  We study isomerizations in quantum mechanics. We consider a neutral molecule
composed of N quantum electrons and M classical nuclei and assume that the
first eigenvalue of the corresponding N-particle Schr\"odinger operator
possesses two local minima with respect to the locations of the nuclei. An
isomerization is a mountain pass problem between these two local
configurations, where one minimizes over all possible paths the highest value
of the energy along the paths. Here we state a conjecture about the compactness
of min-maxing sequences of such paths, which we then partly solve in the
particular case of a molecule composed of two rigid sub-molecules that can move
freely in space. More precisely, under appropriate assumptions on the
multipoles of the two molecules, we are able to prove that the distance between
them stays bounded during the whole chemical reaction. We obtain a critical
point at the mountain pass level, which is called a transition state in
chemistry. Our method requires to study the critical points and the Morse
indices of the classical multipole interactions, as well as to improve existing
results about the van der Waals force. This paper generalizes previous works by
the second author in several directions.
