QUANTUM MECHANICS

Paper Code: 
CHY 513
Credits: 
3
Contact Hours: 
45.00
Max. Marks: 
100.00
Objective: 

Course Objective(s):

This course will enable the students to –

  • understand the limitations of classical mechanics and the need of quantum chemistry, familiarize them with postulates of quantum chemistry and apply the same to derive equations for various models and understand bonding.
  • understand basic concepts and applications of computational chemistry.

Course Outcomes (COs):

Course Outcomes

 

Teaching Learning Strategies

Assessment

Strategies

  
 

On completion of this course, the students will be able to-

CO140: develop an understanding of quantum mechanical operators, concept of quantization, probability distribution.

CO141: setup and solve Schrodinger equation for simple systems such as the one electron system, harmonic oscillator, and rigid rotor.

CO142: interpret the physical form of orbitals from their mathematical descriptions.

CO143: normalize simple wave function and calculate average physical property for system like energy, momentum etc.

CO144: describe chemical bonding theories in quantum mechanical approach.

CO145: know the concept of computational chemistry.
  • Interactive lectures
  • Demonstrations
  • Discussions
  • Tutorials
  • Problem solving exercise

 
  • Quiz
  • Open book tests
  • Assignment
  • Group activity

 

 

 

  

 

9.00
Unit I: 
Basic Quantum Chemistry

Black-body radiation, Planck’s radiation law, photoelectric effect, heat capacity of solids, Bohr’s model of hydrogen atom (no derivation) and its defects, Compton effect, de Broglie hypothesis, Heisenberg’s uncertainty principle.
Theory of Wave motion- classical waves and wave equation, stationary waves and nodes, Schrodinger equation, wave function and its physical meaning, condition of normalisation and orthogonality, quantum mechanical operators, eigen values and eigen functions, basic postulates of quantum mechanics.

 

9.00
Unit II: 
Quantum approach for Translational, Vibrational & Rotational Motion

Application of Schrodinger equation to free particle and particle in a box (rigorous treatment), one dimensional box, quantization of energy levels, zero-point energy and justification for Heisenberg uncertainty principle, extension to three dimensional boxes, degeneracy, wave functions, probability distribution functions, nodal properties,
Simple harmonic oscillator model of vibrational motion- classical treatment and quantum mechanical treatment, setting up of Schrodinger equation and discussion of solution and wave functions, comparison of classical and quantum mechanical results.
Rigid rotator model of rotation of diatomic molecule.

 

9.00
Unit III: 
Quantum approach for Hydrogen Atom

Schrodinger equation, transformation to spherical polar coordinates, separation of variables, qualitative treatment of hydrogen atom and hydrogen like ions- setting up of Schrodinger equation in spherical polar coordinates, radial part, quantization of energy (only final energy expression), radial distribution functions of 1s, 2s, 2p, 3s, 3p and 3d orbitals and polar plots of their shapes.

 

9.00
Unit IV: 
Quantum approach for Bonding

Covalent bonding, valence bond and molecular orbital approaches, LCAO-MO treatment of H2+, calculation of energy levels from wave functions, physical picture of bonding and antibonding wave functions, qualitative extension to H2, comparison of LCAO-MO and VB treatments of H2 (only wave functions, detailed solution not required) and their limitations, hybrid orbitals- sp, sp2, sp3, calculation of coefficients of AO’s used in these hybrid orbitals.
Qualitative description of LCAO-MO treatment of homonuclear and heteronuclear diatomic molecules (HF, LiH), qualitative MO theory and its application to AH2 type molecules, simple Huckel molecular orbital (HMO) theory and its application to simple polyenes (ethene, butadiene).

 

9.00
Unit V: 
An Introduction to Computational Chemistry

An overview of computational chemistry, Hartree-Fock theory, molecular mechanics, electronic structure method, semi-empirical, ab initio and density functional methods, principle of model chemistry, desirable features of a model chemistry.

 

Essential Readings: 
  • Quantum Chemistry, Fourth Edition; R.K. Prasad; New Age International (P) Ltd, New Delhi, 2015.
  • Exploring Chemistry with Electronic Structure Methods; J. B. Frishman and A. Frisel; Gaussian, Inc. Pittsburge, PA.

 

References: 

 SUGGESTED READINGS:

  • Molecular Quantum Mechanics, Fifth Edition; P.W. Atkins, and R.S. Friedman; Oxford University Press Club, New York, 2012.
  • Introductory Quantum Chemistry, Fourth Edition; A. K. Chandra; Tata McGraw-Hill, 2017.
  • Atoms, Molecules and Spectrum; S. K. Dogra and H. S. Randhawa; New Age International (P) Ltd, New Delhi, 2011.
  • Quantum Chemistry, Seventh Edition; Ira N. Levine; Pearson Education India, New Delhi, 2014.
  • Physical Chemistry- A Molecular Approach, First South Asian Edition; D. A. McQuarrie and J. D. Simon; Viva Books, India, 2015.

e-RESOURCES:

Academic Year: 
2022-2023
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