Bimolecular recombination reactions: K-adiabatic and K-active forms of the bimolecular master equations and analytic solutions

Expressions for a K-adiabatic master equation for a bimolecular recombination rate constant k_rec are derived for a bimolecular reaction forming a complex with a single well or complexes with multiple well, where K is the component of the total angular momentum along the axis of least moment of inertia of the recombination product. The K-active master equation is also considered. The exact analytic solutions, i.e., the K-adiabatic and K-active steady-state population distribution function of reactive complexes, g(EJK) and g(EJ), respectively, are derived for the K-adiabatic and K-active master equation cases using properties of inhomogeneous integral equations (Fredholm type). The solutions accommodate arbitrary intermolecular energy transfer models, e.g., the single exponential, double exponential, Gaussian, step-ladder, and near-singularity models. At the high pressure limit, the k_rec for both the K-adiabatic and K-active master equations reduce, respectively, to the K-adiabatic and K-active bimolecular Rice–Ramsperger–Kassel–Marcus theory (high pressure limit expressions). Ozone and its formation from O + O₂ are known to exhibit an adiabatic K. The ratio of the K-adiabatic to the K-active recombination rate constants for ozone formation at the high pressure limit is calculated to be ∼0.9 at 300 K. Results on the temperature and pressure dependence of the recombination rate constants and populations of O₃ will be presented elsewhere.