ON RESONANCE-TYPE EFFECTIVE VIBRATIONAL HAMILTONIANS FOR CO2 .1. THEORETICAL BACKGROUND

This is the first one of a series of two papers aimed at investigating the relation of resonance-type effective Hamiltonians to molecular po tential energy surfaces for linear ABA triatomic molecules, and more p recisely for CO2. Single-or multi-resonance effective vibrational Hami ltonians are much simpler to handle than the exact one, yet retaining all its essential features, at least in the regular energy range. The relations between these effective Hamiltonians and the exact one will be analysed in some details, particularly in connection with the fit o f force constants to experimentally observed transition frequencies. A nother question, which is also addressed, is that of the underlying co ordinates. Indeed, at least two canonical transformations are needed t o derive the effective Hamiltonians from the exact one using Birkhoff- Gustavson perturbation theory. It will be shown that the differences b etween the two sets of coordinates become small, as soon as a second a ngle phi(1) is added to the Fermi resonance phi(1) + 2 phi(2) dependen ce. The theoretical background for this study, namely the expansion of the exact expression for kinetic energy up to fifth order in dimensio nless coordinates and fourth-order Birkhoff-Gustavson perturbation the ory, is to be found in this first paper, whereas the second one is dev oted to explicit numerical results for CO2. (C) 1997 Elsevier Science B.V.