SOME ASPECTS OF THE ALGEBRAIC DESCRIPTION OF ANHARMONIC DYNAMICS

A formally exact Lie-algebraic description of the dynamics on anharmon ic potential energy surfaces is developed. The anharmonic hamiltonians belong to infinite dimensional Lie-algebras. Two ways of decomposing the algebras in the boson representation are presented. The evolution operator resulting from these two methods, which differ in the orderin g of the boson operators, is shown to correspond to the time dependent generalizations of normal coupled cluster method (NCCM) and the exten ded coupled cluster method (ECCM). Relative merits of the two approach es are discussed. The NCCM formalism is applied to calculate the 0 --> n vibrational transition probabilities of an exponentially perturbed harmonic oscillator modeling the collinear inelastic collision of He H-2 system. Good agreement with the basis set expansion approach is o btained with the Lie-algebraic approach showing a better convergence p attern.