Periodic Orbits as a Probe to Reveal Exotic States in Vibrationally Excited Molecules: The Saddle-Node States

We present theoretical results which show the existence of isomerizing localized quantum states above potential barriers for the excited 1B2 states of SO2 and O3. These states are assigned by periodic orbits which emerge from saddle-node bifurcations, the characteristic of which is the simultaneous generation of two families of periodic orbits one stable and one unstable. Similar isomerizing states and bifurcations have been found for other molecules, and this leads to the conclusion, that the appearance of saddle-node type states may be a generic phenomenon for molecular potentials with barriers.

Über der Kopplung von Schwingungsfreiheitsgraden an die Koordinate intramolekularer Umlagerungen / Coupling of Vibrational Degrees of Freedom lo the Coordinate of Intramolecular Rearrangements

Intramolecular rearrangements A ⇌ B are investigated, which can be described in terms of the motion of an effective quantum mechanical ‘‘particle’’ on an energy surface with at least two minima. We regard the energy surface as a function of a limited number of relevant internal degrees of freedom. The rate of isomerization is calculated from the matrix elements of a transition operator W with respect to the localized quantum states of the two isomers, and the coupling to the inter- and intramolecular degrees of freedom, not explizitely considered in the energy surface. It is shown that the matrixelements of W be reduced to integrals over functions of the adiabatic reaction coordinate of the isomerization, and selection rules for the vibrational quantum numbers for the motion perpendicular to this coordinate. The degrees of freedom not relevant for the reaction are summarily taken into account by introducing a heath bath in thermodynamic equilibrium and a simple damping term. Applications are discussed.