Analysis of the highly excited vibrational dynamics of HCP using a high-order Fermi resonance Hamiltonian

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Abstract
Based on an ab initiopotential energy surface, the features of the quantum spectrum of HCP have been recently discussed in terms of the periodic orbits of the exact classical Hamiltonian [J. Chem. Phys. 107, 9818 (1997)]. In particular, it was shown that the abrupt change in the bending character of the states at the lower end of the Fermi polyads, at about 15 000 cm−1 above the origin, can be ascribed to a classical saddle nodebifurcation. The purpose of the present article is to show that the use of a very accurate Fermi resonance Hamiltonian, which was derived very recently from high-order perturbation theory [J. Chem. Phys. 109, 2111 (1998)] can provide a still deeper insight into the highly excited vibrational motion. The principal advantages of the resonance Hamiltonian compared to the exact one rely on the remaining good quantum numbers and classical action integrals, which enable one to consider HCP as a formal one-dimensional system parametrized by the polyad number i and the number v 3 of quanta in the C–H stretching motion. It is shown in this article that all the quantum observations can be interpreted and explained in terms of the positions and bifurcations of the fixed points of this one-dimensional system: the shape of the quantum wave functions depends on the stable elliptic fixed points, whereas the dip in the gap between neighboring quantum levels is governed by the unstable, hyperbolic fixed points. The dependance on v 3 of the bending character of the lowest states in each polyad i is discussed in some detail, whereas the previous work was fundamentally limited to v 3 =0. Moreover, the dependence on i and v 3 of the form of the dip in the distribution of the gap between neighboring levels is given a clear explanation.