Dr. Aniruddha Chakraborty

Course Details:

The aim of this course is to provide a theoretical knowledge of fundamental chemistry and to make scientific background stronger for engineering discipline students.

Module 1:  Introduction to Quantum Mechanics

Wave-particle duality, Schrödinger wave equation, operators, probability density, matrix elements of operators & expectation values, one-dimensional problems in quantum mechanics - particle in a box, potential well, potential barrier & tunnelling.

Module 2: Structure & bonding

Hydrogen atom, Helium atom, Hydrogen molecule, structure & bonding, nature of the chemical bond, donor-acceptor complexes, charge transfer, energy transfer, conductance through DNA, molecular electronic circuits, single molecule transistors, single molecule logic gates.

 
Module 3: Spectroscopic Techniques

Born-Oppenheimer approximation, molecular spectroscopy, selection Rules, vibrational & rotational motion, electronic absorption & emission spectroscopy, Raman spectroscopy.

Suggested Books

1. Introductory Quantum Mechanics, R. L. Liboff (4th edition) Addison-Wesley (2002). 

2. Modern Quantum Chemistry, Attila Szabo, Dover (2000).

3. Molecular Spectroscopy, Jeanne L. McHale, Prentice Hall (1998). 

Lectures:



Lecture 1: Introduction to Quantum Mechanics: Historical Review.

Lecture 2: Waves vs. Particles. Observables and operators.

Lecture 3: Measurement in Quantum Mechanics.

Lecture 4: The state function and expectation value.

Lecture 5: Introduction to Hilbert Space.

Lecture 6: Commutator relations in Quantum Mechanics.

Lecture 7: Commutator relations and Uncertainty Principle.

Lecture 8: Conservation of parity.

Lecture 9: Time dependent Schrödinger Equation.

Lecture 10: Time indepedent Schrodinger Equation - stationary states.

Lecture 11: Harmonic oscillator, Eigenvalues, Eigenfunctions.

Lecture 12: Harmonic oscillator in momentum space.

Lecture 13: Bound and unbound states: Morse oscillator.

Lecture 14: One dimensional Barrier Problems.

Lecture 15: The rectangular Barrier: Tunnelling.

Lecture 16: The Ramsauer Effect.

Lectrure 17: Dynamical Tunneling.

Lecture 18: Free particle wave packet.

Lecture 19: Finite and infinite potential well.

Lecture 20: Hydrogen atom.

Lecture 21: Hydrogen molecule: Electronic structure.

Lecture 22: Nature of Chemical Bond.

Lecture 23: Born-Oppenheimer Approximation.

Lecture 24: Potential energy curves/surfaces.

Lecture 25: Eigenstates of Born Oppenheimer Approximated Hamiltonian.

Lecture 26: Introduction to vibrational spectroscopy.

Lecture 27: Introduction to rotational spectroscopy.

Lecture 28: Ro-vibrational spectroscopy.

Lecture 29: Introduction to electronic absorption spectroscopy.

Lecture 30: Raman Spectroscopy.

Lecture 31: Raman vs. Fluorescence vs. Phosphorescence.

Lecture 32: Eigenstates of exact Molecular Hamiltonian.

Lecture 33: Intensity and selction Rules.

Lecture 34: Solvent Effect on spectra.

Lecture 35: Internal rotation: Ethane.

Lecture 36: Internal rotation: inversion of ammonia.

Lecture 37: Donor-Acceptor Complexes.

Lecture 38: Charge Transfer Complexes.

Lecture 39: Single Molecule Transistors.

Lecture 40: Energy Transfer.

Lecture 41: Helium Atom - Two Electron system.

Lecture 42: Structure and Bonding.

Reading Assignment

Molecular Electronics, James R. Heath and Mark A. Ratner. Physics Today, Page - 43, May 2003.

Literature Survey

Topic: Single Molecule Logic Gate.

Few Interesting Questions

1. What is the difference between 'standard' tunnelling and dynamical tunneling ?

2. What is the difference between local modes and normal modes ?

3. What is the difference between dipole moment and transition dipole moment ?

4. Why light-molecule classical interaction is written as the dot product of dipole moment vector and electric field vector?

5. What is coherent state?

6. What is the difference between mechanical an-harmonicity and electrical an-harmonicity ?

7. Can we know one or more tri-atomic/tetra-atomic molecules which have multiple distinct stable geometric structures or isomers ?

8. What is the basic idea behind 'single molecule spectroscopy' ?
9. Can we have an analytical expression of Tunnelling probability for Dirac Delta potential barrier?

10. Why should one study Molecular Electronics ?

11. How can carbon nano tubes be used as memory device ?

12. What are the benefits of using molecular logic gates ?

13. What is molecular switch ?

14. Homo-nuclear diatomic molecule do not show vibrational spectra. Why ?

15. Will the molecule 17 O-16 O show rotational spectrum ? Explain.

16. Diatomic molecules such as HF, HCl and CO show a rotational spectrum whereas N2,O2 and H2 do not. Why ?

17. List the different regions of the electromagnetic spectrum and mention the type of molecular transitions that occur in each region.

18. Why are anti stokes line less intense than stokes line ?

19.The intensity of J=0 -> J=1 is often not the most intense rotational line. Why?

20. How would the vibrational energy spacing of D2 molecule compare with that of H2 molecule?

21. Explain the effect of an-harmonicity on the vibrational spectra of a diatomic molecule.

22. Explain the effect of isotopic substitution on the rotational spectrum of molecules.

23. Why does an atom generally absorb radiation only from the ground state, while a molecule can absorb radiation from many excited rotational or vibrational states?

24. How would the rotational energy spacing of D2 molecule compare with the rotational energy spacing of H2 and their equilibrium bond distances?

25. What parameters can one get from a study of the rotation-vibration spectrum of a hetero-nuclear diatomic molecule? How are they estimated?

26. What is reaction coordinate ?

27.what is the origin of zero point energy ? Can it be measured experimentally ?

28. What is Transition State ? Can it be detected experimentally ?

29. What is Hydrogen bond ?