The aim of this course is to provide a systematic
treatment of symmetry in chemical systems within the mathematical
framework known as group theory. Once we have classified the
symmetry of a molecule, group theory provides a powerful set of
tools that provide us with considerable insight into many of its
chemical and physical properties. Some applications of group theory
that will be covered in this course include:
Predicting whether a given molecule will be chiral, or polar;
Examining chemical bonding and visualizing molecular orbitals;
Predicting whether a molecule may absorb light of a given
polarisation, and which spectroscopic transitions may be excited if
it does;
Investigating the vibrational motions of the molecule, etc.
Week
Topics
1.
Introduction; Mathematical definition of a group,
Symmetry operations and symmetry elements
2.
Symmetry classification of molecules – point groups,
symmetry and physical properties: Polarity, Chirality
etc.;
3.
Combining symmetry operations: ‘group multiplication’
Review of Matrices, Matrix representations of groups with
examples
4.
Properties of matrix representations: Similarity
transforms, Characters of representations, Irreducible
representations (IR) and symmetry species, character
tables
5.
Reduction of representations: The Great Orthogonality
Theorem; Using the GOT to determine the irreducible
representations spanned by a basis
6.
Symmetry adapted linear combinations, bonding in
polyatomics, constructing molecular orbitals from SALCs,
calculating and solving the orbital energies and expansion
coefficients
7.
Molecular vibrations : determining the number of
vibrational normal modes, determining the symmetries of
molecular motions, Molecular vibrations using internal
coordinates
8.
Spectroscopy –Group theory and molecular electronic
states, electronic transitions in molecules, vibrational
transitions in molecules, Raman scattering. Summary of the
course
Basic knowledge of quantum mechanics would be helpful.
â€˘Â Â â€śChemical Applications of Group Theoryâ€ť by F. A. Cotton; Third Edition, Wiley. â€˘Â Â â€śMolecular Symmetry and Group Theory: A Programmed Introduction to Chemical Applicationsâ€ť by Alan Vincen
NIL
NIL
Important: Please enable javascript in your browser and download Adobe Flash player to view this site
Site Maintained by Web Studio, IIT Madras. Contact Webmaster: nptel@iitm.ac.in