## Details of ID4205 (Spring 2017)

Level: 4 |
Type: Theory |
Credits: 3.0 |

Course Code | Course Name | Instructor(s) |
---|---|---|

ID4205 |
Symmetry in Chemistry |
Amlan Kusum Roy |

Syllabus |
---|

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. |

References |
---|

References:
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. | Programme | Semester No | Course 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 |