For what elements does Born–Oppenheimer approximation fail the most?

[Lotto]

TL;DR

We can consider atomic nucleus fixed, so we suppose it doesn't move. But for what elements is Born–Oppenheimer approximation the least accurate (the nucleus moves a "a lot")?

I would say that for the elements with the lowest atomic numbers, because these elements have their nuclei the lightest and so they can move more and their movement influence electrons more than in some heavier elements, whose nuclei move less. Am I right or not?

 

[DrClaude]

I don't understand the question. The BO approximation applies to molecules, not individual atoms, so I don't understand the consideration of elements.

Also, saying that the BO approximation is "nuclei don't move" is an oversimplification (although it is used often in elementary introductions to the subject). It is more that variations of electronic wave functions with respect to nuclear motion are neglected. In many molecules one will find, for example, crossing electronic states where the BO approximation breaks down. See for instance conical intersection.