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Abstract

Bifurcations of equilibrium points and periodic orbits are common in nonlinear dynamical systems when some parameters change. The vibrational motions of a molecule are nonlinear, and the bifurcation phenomena are seen in spectroscopy and chemical reactions. Bifurcations may lead to energy localization in specific bonds, and thus, they have important consequences for elementary chemical reactions, such as isomerization and dissociation/association. In this article we investigate how elementary bifurcations, such as saddle-node and pitchfork bifurcations, appear in small molecules and show their manifestations in the quantum mechanical frequencies and in the topology of wave functions. We present the results of classical and quantum mechanical calculations on a new (diabatic) potential energy surface of ozone for the ¹B₂ state. This excited electronic state of ozone is pertinent for the absorption of the harmful UV radiation from the sun. We demonstrate that regular localized overtone states, which extend from the bottom of the well up to the dissociation or isomerization barrier, are associated with families of periodic orbits emanated from elementary bifurcations.