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Published March 28, 2016 | Published
Journal Article Open

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

Ghaderi, Nima


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 + O_2 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 O_3 will be presented elsewhere.

Additional Information

© 2016 AIP Publishing LLC. Received 13 October 2015; accepted 3 March 2016; published online 29 March 2016. It is a great pleasure and an honor for the author to acknowledge Professor Rudolph A. Marcus for valuable discussions, comments, and noting a great teacher, the incredible erudition and venerable depth ever present. The constructive comments of the anonymous reviewers are also appreciated very much. N.G. would also like to thank Mrs. Monavareh Vojdani (grandmother) for inquiries, stimulating discussions on bimolecular reactions and kind encouragement, with much appreciation imparted.

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August 20, 2023
August 20, 2023