Relativistische Elektronenstrukturtheorie
Instructors: Dr. Konstantin GaulShortname: 08.128.7033
Course No.: 08.128.7033
Course Type: Vorlesung
Requirements / organisational issues
This lecture will be adjusted to the specific interest of participating students. There are no specific requirements.If you have questions regarding the lecture please contact konstantin.gaul@uni-mainz.de.
Recommended reading list
Kenneth Dyall and Knut Faegri, Introduction to Relativistic Quantum Chemistry, Oxford University Press, 2007Peter Schwerdtfeger (Ed.), Relativistic Electronic Structure Theory - Part 1. Fundamentals, Elsevier, 2002
Peter Schwerdtfeger (Ed.), Relativistic Electronic Structure Theory - Part 2. Applications, Elsevier, 2004
Eberhard Engel and Reiner M. Dreizler, Density Functional Theory: An Advanced Course, Springer Berlin, Heidelberg, 2011, Chapter 8
Markus Reiher and Alexander Wolf, Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science, WILEY-VCH, 2015
Contents
In this course the Lorentz invariant description of the electronic structure and common approximations used in relativistic quantum chemistry will be discussed.Preliminary schedule (probably not all topics can be discussed. The schedule will be adjusted in accordance with the interest of the students):
1.Recapitulation of (special) relativity, Lonrentz symmetry and Poincaré transformations
2.Dirac equation & Lorentz invariant motion of spin-1/2 particles
3.Dirac equation of the hydrogen atom
4.Quantum electrodynamic effects
4.1.Lorentz invariant interactions
4.2.Bound state quantum electrodynamics
4.2.1.Recapitulation: Renormalization and Feynman rules
4.2.2.The Lamb-shift, vacuum polarization and electron self energy
5.Many body systems
5.1.Leading order Lorentz invariant potential: Breit interaction
5.2."No-pair" approximation
5.2.Dirac-Hartree-Fock
5.3.Influence of relativistic effects on atomic/molecular orbitals/band structure (Consequences: color of gold, state of matter of mercury etc.)
6.Relativistic density functional theory
6.1.General quantum field theoretical 4-current formulation
6.2.Rajagopal-Callaway theorem
6.3.Relativistic Kohn-Sham DFT
6.4.Spin-DFT (SDFT)
6.4.1.Non-relativistic (collinear) SDFT
6.4.2.Non-collinear spins
7.Molecular Properties
7.1.Electric fields
7.2.Magnetic fields
7.3.Electroweak quantum chemistry
7.4.Physics beyond the Standard Model
8.Common approximations to the Dirac equation
8.1.Two component/quasi-relativistic approaches
8.1.1.Fouldy-Wouthuysen transformation
8.1.2.Breit-Pauli perturbation theory
8.1.3.Regular approximations
8.1.4.Douglas-Kroll
9.1.5.Exact decoupling and X2C
8.2.One component/scalar-relativistic approaches
8.3.Pseudopotentials/Effective core potentials (ECPs)
Dates
| Date (Day of the week) | Time | Location |
|---|---|---|
| 04/15/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |
| 04/22/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |
| 04/29/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |
| 05/06/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |
| 05/13/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |
| 05/20/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |
| 05/27/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |
| 06/03/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |
| 06/10/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |
| 06/17/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |
| 06/24/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |
| 07/01/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |
| 07/08/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |
| 07/15/2025 (Tuesday) | 14:15 - 15:45 | 01 525 Seminarraum K 2413 - Neubau Physik/Mathematik |