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

Abstract

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 variables of two coupled SU(2)/U(1) coset spaces in a classical way. For a fixed total action N b and vibrational angular momentum l, there is an energy range associated. The analysis shows that the survival probability of the actions initially stored in the trans mode to cis mode does not depend much on N b, l or the energy which a state possesses. Instead, it is demonstrated that as N b is up to 22 and l is small (such as 0) the states in the higher energy region possess significantly larger survival probabilities of this decay. It is also the survival probabilities of these states that are suppressed considerably by the vibrational angular momentum. This simulation is discussed along with the recent observation by Field's group [M.P. Jacobson, 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, quasiperiodic oscillators in its survival probability as N b approaches 22.