spring 2018 KJE-8104 Relativistic quantum chemistry - 10 ECTS

Application deadline

Registration deadline for PhD students at UiT - The Arctic University of Norway: Februar 1st

Application deadline for external applicants: December 1st


Type of course

 Theoretical subject. The course is available as a singular course. The course is offered on condition that a minimum number of students register for the course.

Admission requirements

PhD students or holders of a Norwegian master´s degree of five years or 3+ 2 years (or equivalent) may be admitted. Valid documentation is a statement from your institution that you are a registered PhD student or a Master´s Diploma with Diploma Supplement / English translation of the diploma. PhD students are exempt from semester fee.

Students should have a good background in quantum-mechanical theory. Knowledge of electronic structure theory, point group symmetry as well as electromagnetic theory will be advantageous.

PhD students at UiT The Arctic University of Norway register for the course through StudentWeb .

External applicants apply for admission through  SøknadsWeb. Application code 9303.

All external applicants have to attach a confirmation of their status as a PhD student from their home institution. Students who hold a Master of Science degree, but are not yet enrolled as a PhD-student have to attach a copy of their master's degree diploma. These students are also required to pay the semester fee.

More information regarding PhD courses at the Faculty of Science and Technology is found here .


Course overlap

If you pass the examination in this course, you will get an reduction in credits (as stated below), if you previously have passed the following courses:

KJE-3104 Relativistic Quantum Chemistry 10 stp

Course content

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.


Recommended prerequisites

KJE-3101 Quantum Chemistry

Objectives of the course

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.


Language of instruction and examination

The language of instruction is English and all of the syllabus material is in English. Examination questions will be given in English, and may be answered in either English or a Norwegian/Scandinavian language.

Teaching methods

Lectures: 20 h, Seminars: 8 h. Lectures and seminars will be given intensively during a week's gathering. Additionally, students be given a set of recent publications in which relativistic has been handled, and will be asked to analyse and criticize the treatment of relativistic effects in these studies, and elaborate on how results might change as a s consequence of using appropriate relativistic approximations.

Assessment

Grades based on a final, oral examination. Passed/Not passed.

Coursework requirements: A report analyzing recent publications where relativistic effects are important.


Recommended reading/syllabus

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

Chemistry , Oxford University Press, USA, New York, 2007.

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  • About the course
  • Campus: Tromsø |
  • ECTS: 10
  • Course code: KJE-8104