1. The significance of group theory for chemistry is that molecules can be categorized
on the basis of their symmetry properties, which allow the prediction of many
2. The process of placing a molecule into a symmetry category involves identifying all
of the lines, points, and planes of symmetry that it possesses; the symmetry categories
the molecules may be assigned to are known as point groups.
3. It allows you to determine that Which vibrational transitions are allowed or
forbidden on the basis of symmetry.
Group Theory and Applications in Chemical Bonding
- Symmetry elements and symmetry
- Determination of point groups of molecules and ions (organic / inorganic / complex) belonging to Cn, Cs, Ci, Cnv, Cnh, C∞v, Dnh, D∞h, Dnd, Td and Oh point
- Symmetry in crystals:32 crystallographic point groups (no derivation), Hermann- Mauguin Screw axis-pitch and fold of screw axis, glide planes, space groups(elementary idea only)
- Mathematical groups :Properties, Abelian groups, cyclic groups, sub groups, similarity transformation ,classes – C2v, C3v and C2h.
- Group multiplication tables (GMTs) – C2v, C3v and C2h, isomorphic
- Matrix representation of elements like E,Cn,Sn,I, σ-matrix representation of point groups like C2v,C3v,C2h,C4v – trace /character, block factored
- Reducible and irreducible representations, standard reduction formula, statement of great orthogonality theorem (GOT). ,construction of character tables for C2v, C2h, C3v and C4v.
- Application in chemical bonding: Projection operator, transformation properties of atomic orbitals, construction of symmetry adapted linear combination of atomic orbitals (SALCs) of C2v, C3v,D3h and C2h
- Application in hybridization, determination of hybridization and hybrid functions in CH4,BF3 and PCl5
- Vibrational mode analysis using group theory taking H2O,NH3 and trans-N2F2 as examples using symmetry coordinates and internal coordinates method, prediction of IR and Raman activity,-rule of mutual exclusion,-redundant modes , out of plane
Unit 1 : Group theory - an introduction
Unit 2: Point groups
Unit 3: Symmetry in crystals
Unit 4 : Mathematical groups
Unit 5: Group Multiplication Table
Unit 6 : Matrix representation of elements
Unit 7 : Reducible and Irreducible representations
Unit 8: Character Table
Unit 9 : Applications of group theory in chemical bonding
Unit 10 : Hybridization
Unit 11: Application of Group Theory in Spectroscopy
- Vibrational mode analysis using group theory taking water, ammonia and trans-N2F2 as examples
- Determination of modes of vibrations in IR and Raman spectra using character tables in tetrahedral complexes
- Determination of modes of vibrations in IR and Raman spectra using character tables in square planar complexes
- Determination of modes of vibrations in IR and Raman spectra using character tables in octahedral complexes