Introduction to Relativistic Quantum Chemistry

  • Lecturer: Xiaoyan Cao-Dolg
  • Assistant: Ilyas Türkmen

Lecture Contents:

  1. Special Relativity
    1. The Situation Before 1900
    2. Einstein’s Two Postulates
    3. Consequences
  2. Relativistic Electromagnetic Interactions
    1. The Maxwell Equations
    2. Potentials and Gauge Transformations
    3. The Relativistic Potential from a Moving Charge
    4. The Potential Experienced by a Moving Charge
    5. The Interaction of Two Charged Particles
  3. Relativistic Wave Equation
    1. Klein-Gordon Equation
    2. Dirac’s Free Particle Equation
    3. Dirac One Particle Hamiltonian
    4. Free-electron Solutions of the Time-independent Dirac Equation
    5. Hydrogen Solutions of the Time-independent Dirac Equation
  4. Relativistic Symmetry
    1. Double Groups
    2. Spin and the SU(2) Group
    3. Spatial Rotations and the SO(3) Group
    4. Transformation of Operators
    5. Transformation of the Dirac Equation under SU(2) and SO(3)
    6. Space Inversion
    7. Reflection and Rotation-Inversions
    8. Time Reversal
    9. Lorentz Transformations and the Lorentz Group
  5. All-electron Methodology
    1. Four-component methods
    2. Spin Separations and the Modified Dirac Equation
    3. The Foldy-Wouthuysen Transformation
    4. Douglas-Kroll-Hess Hamiltonian
    5. Elimination of Small Components
    6. Perturbation Methods
  6. Valence-Electron Methods
    1. Core-valence Separation
    2. Valence-only Model Hamiltonian
    3. Pseudopotentials
    4. Core-Polarization Potentials
    5. Core-core/nucleus Repulsion Corrections
    6. Valence Basis Sets
  7. Relativistic Effects in Periodic Table
    1. Main Group Elements
    2. Transition Metals
    3. Lanthanides and Actinides
    4. Superheavy Elements