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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

  • Mathieu LewinEmail author
Original Paper

Abstract.

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

Keywords

Dynamical System Field Theory Transition State Elementary Particle Quantum Field Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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