| Theoretical basis of optical spectroscopy | |
| Unit Code | ASC 06 - KR (semestr 2) |
| Credits | 5 |
| Prerequisites | ASC 1 to 4 (semester I) |
| TEACHING STAFF | Prof. Piotr Petelenz, Dr. hab. Andrzej Eilmes |
COURSE DESCRIPTION: The course presents the theoretical background necessary to understand
the optical spectroscopies. It starts from the time-dependent Schrödinger equation, which is subsequently solved by time-dependent perturbation theory, with special
emphasis on the case of periodic perturbation. Transition probability per unit time is derived (Fermi Golden Rule), and discussed in some detail for the first order
of perturbation theory within the dipole approximation (absorption/emission spectroscopy). The selection rules are derived for the rotational, vibrational and
electronic transitions (also combinations thereof) in a diatomic molecule. The treatment is generalized for polyatomic molecules, with emphasis on the role
of normal vibrational modes in IR and UV/Vis spectroscopy (including vibronic structure of allowed and forbidden electronic transitions). Radiationless transitions
are explained in the context of adiabatic approximation and limits of its applicability. Raman and Rayleigh scattering are discussed based on the second-order
perturbational result for transition probability; higher orders of perturbation theory are mentioned in the context of nonlinear optical phenomena.
Some consequences of symmetry in spectroscopy are shown. To this end, the basic concepts of group theory are recalled, such as reducible and irreducible
representations, characters and character orthogonality theorem, decomposition of a reducible representation into irreducible representations.
Applications of group theory for IR, Raman and electronic spectroscopy are illustrated on specific examples of molecular structure determination based
on spectroscopic information.
OBJECTIVE OF THE COURSE:
The aims of this unit are:
- To present the theoretical background of spectroscopy as a consequence of the quantum mechanical principles introduced during the bachelor degree programme
- To develop the understanding of the physics underlying the probing of matter by radiation
- To identify the limits of validity of the underlying approximations
- To highlight the general usefulness of group theory in spectroscopic interpretations
INTENDED LEARNING OUTCOMES:
After completing this unit the student should be able to:
- Discuss in a comprehensive way the approximations underlying the selection rules of absorption/emission/Raman spectroscopy, and the limits of their validity
- Identify the potential conceptual pitfalls and review critically the resultant interpretational errors
- Outline the salient steps of extending the treatment to cover non-linear optical phenomena
- Competently apply group theory for interpretation of individual spectra and for spectroscopy-based structural research
TEACHING AND LEARNING ACTIVITIES:
| TERM | NAME | L | S/E | P |
| 2 | Theoretical basis of optical spectroscopy | 50 |
LANGUAGE OF INSTRUCTION: English
SCHEDULE AND LEARNING METHOD:
| Weeks | Type | Duration | Course description |
| 1-2 | L | 7 | Theoretical background |
| 3-4 | L | 6 | Selection rules for diatomic molecules |
| 5-8 | L | 12 | Spectroscopy of polyatomic molecules |
| 9 | L | 4 | Radiationless transitions |
| 10-11 | L | 5 | Raman and Rayleigh scattering |
| 11 | L | 2 | Nonlinear optical phenomena |
| 12-13 | L | 5 | Basic concepts of group theory |
| 13-15 | L | 9 | Applications of group theory |
ASSESSMENT:
Examination on completion of teaching period: written or oral (weighting 100%).
BIBLIOGRAPHY:
L.I.Schiff, Quantum Mechanics, McGraw-Hill, New York 1968
P.W.Atkins, Molecular Quantum Mechanics, Oxford University Press 1992
F.A.Cotton, Chemical Applications of Group Theory, Wiley, New York 1990
P.Jacobs, Group Theory with Applications in Chemical Physics, Cambridge University Press 2004