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Indian Institute of Science Education and Research Berhampur

Chemistry

CHM 322: Principles of Quantum Chemistry (4)

Pre-requisites :MTH 101, PHY 101, CHM 101, MTH 102, PHY 102, MTH 201, PHY 201 or their equivalent (Not allowed for Physics majors)

Learning Objectives:

This course will give basic conceptual understanding and application of quantum mechanics to simple atomic and molecular systems, and prepare the students for learning more in-depth quantum chemistry.

Course Contents:

  1. A brief review of classical mechanics:  Newton’s laws of motions – kinetic energy and potential energy, conservative force. Generalized coordinates. Lagrange’s equations of motions. Hamilton’s equations of motions. Poisson brackets.
  2. The need for quantum mechanics: Review of early experiments and old quantum theory: Black-body radiation, photoelectric effect, line spectra of atoms and Bohr model of hydrogen atom, Compton effect, Frank-Hertz experiment. Young’s double-slit experiment and wave-particle duality. de Broglie wavelength, uncertainty principle, superposition and state of a quantum system.
  3. States in quantum mechanics: Stern-Gerlach experiments and its different variations. States, superposition of states. Statistical nature of quantum measurements.
  4. Postulates of quantum mechanics: States and wavefunctions, Time-dependent Schrödinger equation. Observables and the measurement hypothesis, Born’s interpretation of wavefunction, time evolution of states, stationary states, time-independent Schrödinger equation. Heisenberg’s equation of motion and Ehrenfest’s relations.
  5. Mathematical background: Operators in quantum mechanics and their properties, eigenvalues and eigenfunctions, commutation relations, unitary transformations and change of basis. Matrix representation of operators. Compatible observables and the generalized uncertainty principle.
  6. One-dimensional problems: A free particle, particle in a well and transmission through a barrier. Probability currents and the equation of continuity. Two and three-dimensional potential wells and degeneracy. Applications to conjugated molecules and other one-dimensional systems. Linear harmonic oscillator – ladder operator method, parity of harmonic oscillator eigenfunctions. Rigid rotor problem, angular momentum, angular momentum eigenvalues and eigenfunctions.
  7. The hydrogen atom: Atomic orbitals – radial and angular wavefunctions and distributions, electron-spin and spin operators. Virial theorem and application to hydrogen atom and other problems. Hydrogen-like atoms.
  8. Approximation methods: Variation method – He atom,Time-independent perturbation theory – Anharmonic oscillator, He atom, H 2 + molecular ion. H 2 molecule and the LCAO approach. Time-dependent perturbation theory, Fermi’s golden rule, transition probability and the basis of selection rules.
  9. Atoms in external fields: Zeeman effect and Stark effect.
Suggested Books:

  1. Pilar, F. L., Elementary Quantum Chemistry, 2nd ed., McGraw-Hill, New York, 1990.
  2. Sannigrahi, A. B., Quantum Chemistry, 2nd ed., Books & Allied, Kolkata, 2020.
  3. Levine, I., Quantum Chemistry, 6th ed., Pearson Press, 2009.
  4. McQuarrie, D. A., Quantum Chemistry, 2nd ed, University Science Books, 2008.
  5. Pauling, L., Wilson, E. B., Introduction to Quantum Mechanics, McGraw-Hill, New York, 1935.
  6. Atkins, P. W., Friedman, R. S., Molecular Quantum Mechanics, Oxford University Press, 2008.
  7. Eyring, H., Walter, J., and Kimball, G. E., Quantum Chemistry, John Wiley, New York, 1944.
  8. Zettili, N., Quantum Mechanics, 2nd ed., John Wiley, 2009.
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