Publication Date:
2016-03-30
Description:
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.
Print ISSN:
0021-9606
Electronic ISSN:
1089-7690
Topics:
Chemistry and Pharmacology
,
Physics
Permalink
