Solid state and Quantum chemistry (CUNT2473)

Credit:  (3-0-1) (T-P-Pro)

Course objective

• To have sound knowledge on concepts of quantum chemistry.
• To understand the structure bonding in solids and their mechanical behavior.
• To have sound understanding on structure of atom and quantum mechanical treatment of various type of bondings.

Course Outcomes

Module I :Solid state: Crystal structures; Bragg’s law and applications; band structure of solids.  Chemistry in nanoscience and technology. Crystal systems and lattices, Miller planes, crystal packing, crystal defects, ionic crystals, structures of AX, AX₂, ABX₃ type compounds, spinels, band theory, metals and semiconductors.   (4 hours)

Module II: Basic principles of quantum mechanics: Postulates of quantum mechanics; operator algebra; exactly- solvable systems: particle-in-a-box, Schrodinger equation and discussion of solutions of the Schrodinger equation to some model systems viz., particle in a box.                                                                                                            (4 hours)

Module III:Harmonic oscillator and the hydrogen atom, including shapes of atomic orbitals;                                                                                                   (4 hours)

Module IV: Orbital and spin angular momenta; tunneling, Angular Momentum Ordinary angular momentum, generalized angular momentum, eigenfunctions for angular momentum, eigenvalues of angular momentum, operator using ladder operators, addition of angular moments, spin, antisymmetry and Pauli exclusion principle. (4 hours)

Module V:Approximate methods of quantum mechanics: Variational principle; perturbation theory up to second order in energy, The variation theorem, linear variation principle. Perturbation theory (first order and nondegenerate). Applications of variation method and perturbation theory to the Helium atom.                (4 hours)

Module VI: Atomic structure and spectroscopy; term symbols; many-electron systems and antisymmetry principle.                                                                        (4 hours)

Module VII:Chemical bonding in diatomics; elementary concepts of MO and VB theories; Huckel theory for conjugated n-electron systems:Huckel theory of conjugated systems, bond order and charge density calculations. Applications to ethylene, butadiene, cyclopropenyl radical, cyclobutadiene etc.

Data analysis: Mean and standard deviation; absolute and relative errors; linear regression; covariance and correlation coefficient.                                                 (6 hours)

Project:

Students shall have to complete a given project related to the domain topics and submit report.

Session-1

Crystal structures; Bragg’s law and applications; band structure of solids.

https://www.youtube.com/watch?v=wEeh7WR8eEI&t=622s

Session-2

Chemistry in nanoscience and technology.

https://www.youtube.com/watch?v=Rw0RhqJFh88&t=7s

Session-3

Crystal systems and lattices, Miller planes, crystal packing, crystal defects, ionic crystals, structures of AX, AX₂, ABX₃ type compounds

https://www.youtube.com/watch?v=nUVuKSnA_gM

https://www.youtube.com/watch?v=kJOHeT4vDSc&t=10s

Session-4

Band theory, metals and semiconductors

https://www.youtube.com/watch?v=Bys9AiSGl4s

Session-5

Postulates of quantum mechanics; operator algebra; exactly- solvable systems

https://www.youtube.com/watch?v=R63K_2NHCSk&list=PLYXnZUqtB3K9w5avEWjezmZta00q9XROh

https://www.youtube.com/watch?v=nnenqcKkwRc

Session-6

Particle-in-a-box, Schrodinger equation

https://www.youtube.com/watch?v=Htf7crlCeSw

Session-7

Discussion of solutions of the Schrodinger equation to some model systems viz., particle in a box.

https://www.youtube.com/watch?v=uPvWlwOhCTo

Session-8

discussion of solutions of the Schrodinger equation to some model systems viz., particle in a box.

https://www.youtube.com/watch?v=TAEfk22RAZo

Session-9

Harmonic oscillator