Annales Henri Poincaré

, Volume 7, Issue 2, pp 365–379 | Cite as

Solution of a Mountain Pass Problem for the Isomerization of a Molecule with One Free Atom

Original Paper


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


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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CopenhagenCopenhagen ØDenmark

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