Quantum Chemistry and Group Theory

Paper Code: 
24DCHY803
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to

gain the knowledge of principles of quantum mechanics so that the students will be able to apply quantum mechanical principles to solve simple systems and make students aware of symmetry and group theory.

 

Course Outcomes: 

Course

Learning Outcome

(at course level)

Learning and Teaching Strategies

Assessment Strategies

Course Code

Course

Title

 

24DCHY 803

 

Quantum Chemistry and Group Theory

(Theory)

CO143: Develop the understanding of quantum mechanics and solve simple systems using Schrodinger wave equation and calculate physical properties.

CO144: Interpret and apply schrodinger wave equation for hydrogen atom and describe approximate methods for evaluating wavefunction. and

CO145: Describe angular momentum operator and

apply the quantum mechanical approach for chemical bonding.

CO146: Recognize symmetry elements, symmetry operations, point group in a molecule and construct character table for different point groups.

CO147: Reproduce the concept of symmetry adapted linear combinations and apply it for understanding bonding (σ and π).

CO148: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive lectures, tutorials, group discussions and e-learning.

 

 

Learning activities for the students:

Peer learning, e- learning, problem solving through tutorials and group discussions.

 

 

Written examinations,

assignments and quiz.

 

 

13.00
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 and factorization method, calculation of various average values using ladder operator and recursion relation of Hermite polynomial, rigid rotor.

 

11.00
Unit II: 
Approximate Methods and Angular Momentum

Hydrogen atom, radial distribution function of 1s, 2s, 2p, 3s, 3p and 3d orbitals and polar plots, node, nodal plane and nodal sphere.

The variation theorem, linear variation principle, perturbation theory (first order and non – degenerate), application of variation method and perturbation theory to helium atom.

11.00
Unit III: 
Molecular Orbital Theory

Ordinary and generalized angular momentum, eigen functions and eigen values for angular momentum operator using ladder operators, spin, antisymmetry and Pauli’s exclusion principle.

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

 

14.00
Unit IV: 
Symmetry and Group Theory

Symmetry elements and symmetry operations, 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.

 

11.00
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.

 

Essential Readings: 
  1. Quantum Chemistry, Fourth Revised Edition; R.K. Prasad; New Age International (P) Ltd, New Delhi, 2009.
  2. Chemical Applications of Group Theory, Third Edition; F. A. Cotton; John Wiley and Sons, Singapore 2008.
  3. Group theory and its Chemical Applications, P. K. Bhattacharya; Himalaya Publishing House, 2014.

 

References: 
  1. Quantum Chemistry, Seventh Edition; I. N. Levine; Pearson Education India, New Delhi, 2016.
  2. Introductory Quantum Chemistry, Fourth Edition; A.K. Chandra; Tata McGraw Hill Publishing Company, New Delhi, 2017.
  3. Molecular Quantum Mechanics, Fifth Edition; P.W. Atkins and R.S. Friedman; Oxford University Press Club, New York, 2012.
  4. Symmetry and Group Theory in Chemistry, Second Edition, S. K. Dogra and H. S. Randhawa; New Academic Science, 2017.
  5. Symmetry and Spectroscopy of Molecules, Revised Second Edition; K. Veera Reddy; New Age Publishers, New Delhi, 2009.

 

e-Resources:

  1. https://epgp.inflibnet.ac.in/Home/ViewSubject?catid=13G8VouhmrFfuhs6rkiyTA== (Unit I)
  2. https://nptel.ac.in/courses/104101124 (Unit I, II and III)
  3. https://global.oup.com/uk/orc/chemistry/mqm5e/01student/solutions/ (Unit I, II)
  4. https://nptel.ac.in/courses/104104080    (Unit IV and V)
  5. https://nptel.ac.in/courses/104101094     (Unit IV and V)
  6. https://symotter.org/  (Unit IV)

 

Academic Year: 
2024-2025
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