Semiclassical study of the isomerization states of HCP

The vibrational spectrum of HCP (phosphaethyne) is studied and analyzed in terms of a 1:2 resonance effective Hamiltonian. The parameters of the model Hamiltonian are determined by fitting 361 out of the first 370 energy leve ls obtained from diagonalization of the full Hamiltonian, which is based on a newly calculated potential-energy surface with near spectroscopic accura cy. It is demonstrated that all features characteristic of the approach to the HCP <----> CPH isomerization, such as the strong mixing between the ben ding and CP-stretching motions, the appearance of "isomerization states" (l arge amplitude bending motion) at intermediate energies, and the diagnostic ally significant appearance of a zig-zag pattern in the energy spacings bet ween neighboring levels within each polyad, are quantitatively reproduced b y the effective Hamiltonian. The semiclassical analysis of the model Hamilt onian for specific combinations of the HC-stretch and polyad quantum number s explains all of the observed features of the full Hamiltonian in terms of stable and unstable periodic orbits. In particular, the birth of the isome rization states is found to be related to a saddle-node bifurcation of the classical phase space. The connection with the "polyad phase sphere" repres entation of quantum polyads is also discussed. (C) 2000 American Institute of Physics. [S0021-9606(00)00809-6].