How to calculate a Vibronic Coupling?

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Discussion Overview

The discussion centers on the calculation of vibronic couplings in quantum physics, particularly in relation to their application in understanding absorption spectra of doped crystals. Participants explore the mathematical and theoretical foundations necessary for such calculations, including the Born-Oppenheimer approximation and potential computational methods.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses a desire to learn about calculating vibronic couplings and questions the relevance of the Born-Oppenheimer approximation in this context.
  • Another participant asserts that QED does not aid in calculating vibronic couplings and explains that once electronic wavefunctions are obtained, the coupling can be calculated using a specific matrix element.
  • A participant suggests using quantum chemistry programs like MOLPRO for these calculations and references a classic article on the topic.
  • One participant seeks recommendations for literature that discusses phonon-electron and vibronic couplings in relation to absorption spectra.
  • Another participant shares a resource on vibronic effects in spectra, noting that it is in German, and suggests an English-language book on vibronic interactions in molecules and crystals.

Areas of Agreement / Disagreement

Participants generally agree on the importance of the Born-Oppenheimer approximation for calculating vibronic couplings, but there is no consensus on the role of QED. Multiple viewpoints on the necessary resources and methods for calculation are presented, indicating a lack of resolution on the best approach.

Contextual Notes

Some participants express uncertainty about the definition and implications of vibronic coupling, suggesting that foundational knowledge may be lacking. The discussion also highlights the dependence on specific computational tools and the limitations of available literature.

Who May Find This Useful

This discussion may be useful for students and researchers interested in quantum chemistry, particularly those focusing on vibronic effects and their applications in spectroscopy.

mubashirmansoor
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I am very interested in calculating the vibronic couplings of a particular system quantitatively, but I am very new to Quantum Physics... so I will highly appreciate your guidance on where to start from? What kind of mathematics do I need to learn?

I am quite puzzled because If I have understood correctly, The Born-Oppenheimer approximation of Schrödinger eq can't evaluate the vibronic couplings...!

Is it possible to use QED? does it make the problem simpler?

Thanks in advance.
 
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Dear mubashirmansoor,
no, QED certainly doesn't help here.
Once you have calculated the electronic wavefunctions in Born-Oppenheimer approximation of two electronic states i and j as a function of the nuclear coordinates R you can calculate the vibronic coupling.
Let the states be |i,R\rangle and |j,R\rangle, the coupling matrix element is given as
\langle j,R | \partial /\partial R |i, R\rangle.
This can be done with some quantum chemistry programs like e.g. MOLPRO (at least it was possible some 10 years ago when I last used it).
But probably your main problem is that you don't know what a vibronic coupling is exactly?
A by now classic article on that topic is:
H. Koppel, W. Domcke, L. S. Cederbaum, Multimode Molecular Dynamics Beyond the Born-Oppenheimer Approximation, Advances in Chemical Physics 57, 59 (1984)
 
DrDu said:
Dear mubashirmansoor,
no, QED certainly doesn't help here.
Once you have calculated the electronic wavefunctions in Born-Oppenheimer approximation of two electronic states i and j as a function of the nuclear coordinates R you can calculate the vibronic coupling.
Let the states be |i,R\rangle and |j,R\rangle, the coupling matrix element is given as
\langle j,R | \partial /\partial R |i, R\rangle.
This can be done with some quantum chemistry programs like e.g. MOLPRO (at least it was possible some 10 years ago when I last used it).
But probably your main problem is that you don't know what a vibronic coupling is exactly?
A by now classic article on that topic is:
H. Koppel, W. Domcke, L. S. Cederbaum, Multimode Molecular Dynamics Beyond the Born-Oppenheimer Approximation, Advances in Chemical Physics 57, 59 (1984)

Thanks for the reply DrDu,

I am willing to calculate the phonon-electron & Vibronic couplings so that I can figure out some of the changes in the absorption spectra of doped crystals.

I will highly appreciate if you recommend a book or paper which has done such calculations and applied them on calculations of absorption spectra.

Prosperous Regards,

Mubashir.
 
I learned about vibronic effects in spectra of complexes from Hans Herbert Schmidtke, Quantenchemie. However, it is in German.
You may also try:
I. B. Bersuker, V. Z. Polinger
Vibronic Interactions in Molecules and Crystals
Spinger Series in Chemical Physics, Vol. 49, 1989
 
DrDu said:
I learned about vibronic effects in spectra of complexes from Hans Herbert Schmidtke, Quantenchemie. However, it is in German.
You may also try:
I. B. Bersuker, V. Z. Polinger
Vibronic Interactions in Molecules and Crystals
Spinger Series in Chemical Physics, Vol. 49, 1989


Thanks a lot :)
 

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