KE503: Symmetry (5 ECTS)

STADS: 10007001

Level
Bachelor course

Teaching period
The course is offered in the autumn semester.
2nd quarter .

Teacher responsible
Email: pwj@sdu.dk

Additional teachers
hjj@sdu.dk

Timetable
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Prerequisites:
None

Academic preconditions:
KE501 Fundamental Chemistry, MM501 Calculus I and MM502 Calculus II or MM503 Biomath and Calculus IImust be passed. The fundamental principles for IR and BMR 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.
• 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.

Subject overview
The following subjects will be treated and discussed:

1. Symmetry elements and symmetry operations, determination of point groups;
2. Matrix representations;
3. Reducible and irreducible representations;
4. Characters;
5. Use of characters for determination of symmetry-adjusted functions;
6. Orthogonalisation and normalization of functions;
7. Direct product;
8. Conditions for integrals being different to zero;
9. Spectroscopic selection rules;
10. Vibrational spectra (IR, Raman);
11. 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
None

Assessment and marking:
a) Approval of 3 mandatory assignments is a prerequisite for participation in the exam. (0 ECTS)
b) A 3-hour written examination with books and notes of your own choice as well as pocket calculator. Marks according to the Danish 7-point marking scale. Internal examiner. (5 ECTS)

Reeksamination after 4th quarter.

Expected working hours
The teaching method is based on three phase model.

Undervisningen vil bestå af forelæsninger (13 timer), som suppleres med eksaminatorier (32 timer).
Educational activities

Language
This course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.