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 levels obtained from diagonalization of the full Hamiltonian, which is based on a newly calculated potential-energysurface with near spectroscopic accuracy. It is demonstrated that all features characteristic of the approach to the HCP↔CPH isomerization, such as the strong mixing between the bending and CP-stretching motions, the appearance of “isomerization states” (large amplitude bending motion) at intermediate energies, and the diagnostically significant appearance of a zig–zag pattern in the energy spacings between neighboring levels within each polyad, are quantitatively reproduced by the effective Hamiltonian. The semiclassical analysis of the model Hamiltonian for specific combinations of the HC-stretch and polyad quantum numbers explains all of the observed features of the full Hamiltonian in terms of stable and unstable periodic orbits. In particular, the birth of the isomerization states is found to be related to a saddle-node bifurcation of the classical phase space. The connection with the “polyad phase sphere” representation of quantum polyads is also discussed.

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