Quantum Chemistry and Group Theory

Paper Code: 
CHY 123
Contact Hours: 
Max. Marks: 

Course Objectives :

The course aims to give the knowledge of principles of quantum mechanics so that the students will be able to apply quantum mechanical principles to solve simple systems. To make students aware of symmetry and group theory so that they will be able to use group theory as a tool to understand bonding.

Course Outcomes (Cos):                                                                              


Learning outcomes (at course level)

Learning and teaching strategies

Assessment Strategies

Paper Code

Paper Title

CHY 123

Quantum Chemistry and Group Theory 

The students will be able to-


CO10-reproduce the concepts of quantum mechanics and solve simple systems using Schrodinger wave equation.

CO11-calculate physical properties for simple systems.

CO12-interpret and apply approximate methods for evaluating wavefunction.

CO13-describe quantum mechanical approach of angular momentum, spin and rules for quantization and evaluate expressions for it.

CO14-discuss bonding in diatomic, triatomic and systems containing double bonds using molecular Orbital theory.

CO15-recognize symmetry elements, symmetry operations, point group in a molecule and construct character table for different point groups.

CO16-reproduce the concept of symmetry adapted linear combinations and apply it for understanding bonding in simple (σ and π) as well as conjugated systems.

Interactive lectures






Reading assignments




Interactive quiz





Written test




Google quiz


Semester end examination


Unit I: 
Introduction to Quantum Mechanical Results

Schrodinger equation, postulates of quantum mechanics, operators, Hamiltonian and Hermitian operator, discussion of solutions of the Schrodinger equation of some model systems:  particle in a box and its extension to 3D box, quantization of energy levels, degeneracy, zero point energy and justification for Heisenberg uncertainty principle, simple harmonic oscillator and its solution using series solution or factorization method, calculation of various average values using ladder operator and recursion relation of Hermite polynomial, rigid rotor, hydrogen atom, radial distribution function of 1s, 2s, 2p, 3s, 3p and 3d orbitals and polar plots, node, nodal plane and nodal sphere.

Unit II: 
Approximate Methods and Angular Momentum

The variation theorem, linear variation principle, perturbation theory (first order and non – degenerate), application of variation method and perturbation theory to helium atom. Ordinary and generalized angular momentum, eigen functions and eigen values for angular momentum operator using ladder operators, spin, antisymmetry and Pauli’s exclusion principle.

Unit III: 
Molecular Orbital Theory

Extension of MO theory to homonuclear and heteronuclear diatomic molecules, qualitative MO theory and its applications to AH2 type molecule, Huckel theory of conjugate systems, bond order and charge density calculations. Applications to ethylene, butadiene, cyclobutadiene, benzene, allyl system and cyclopropenylsystem. Introduction to extended Huckel theory.

Unit IV: 
Symmetry and Group Theory

Symmetry elements and symmetry operations, definition of group and subgroup, conjugacy relation and classes, product of symmetry operations, relation between symmetry elements and symmetry operations, orders of a finite group and its subgroup, point group symmetry, schonfiles symbols, representations of groups by reducible and irreducible representations and relation between them (representation for the Cn, Cnv, Dnh etc. groups to be worked out explicitly), character of a representation, the great orthogonality theorem (without proof) and its importance, character tables of C2v and C3v and their use.

Unit V: 
Applications of Group Theory in Chemistry

Formation of hybrid orbitals: sigma bonding in linear structure (BeCl2), trigonal planar (BF3), tetrahedral (CH4), square pyramid (BrF5) and square planar (XeF4), octahedral and square planar complexes, π bonding in complex compounds: square planar molecule and tetrahedral molecule.

Molecules with delocalized π orbitals, cyclopropenyl system, cyclobutenyl system, cyclopentadienyl system and benzene.

  • Quantum Chemistry; Seventh Edition; I. N. Levine; Pearson Education India, New Delhi, 2016.
  • Introductory Quantum Chemistry; Fourth Edition; A.K. Chandra; Tata McGraw Hill Publishing Company, New Delhi, 2017.
  • Quantum Chemistry Including Molecular Spectroscopy; B.K. Sen; Tata McGraw Hill Publishing Company, New Delhi, 1996.
  • Quantum Chemistry; Fourth Revised Edition;  R.K. Prasad; New Age International (P) Ltd, New Delhi, 2009.
  • Molecular Quantum Mechanics; Fifth Edition; P.W. Atkins and R.S. Friedman; Oxford University Press Club, New York, 2012.
  • Chemical Applications of Group Theory; Student Third Edition, F. A. Cotton; Wiley-India(P) Ltd, New Delhi, 2008.
  • Chemical Applications of Group Theory; Third Edition, F. A. Cotton; John Wiley and Sons, Singapore 2008.
  • Symmetry and Group Theory in Chemistry; Second Edition, S. K. Dogra and H. S. Randhawa; New Academic Science, 2017.
  • Group theory and its Chemical Applications; P. K. Bhattacharya, Himalaya Publishing House, 2014.
  • Symmetry and Spectroscopy of Molecules; RevisedSecond Edition; K. Veera Reddy; New Age Publishers, New Delhi, 2009.
Academic Year: