NONLINEAR DYNAMICS OF TORSION-ROTATION INTERACTIONS - A MODEL STUDY OF TOLUENE

The internal rotation, or torsion, of a methyl group has been implicat ed in the acceleration of intramolecular vibrational redistribution (I VR) in numerous experimental studies. In the present work, we investig ate its interaction with overall molecular rotation. To isolate the ef fects of torsion-rotation coupling, a simple two-degree-of-freedom mod el, including only torsion and three-dimensional rotation, is construc ted and its dynamics at j=45 for several energies are studied. Investi gation of other values of angular momentum indicate that the results r eported are largely independent of j. Two primary effects are observed : (i) a shifting of the stable and unstable axes of rotation due to fr ee methyl torsion, and (ii) a limited degree of weakly chaotic dynamic s for trajectories whose torsional energy is near the top of its barri er. Chaos is first observed at the lowest energy at which torsion can surmount its barrier, but then disappears from the system at higher en ergies. Model toluene exhibits only narrow, high-order nonlinear reson ances due to the frequency disparity between torsion and rotation, and these resonances are reduced in number by ''selection rules'' that ar ise in part from the symmetry of the Hamiltonian. These observations a re analyzed in depth and simple, but quantitative, models are proposed to explain the magnitude of the rotational axis shift, the limited ex tent of chaos, and the resonance selection rules. (C) 1997 American In stitute of Physics. [S0021-9606(97)03341-2].