Semiclassical methods for calculating radiative association rate constants for different thermodynamic conditions: Application to formation of CO, CN, and SiN

It is well-known that resonances can serve as a catalyst for molecule formation. Rate constants for resonance-induced molecule formation are phenomenological as they depend upon the mechanism used to populate the resonances. Standard treatments assume tunneling from the continuum is the only available population mechanism, which means long-lived quasibound states are essentially unpopulated. However, if a fast resonance population mechanism exists, the long-lived quasibound states may be populated and give rise to a substantial increase in the molecule formation rate constant. In the present work, we show that the semiclassical formula of Kramers and ter Haar [Bull. Astron. Inst. Neth. 10, 137 (1946)] may be used to compute rate constants for radiative association in the limit of local thermodynamic equilibrium. Comparisons are made with quantum mechanical and standard semiclassical treatments, and results are shown for two limits which provide upper and lower bounds for the six most important radiative association reactions leading to the formation of CO, CN, and SiN. These results may have implications for interstellar chemistry in molecular clouds, where the environmental and thermodynamic conditions often are uncertain.