Vibrational energy transfer rates using a forced harmonic oscillator model

This paper addresses the analysis, validation, and application of analytic, nonperturbative, semiclassical vibration-translation (V-T) and vibration-vibration-translation (V-V-T) rate models for atom-diatom and diatom-diatom vibrational molecular energy transfer collisions. These forced harmonic oscillator (FHO) rate models are corrected and validated by comparison with recent experiments, and with three-dimensional semiclassical trajectory calculations for N-2-N-2, O-2-O-2, and N-2-O-2, which are considered to be the most reliable theoretical data available. A remarkably good overall agreement is shown for both the temperature and quantum number dependence of single-quantum and double-quantum V-V-T transitions in the temperature range 200 less than or equal to T less than or equal to 8000 K and for vibrational quantum numbers 0 less than or equal to upsilon less than or equal to 40. It is demonstrated that the multiquantum vibrational energy transfer processes occur via a sequential FHO mechanism, as a series of virtual single-quantum steps during one collision. An important exception, asymmetric multiquantum V-V exchange at low temperatures, that occurs via a direct first-order mechanism, is discussed. Analytic thermally averaged FHO V-T and V-V rates are suggested. The FHO model gives new insight into vibrational kinetics and may be easily incorporated into kinetic modeling calculations under conditions when first-order theories are not applicable.