J. Phys. Chem. 1988, 92, 7193-7204 7193 Interaction of Molecular Rotation with Large-Amplitude Internal Motions: A Rigid Twister Model of Hydrogen Peroxide Bobby G. Sumpter, Craig C. Martens:.: and Gregory S. Ezra*,$ Department of Chemistry, Baker Laboratory, Cornell University, Ithaca, New York 14853 (Received: March 9, 1988; In Final Form: June 7, 1988) The classical dynamics of interaction between molecular rotation and large-amplitude internal rotation is studied for a rigid twister model of hydrogen peroxide, obtained by assuming an adiabatic separation of the torsional degree of freedom from the remaining 3N - 7 vibrational modes. Use of the Augustin-Miller canonical transformation to express the molecule-fixed components of the total anguler momentum j in terms of the magnitude, j, the component along the body-fixed z axis, k, and x, the angle conjugate to k, results in a two degree of freedom rotation-torsion Hamiltonian, whose phase space structure can be characterized by using surfaces of section. Rigid twister surfaces of section are presented for several values of angular momentum and energy. Quasi-periodic trapping and crossing tori are found, together with regions of large-scale rotation-torsion chaos. The effects of deuteriation and variation of torsional barrier heights on phase space structure are investigated. Removing either the centrifugal or Coriolis coupling terms from the rigid twister Hamiltonian leads to a significantincrease in stochasticity; we infer that there is a cancellation of coupling terms in the full Hamiltonian. I. Introduction The importance of molecular rotation in the dynamics of polyatomic molecules has been illustrated in a number of recent theoretical studies.1*2 Rotation can either increase3-I4 or de- crease'+ the rate and extent of intramolecular vibrational energy transfer. Rates of unimolecular decay and isomerization have been shown to be strongly dependent on the total angular mo- mentum j.lS2I Energy transfer between vibrational and rotational degrees of freedomlm-N has been suggested as an important factor in determining rates of collisionally induced vibrational relaxa- tion,25v26 and is probed in the fluorescence depolarizationz7 and electric deflection2*experiments of McClelland and co-workers. Although the mechanisms responsible for rotational effects are not yet understood in complete detail, it has been established that centrifugal coupling is primarily responsible for extensive rota- tion-vibration energy f10w,12922-23 while Coriolis interaction^^^ provide an additional coupling between vibrational modes not present in the rotationless case.l0*ll Quantum calculations of rotation-vibration states of polyatomic molecules have so far been restricted to states with relatively low angular m o m e n t ~ m , ' ~ - ~ ~ , ~ ~ since the size of the rotation-vibration Hamiltonian matrix increases linearly with j (cf., however, ref 32). Classical and semiclassical methods33 therefore continue to be essential for the study of highly excited rotation-vibration states. Work has been done on the semiclassical quantization of the asymmetric rigid rotor,- the rigid bender$I and the triatomic H20 with inclusion of all three vibrational degrees of f r e e d ~ m . ~ ~ * ~ ~ The classical trajectory method has been widely used to in- vestigate the influence of molecular rotation on the internal dy- namics of polyatomic molecules. The pioneering studies of Bunker3 (see also ref 4) established the activity of rotational degrees of freedom at high internal energies. Parr, Kupperman, and Porter5 showed for several triatomic molecules that rotation can signif- icantly increase the rate of intramolecular energy redistribution. More recently, Clodius and Shirts7 investigated the effect of rotational coupling on intramolecular vibrational energy flow for H20 and D20 and found that rotation can either increase or decrease the amount of bond-bond energy transfer, depending on the relative signs and magnitudes of the various contributions to the 1 : 1 resonant bond-bond coupling. Subsequently, Shirts has studied both the classical and quantum mechanics of rotational decoupling of the local stretch modes in model H208 and HD09 rotating in the plane. Mathematical Sciences Institute Fellow. f Present address: Department of Chemistry, University of Pennsylvania, Alfred P. Sloan Fellow; Camille and Henry Dreyfus Teacher-Scholar. Philadelphia, PA 19104. Rotational effects on resonant interactions of normal modes in rotating molecules have been studied by using classical me- (1) McClelland, G. M.; Nathanson, G. M.; Frederick, J. H.; Farley, F. w. In ExcitedStates; Lim, E. C., Innes, K. 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