Some aspects of the algebraic description of anharmonic dynamics

Abstract

A formally exact Lie-algebraic description of the dynamics on anharmonic 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 ordering of the boson operators, is shown to correspond to the time dependent generalizations of normal coupled cluster method (NCCM) and the extended coupled cluster method (ECCM). Relative merits of the two approaches are discussed. The NCCM formalism is applied to calculate the O→n vibrational transition probabilities of an exponentially perturbed harmonic oscillator modeling the collinear inelastic collision of He + H₂ system. Good agreement with the basis set expansion approach is obtained with the Lie-algebraic approach showing a better convergence pattern.