# How to calculate a Vibronic Coupling?

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?

Thanks in advance.

## Answers and Replies

DrDu
Science Advisor
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.

DrDu
Science Advisor
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 :)