Classical calculations of radiative association in absence of electronic transitions

A formula for the cross section of radiative association where no electronic transitions take place is derived and tested for diatomic molecules. The approach is based on classical mechanics and therefore it is valid for direct, i.e., non-resonant, radiative association. For the formation of carbon monoxide (CO) and the cyano radical (CN), in the X1Σ+ and A1Π states, respectively, the treatment reproduces the baselines of the cross sections obtained using quantum mechanical perturbation theory. The method overestimates the formation cross section of potassium sodide (NaK) by about 8%. For the lower mass diatoms hydrogen fluoride (HF) and deuterium hydride (HD), the formula overestimates the cross sections by 12% and 60%, respectively. The formula can be used alone for estimates of radiative association rate constants, or in combination with Breit-Wigner theory to include resonance contributions.