# How to calculate a Vibronic Coupling?

• mubashirmansoor
In summary, to calculate the vibronic couplings of a system quantitatively, you need to be familar with mathematics related to quantum mechanics such as the Born-Oppenheimer approximation. Additionally, you need to be familiar with spectroscopy and the different types of vibronic coupling.f

#### mubashirmansoor

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 schrodinger eq can't evaluate the vibronic couplings...!

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

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)

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

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 :)