On the application of canonical perturbation theory to floppy molecules

Canonical perturbation theory (CPT) is a powerful tool in the field of mole cular physics. It consists of a series of coordinate transformations aimed at rewriting the Hamiltonian in a simpler form without modifying the geomet ry of the phase space. The major achievement of CPT is the straightforward derivation of relations between the physically meaningful parameters of pot ential energy surfaces and the coefficients of the so-called effective Hami ltonians. While most of the studies performed up to date deal with surfaces expanded in polynomial series around a single minimum, CPT has also been a pplied to mixed polynomial/trigonometric expansions in the treatment of tor sions. In this latter case, however, the accuracy of CPT has not been verif ied. The goal of this article is to suggest some modifications of the proce dures, which allow for the successful application of CPT to floppy molecule s with several equilibrium positions and nonpolynomial expansions. The leve ls belonging to all the wells or located above the saddle points are satisf actorily reproduced by the perturbative Hamiltonian. More precisely, the vi brational modes are sorted into two categories, namely oscillator-like ones and hindered-rotor-like ones. The application of CPT enables the expressio n of the Hamiltonian in terms of the good quantum numbers and/or classical constants of the motion associated with the oscillator-like modes. The pert urbative Hamiltonian then acts on the reduced dimensional space of the hind ered-rotor-like modes. The validity and accuracy of this approach are teste d on two-dimensional and three-dimensional models mimicking, respectively, nonlinear and linear HCN. (C) 2000 American Institute of Physics. [S0021-96 06(00)00101-X].