User:Sudip1993

Hello, I am Sudip Chakraborty (সুদীপ চক্রবর্তী in Bengali). This is my user page.

About Me

I am a research scholar at Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Mumbai, India.

Plan of Work

I am going to work on Symmetry of diatomic molecules. There is no separate wikipedia page on it, so I am going to create one. My plan about the page is as following:

• I will start with an introduction, I will give a brief overview of why we want to look into molecular symmetry (because it gives us insights about the properties such as structure and spectra without doing the actual rigorous calculation).
• This will be followed by a section on how symmetry is related to group theory and the idea of point groups.
• Then I will state and describe the 5 kinds of geometrical symmetries (symmetry axis, plane of symmetry, inversion center, rotation-reflection axis, identity) and the corresponding operations (I will also introduce Schoenflies notation).

• Then I will enlist the different kinds of point groups associated with molecular symmetry. I specific, I will discuss in detail the most prominent symmetry groups in diatomic molecules, namely C_∞v(linear) and D_∞h(linear with inversion center). In case of a Homonuclear diatomic molecule, we see both the symmetries and in case of Heteronuclear diatomic molecule, we see only the former one.
• Then I am planning to give a brief description of group representation and irreps (I am not sure about whether this will be relevant for my current reading or not, so there is a possibility that I will not include it).
• Then I would like to include a section on how the symmetry and the corresponding commuting operators differ in diatomic molecules from the atomic case. Here, Hamiltonian does not commute with L² and thus 'l' is no longer a good quantum number. The CSCO in this case is {H, J_z,L_z,S²,S_z,A, Π} (A inverts only one of the spatial co-ordinates).
• Then I would like to discuss about the most general Hamiltonian of a diatomic molecule and Born-Oppenheimer approximation and the 'electronic ket' (or electronic wave function, or the word 'electronic term' used by Landau-Lifshitz).
• Then I would like to probe into the role of symmetry in this electronic structure, and would introduce the molecular term symbol and discuss about Λ-doubling, gerade and ungerade states.
• Now I would like to explore the observable consequence of symmetry in physical observations, i. e., the difference in spectral lines of homonuclear and heteronuclear molecules.

Here, I would like to state the selection rules for the purely vibrational, purely rotational and vibration-rotation (or vibronic) transition for the two kinds of diatomic molecules. It will turn out that in order to show a purely vibrational spectrum, a diatomic molecule must have dipole moment that varies with distance. So, homonuclear molecules don't undergo electric dipole vibrational transitions; it shows, however, vibronic transition spectrum. A heteronuclear molecule shows both the spectra, although it needs to abide by the corresponding selection rules. It turns out that both the vibrational and rotational quantum numbers must change in the transition. So, the so called 'Q' (Δv=(+/-)1, ΔJ=0) branch of rotational spectra is forbidden.

• In the last section, I will discuss the intersection of potential curves for a diatomic molecules and the role of symmetry in it. Here, I would also like to discuss the von Neumann- Wigner non-crossing rule.

- This is my detailed plan till now. It can change depending on my further studies and discussions.

References I will be using

I will be referring the following sources mainly:

1. Quantum Mechanics, Third Edition: Non-Relativistic Theory (Volume 3)by L. D. Landau, L. M. Lifshitz; ISBN-13: 978-0750635394 ISBN-10: 0750635398 Edition: 3rd; chapters: XI and XII.
2. Physics of Atoms & Molecules by B.H. Bransden, C.J. Joachain; ISBN-13: 978-8177582796 ISBN-10: 8177582798 Edition: 2nd edition; chapter:9
3. Molecular Spectra and Molecular Structure: Spectra of Diatomic Molecules by Gerhard Herzberg; ISBN-13: 978-0894642685 ISBN-10: 0894642685 Edition: 2nd
4. Molecular Quantum Mechanics by Peter W. Atkins, Ronald S. Friedman; ISBN-13: 978-0199541423 ISBN-10: 0199541426 Edition: 5th; chapter:10.
5. Lecture notes on Quantum Mechanics (handouts:12,10) by Prof. Sourendu Gupta, Tata Institute of Fundamental Research, Mumbai.
6. Symmetry in Physics: Principles and Simple Applications Volume 1 by James Philip Elliott, P.G. Dawber;ISBN-13: 978-0195204551 ISBN-10: 0195204557.
7. http://www.astro.uwo.ca/~jlandstr/p467/lec5-mol_spect/index.html

Contact Details

Email id : sudip.chakraborty@tifr.res.in