GUSTAVSONS PROCEDURE AND THE DYNAMICS OF HIGHLY EXCITED VIBRATIONAL-STATES

The well-known Birkhoff-Gustavson canonical perturbation theory has be en used so far to obtain a reasonable approximation of model systems n ear the bottom of the well. It is argued in the present work that Gust avson's calculation procedure is also a powerful tool for the study of the dynamics of highly excited vibrational states, as soon as the req uirement that the transformed Hamiltonians be in Birkhoff's normal for m is dropped. Mathematically, this amounts to modifying the content of Gustavson's null space. Physically, the transformed Hamiltonians are of the single or multiresonance type instead of just trivial Dunham ex pansions, even though no exact resonance condition is fulfilled. This idea is checked against 361 recently calculated levels of HCP up to 22 000 cm(-1) above the bottom of the well and involving up to 30 quanta in the bending degree of freedom. Convergence up to 13th order of per turbation theory and an average absolute error as low as 2.2cm(-1) are reported for a two-resonance Hamiltonian, whereas the Dunham expansio n converges only up to 4th order at an average error of 215 cm(-1). Th e principal advantages of the resonance Hamiltonians compared to the e xact one rely on its remaining good quantum numbers and classical acti on integrals. Discussions of the limitations of the method and of the connections to other canonical perturbation theories, like Van Vleck o r Lie transforms, are also presented. (C) 1998 American Institute of P hysics.