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*:

**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.**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.**States in quantum mechanics**: Stern-Gerlach experiments and its different variations. States, superposition of states. Statistical nature of quantum measurements.**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.**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.**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.**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.**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.**Atoms in external fields**: Zeeman effect and Stark effect.

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

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