KJE-3104 Relativistic Quantum Chemistry - 10 stp

For molecules containing heavy elements, relativistic effects are important. These effects can significantly affect the chemistry and physics of atoms and molecules, as well as the interaction of the electron density with external fields. To understand the chemistry of the lower part of the periodic table, the effects of relativity on the electronic structure of atoms molecules must be taken into account

The course will provide an introduction to the foundations of special relativity and will describe how relativistic effects changes the chemistry and physics of atoms and molecules. The course will describe discuss Maxwell¿s equation in the context of special relativity, and how electromagnetic fields and the interaction of molecules with external fields arises in a relativistic framework. The course will also address how different levels of approximation to the full Dirac equation can be used both to analyse relativistic effects and to simplify quantum-chemical calculations. Symmetry, orbital angular momentum and spin in a relativistic framework. One- and many-electron interactions in a relativistic framework.

The candidate..

Knowledge

Relativistic kinematics and dynamics

• Can describe the effects of relativity on the structure of the periodic table and anomalous spectroscopic properties in atoms and molecules..
• Understand the origin and difference of scalar and spin-orbit effects, and can describe the effects of relativity on the electron density of atoms and molecules
• Understands the theory and principles of special relativity, the Galilean and Lorentz transformations.

Electrodynamics

• Has a deep understanding of Maxwell¿s equation and its 4-vector formulation.
• Understands how Maxwell¿s equation define electric and magnetic fields in the stationary case and the concept of gauge transformations
• Can describe the potentials of a moving charge and the non-relativistic limit of electrodynamics

Dirac equation for a free particle and in a molecular fields

• Has knowledge of the Dirac equation for a free particle, and can define the Pauli spin matrices
• Has knowledge of the Klein-Gordon equation
• Understands the principle of minimal electromagnetic coupling and can set up the Dirac equation in external fields
• Understands spin and orbital angular momentum in a relativistic framework
• Understands how the non-relativistic limit can be recovered and understands how the Levy-Leblond and Schrödinger equations arises when going to a non-relativistic limit.
• Has knowledge about different one- and two-component relativistic Hamiltonians.

Two-electron interactions and hydrogenic atoms

• Has knowledge about charge and current density
• Can describe different two-electron interaction operators in the relativistic framework
• Understands the difference between the electronic structure of hydrogenic atoms in the relativistic and non-relativistic framework

Relativistic Symmetry

• Understands and can apply general rotation operations and rotations in spin space.
• Understands and can apply double groups and the algebra of spinors.

Skills

• Can identify when relativistic effects will be important.
• Can deduce how relativistic effects changes the properties of atoms and molecules compared to the conventional periodic trends defined by non-relativistic theory.
• Can analyse the symmetry in relativistic systems and analyse the electronic structure of atoms and molecules in terms of relativistic electronic structure theory
• Can evaluate when different approximations to the full Dirac equation can be applied in computational studies of atoms and molecules.

General competence

• Understands how the effects of special relativity affect the chemistry and physics of atoms and molecules and their interactions with electromagnetic fields.
• Can read and understand research articles where relativistic effects are central to the scientific content of the article.

K. G. Dyall and K. Faegri Jr., Introduction to Relativistic Quantum

Chemistry , Oxford University Press, USA, New York, 2007.Available on request