Molecular Reaction Pathways and Elementary Bifurcation Tracks of Periodic Orbits

Stavros C. Farantos

Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, and
Department of Chemistry, University of Crete, Iraklion, Crete, Greece

The Molecular Potential Energy Surface (PES) is the common foundation of quantum and classical Chemical Dynamics. The next fundamental concept it turns out to be the Periodic Solutions of the classical equations of motions. At the semiclassical approximation a correspondence between Periodic Orbits (POs) and quantum density of states or even individual eigenstates can be established. For several years and with a lot of collaborators we have systematically studied the families of periodic orbits which emanate from the equilibrium points of the PES for a variety of molecules, triatomic [1-5] and tetratomic [6], and at energies below and above dissociation. These studies, reveal the importance of elementary bifurcations (particularly the saddle-node (SN)) for isomerization and dissociation reactions. Periodic orbits which emerge from SN bifurcations appear abruptly at some critical value of the energy and penetrate in regions of nuclear phase space where the normal mode motions can not reach. Saddle-node bifurcations are of generic type, i.e. they are robust and remain for small (perturbative) changes of the potential function. The spectroscopic signature of SN bifurcations has been found for a few triatomic molecules [3,4].


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