## Details of CH4102 (Autumn 2018)

 Level: 4 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
CH4102 Molecular Structure and Symmetry Amlan Kusum Roy

Syllabus
Introduction to many electron system: Many electron Hamiltonian, Hartree product, Spin and spatial orbitals, Antisymmetry and Slater determinant, Rules for matrix elements, Exchange and Correlation, Fermi hole and Coulomb hole, Hartree Fock method, Introduction of basis, Self consistency, Restricted and unrestricted Hartree Fock method, Eletctron density and density matrix, Roothaan equation, Pople Nesbet equation, Koopmans & Brillouins theorem, Second quantization, Virial theorem, HellmannFeynman theorem, Electrostatic theorem.

Configuration Interaction: Form of exact wave function and Configuration Interaction, Excited determinant, Structure of Full CI matrix, Truncated CI and size consistency, Potential energy curves.

Mller Plesset Perturbation Theory: Rayleigh Schrodinger Perturbation theory, Orbital perturbation theory, MllerPlesset Perturbation theory, Perturbation expansion of correlation energy.

Coupled Cluster Theory: Basic principles of coupled cluster theory, Cluster expansion many electron wave function

Semiempirical Methods: Hckel, Extended Hckel theory, Other approaches such as CNDO, INDO, MNDO, PPP, PM3.

Group Theory and Point Group: 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.

Representation Theory: 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.

Group Theory and Quantum Mechanics: 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.

References

#### Course Credit Options

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