativistic density functional theory.

Grading Policy:
The course will be assessed on the basis of class participation, exercises to be handed in, and a final written examination.


  1. K. G. Dyall and K. Faegri Jr. “Introduction to Relativistic Quantum Chemistry” Oxford University Press, 2007
  2. M. Reiher and A. Wolf, “Relativistic Quantum Chemistry”, Wiley-VCH Verlag GmbH&Co 2009.
  3. W. Greiner, “Relativistic Quantum Mechanics” 3rd Edition Springer.Verlag 2000
  4. I. P. Grant, “Relativistic Quantum Theory of Atoms and Molecules”,Springer-Verlag 2007


Day Hour Room
Monday June 24 14:55 A 16:35 R4-202
Tuesday June 25 14:55 A 16:35 R4-202
Wednesday June 26 14:55 A 16:35 R10-306
Thursday June 27 14:55 A 16:35 R10-306
Friday June 28 14:55 A 16:35 R4-202
Monday July 1 to Thursday July 4 10:20 A 12:55
14:55 A 17:30


Ing.P.R. Claudia Valdivia Estay
Universidad Andres Bello
Campus Republica
Av. Republica 275, Santiago, Chile
Phone: +56 – 2 – 26 61 85 70

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