Details of ID4205 (Spring 2017)

Level: 4 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
ID4205 Symmetry in Chemistry Amlan Kusum Roy

Symmetry element, operator and associated algebra; Rotation, reflection, inversion, roto-reflection operation; Product of operations; Equivalent atom; Optical isomerism, dipole moment.

Group postulates; Closure, association, combination, identity, inversion; Multiplication table; Similarity transformation; Subgroup, coset, class, conjugate; Permutation group, simple group, semi-simple group, color (magnetic) group, point group, space group; generating elements of a group; direct product of groups.
Elementary theory of representation of group; Transformation of function and operator; Matrix representation of operators; Representation on position vector, basis vector, atom vector, function space and direct product function space; Invariant subspace; Equivalent, reducible and irreducible representation; Unitary representation; Character table; Notation for character table of point groups; Complex character and cyclic group; Grand orthogonality theorem; Reduction of reducible representation; Group-subgroup relation, descent and ascent in symmetry, correlation table; Representation of groups with infinite order.Operators in function space; Invariance of Hamiltonian operator under; Wave functions as bases for IRREPs; Using operators with direct products; Identifying non-zero matrix elements; Setting up symmetry-adapted linear combinations; Deriving and using projection operators to construct SALCs.LCAO-MO approximation; Factoring of secular equation; -electron approximation (carbonate ion, trans-butadiene, cyclobutadiene, etc.), -MOs of carbocyclic systems (e.g., benzene, naphthalene); Hckel MO theory.
Transformation properties of AOs; Hybrid orbitals for and bonding systems; Homo-nuclear and hetero-nuclear diatomics (second-row atoms); SALCs of AHn (A=second-row element); SALCs for -bonding in ABn (e.g. BrF5); SALCs for -bonding in ABn (e.g., CO2, SF6).

Electronic structure of free ions, term symbols, R-S coupling; Splitting of levels and terms in a
chemical environment (octahedral, tetrahedral, square planar, trigonal bipyramid, etc); Construction of energy-level diagram; Strong and weak field; Correlation diagram in Oh, Td symmetry, holes in d orbitals; MO of -donor complex, Complexes containing ligands of ? symmetry; Jahn-Teller distortion and other crystal fields. Normal modes of vibration and their symmetry; selection rules in IR and Raman spectroscopy; General approach to analyzing vibrational spectroscopy; Rules of mutual exclusion; SALCs, Projection operator
Electron spin; Electronic transition among degenerate states; Electron transition in transition-metal
complexes; Selection rule for single-photon and two-photon spectroscopy; Forbidden transition; Magnetic dipole selection rules.

1. Symmetry and Structure, by S. F. A. Kettle, JohnWiley & Sons. NY.
2. Molecular Symmetry and Group Theory, by R. L. Carter, JohnWiley & Sons. NY.
3. Molecular Symmetry, by D. J. Willock, JohnWiley & Sons. NY.
4. Chemical Applications of Group Theory, by F. A. Cotton, JohnWiley & Sons. NY.
5. Group Theory and Chemistry, by D. M. Bishop, Dover Publication. NY.
6. Symmetry and Group Theory in Chemistry, by M. Ladd, Horwood Publishing. Chichester.

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 2 Not Allowed
2 IP 4 Elective
3 IP 6 Not Allowed
4 MR 2 Not Allowed
5 MR 4 Not Allowed
6 MS 8 Elective
7 RS 1 Elective
8 RS 2 Elective