KE503: Symmetry (5 ECTS)

STADS: 10008101

Level
Bachelor course

Teaching period
The course is offered in the autumn semester.

Teacher responsible
Email: pwj@sdu.dk

Additional teachers
hjj@sdu.dk

Timetable
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Show personal time table for this course.

Prerequisites:
None

Academic preconditions:
KE501 Fundamental Chemistry, MM501 Calculus I and MM502 Calculus II or MM503 Biomath and Calculus II (or FF502 and FF503 or FF504) must be passed. The fundamental principles for IR and NMR spectroscopy are presupposed known.

Course introduction
The aim of the course is to introduce the students to the use of symmetry within chemistry, especially with a view to description of the electron structures and spectroscopic properties of molecules. The course will focus on a detailed study of the group theory as well as its consequences for the molecular properties. The course will form the basis of subsequent courses in quantum chemistry, inorganic chemistry and spectroscopy.

Expected learning outcome
At the end of the course, the students are expected to be able to:

• Decide, if a molecule is chiral
• Determine symmetry elements, symmetry operations and point groups. 
• Describe the crystal structures of molecular materials using the concepts of lattices, unit cells and symmetry
• Determine irreducible representations for functions and products of these.
• Construct symmetry orbitals from a set of atomic orbitals.
• Construct symmetry coordinates from a set of atomic coordinates.
• Determine if a given normal coordinate will give rise to an absorption in the IR and Raman spectra, respectively.
• Estimate which symmetry orbitals that will be able to interact.
• Determine if an electronic transition is allowed or not.

Subject overview
The following subjects will be treated and discussed:

1. Symmetry elements and symmetry operations, determination of point groups; 
2. Matrix representations
3. Description of molecular crystals (lattices, unit cells and symmetry)
4. Reducible and irreducible representations; 
5. Characters;
6. Use of characters for determination of symmetry-adjusted functions; 
7. Orthogonalisation and normalization of functions; 
8. Direct product; 
9. Conditions for integrals being different to zero; 
10. Spectroscopic selection rules; 
11. Vibrational spectra (IR, Raman); 
12. Electronic spectra;

Literature

• David J. Willock: Molecular Symmetry, John Wiley 2009.
• Supplerende læsning (kan lånes ved øvelserne): A.Vincent: Molecular Symmetry and Group Theory, John Wiley 2009.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
Approval of 3 mandatory assignments is a prerequisite for participation in the exam.

Assessment and marking:

1. A 3-hour written digital examination with books and notes of your own choice. Internet access is not allowed. Marks according to the Danish 7-point marking scale. Internal examiner. (5 ECTS)

Reeksamination in the same exam period or immediately thereafter.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 15 hours
Skills training phase: 30 hours, hereof:
 - Tutorials: 30 hours

Educational activities Study phase: 80 hours

Language
This course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.