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 hydrogen atoms in small gas-phase molecules such as HCN, HCP, and acetylene can undergo internal rotation about the heavy-atom core (CN–CP–CC), breaking and reforming covalent bonds in the process. This article investigates the quantum and classical dynamics of covalent bond-breaking internal rotation, particularly the vibrational energy flow between the hindered internal rotor mode and a stretch mode. The aim is to relate polyad effective Hamiltonian techniques, which have been highly successful in the analysis of high overtone spectra, to the theory of isomerization rates. That is, as approximate constants of motion, polyad numbers constrain vibrational energy flow, and we investigate the extent and mechanism of their breakdown due to nascent bond-breaking internal rotation. Our simple model consists of a spherical pendulum coupled to a harmonic oscillator, which admits a number of analytical results. The central conclusion is that polyad breakdown is a generic consequence of higher order resonances induced by a saddle point but is far from 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 those 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 which has been well studied up to ∼19 000 cm−1; our model predicts systematic polyad breaking at higher energies.