Inverse problems of vibrational spectroscopy
Gulnara Kuramshina
Department of Physical Chemistry, Faculty of Chemistry, Lomonosov Moscow State
University
Moscow 119991, RUSSIA
E-mails: kuramshi@phys.chem.msu.ru
gmkur@yahoo.com
Short description
The first part of this course gives a basic introduction to the physical and mathematical
backgrounds of the data processing in vibrational (Infrared and Raman) spectroscopy. The
second part deals with the application of new stable numerical methods based on the theory of
regularization to the inverse problems of vibrational spectroscopy (of determining parameters of
the molecular force field from given experimental data) formulated within different models.
Particularly, joint treatment of experimental data on vibrational spectra and results of quantum
mechanical calculations within new approaches is considered.
Location and dates
Department of Mathematical Sciences, Fall semester 2013.
Sept. 30 – Oct. 12, 2013.
Introductory lecture:
Should be fixed later.
Aim of the course
After a successful completion of the course the students will be able to use the normal coordinate
analysis for the interpretation of vibrational spectra, to determine molecular force fields within
different models (including the scaling approach of quantum mechanical molecular force fields)
and to propose the complete interpretation of infrared and Raman spectra.
Target group
Graduate students in physics and physical chemistry.
Entry requirements
Basic undergraduate courses in physics, linear algebra and calculus.
Course organizers
Gulnara Kuramshina (kuramshi@phys.chem.msu.ru) and Larisa Beilina (larisa.beilina@chalmers.se )
Teachers
Gulnara Kuramshina (kuramshi@phys.chem.msu.ru)
Course program
Introduction to the experimental methods of vibrational spectroscopy and physical model of molecular
vibrations. Small vibrations, quantum mechanical model of molecular vibrations. Mathematical models of
molecular vibrations, model parameters: ab initio, semiempirical and empirical methods. Molecular force
fields models. Generalized coordinates, redundant and symmetry coordinates. Direct and inverse
problems of vibrational spectroscopy. Correctness of mathematical problems. Ill-posed problems in
vibrational spectroscopy. Mathematical statement of inverse vibrational problem. Joint treatment of
experimental and ab initio data within regularization algorithms.
Lectures
14 double hours.
Exam
Project work with a written report.
Registration
Please contact the course organizers for information.
Literature
1. A.G. Yagola, I.V.Kochikov, G.M.Kuramshina, Yu.A.Pentin. Inverse problems of vibrational spectroscopy. VSP,
Zeist, The Netherlands, 1999. ISBN 90-6764-304-1, p. 1-298
2. I.V.Kochikov, G.M.Kuramshina, A.G.Yagola. Surveys on Mathematics for Industry 8 (1998) 63-94.
3. G.M.Kuramshina, F.A.Weinhold, I.V.Kochikov, Yu.A.Pentin, A.G.Yagola, J. Chem. Phys. 100 (1994). 1414-1424.
4. I.V.Kochikov,G.M.Kuramshina,A.V.Stepanova, Int. J. Quant. Chem. 109 (2009) 28-33.