Spectroscopic signatures of bond-breaking internal rotation. I. Saddle point induced polyad breakdown

With the input of order 10-20 000 cm(-1) of vibrational energy, the hydroge n atoms in small gas-phase molecules such as HCN, HCP, and acetylene can un dergo internal rotation about the heavy-atom core (CN-CP-CC), breaking and reforming covalent bonds in the process. This article investigates the quan tum and classical dynamics of covalent bond-breaking internal rotation, par ticularly the vibrational energy flow between the hindered internal rotor m ode and a stretch mode. The aim is to relate polyad effective Hamiltonian t echniques, which have been highly successful in the analysis of high overto ne spectra, to the theory of isomerization rates. That is, as approximate c onstants of motion, polyad numbers constrain vibrational energy flow, and w e investigate the extent and mechanism of their breakdown due to nascent bo nd-breaking internal rotation. Our simple model consists of a spherical pen dulum coupled to a harmonic oscillator, which admits a number of analytical results. The central conclusion is that polyad breakdown is a generic cons equence of higher order resonances induced by a saddle point but is far fro m complete, in the sense that the majority of states with energies close to the saddle point can continue to be labeled with polyad numbers; only thos e with substantial probability density close to the saddle point itself no longer belong to moderately well defined polyads. Our model is particularly relevant to the vibrational structure of HCP, the polyad structure of whic h has been well studied up to similar to 19 000 cm(-1); our model predicts systematic polyad breaking at higher energies. (C) 2001 American Institute of Physics.