Or in other words show that in the Marcus-Levich-Hush theory, electron transfer stops when you approach zero temperature. Mathematica tells me that this is the case but I could not really show it. The problem has the following type:
It is not an apparent l'Hospital application and I do not really know what else to do. Anyway, I believe Mathematica and it is also the thing you'd expect physically.
In the full quantum picture you actually have a non-zero transfer rate even when approaching zero temperature that comes from nuclear tunneling (as was derived here and is reviewed here).
Interestingely it is quite easy to find derivations of this quantum formula. But I did not find much about the semi-classical formula, that is shown above. Only that it is some kind of application of Fermi's golden rule which apparently gives this prefactor for the rate equation.