Solution of a mountain pass problem for the isomerization of a molecule with one free atom

In this paper, we continue the mathematical study of adiabatic chemical reactions, started in a previous work (Ann. Henri Poincarè 5, 477-521, 2004). We consider a molecule with one free atom, the latter having two distinct possible stable positions. We then look for a mountain pass point between these two local minima in the non-relativistic Schrödinger framework. We prove the existence of a mountain pass point without any assumption on the molecules at infinity, improving our previous results for this model. This critical point is interpreted as a transition state in Quantum Chemistry. Communicated by Rafael D. Benguria.