I am confused with a couple of terms usually used in the context of non-radiative transitions. I believe that I understand the concept of diabatic and adiabatic states described in(adsbygoogle = window.adsbygoogle || []).push({});

http://en.wikipedia.org/wiki/Adiabatic_theorem. The basic finding is that the coupling terms in the Hamiltonian matrix (in the basis of the diabatic states) result in an avoided crossing.

I want to transfer this finding to the case of the Born-Oppenheimer approximation, which is said to break down in the region around a level-crossing. And this is actually the point where I come across my first problem. When neglecting the first and the off-diagonal elements (closely related to the non-adiabacity operator), do I get diabatic states (case A) or adiabatic states (case B)?

If the case A is valid, the situation as depicted below would seem logical.

Here we face a level crossing, which is regarded as the breakdown of the Born-Oppenheimer approximation. As soon as the off-diagonals elements taken into account again, the avoided crossing would be obtained then.

But from my literature search I get the impression that Born-Oppenheimer approximation leads to adiabatic states. But what is the breakdown of the Born-Oppenheimer approximation then? And what are the non-adiabatic transitions resulting from the non-adiabacity operator in the last figure?

I hope anybody can resolve my problems with this stuff!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Born-Oppenheimer approximation

**Physics Forums | Science Articles, Homework Help, Discussion**