A classical algebraic approach to the bend motion of acetylene: the formalism by two coupled cosets

It is shown that the bend Hamiltonian of acetylene of Darling-Dennison bend I, II and vibrational l doubling resonances can be modeled by two coupled su(2) algebras which, in turn, can be expressed in terms of the dynamical v ariables of two coupled SU(2)/U(1) coset spaces in a classical way. For a f ixed total action N-b and vibrational angular momentum l, there is an energ y range associated. The analysis shows that the survival probability of the actions initially stored in the trans mode to cis mode does not depend muc h on N-b. 1 Or the energy which a state possesses. Instead, it is demonstra ted that as N-b is up to 22 and l is small (such as 0) the states in the hi gher energy region possess significantly larger survival probabilities of t his decay. It is also the survival probabilities of these states that are s uppressed considerably by the vibrational angular momentum. This simulation is discussed along with the recent observation by Field's group [M.P. Jaco bson, J.P. O'Brien, R.J. Silbey, R.W. Field, J. Chem. Phys. 109 (1998) 121; M.P. Jacobson, J.P. O'Brien, R.W. Field, J. Chem. Phys. 109 (1998) 3831; M .P. Jacobson, R.J. Silbey, R.W. Field, J. Chem. Phys. 110 (1999) 845] that bend dynamics of acetylene shows anomalously simple behavior and strong, qu asiperiodic oscillators in its survival probability as N-b approaches 22. ( C) 2000 Elsevier Science B.V. All rights reserved.