Loading…
Bimolecular Master Equations for a Single and Multiple Potential Wells with Analytic Solutions
The analytic solutions, that is, populations, are derived for the K-adiabatic and K-active bimolecular master equations, separately, for a single and multiple potential wells and reaction channels, where K is the component of the total angular momentum J along the axis of least moment of inertia of...
Saved in:
| Published in: | The journal of physical chemistry. A, Molecules, spectroscopy, kinetics, environment, & general theory Molecules, spectroscopy, kinetics, environment, & general theory, 2018-04, Vol.122 (14), p.3506-3534 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | The analytic solutions, that is, populations, are derived for the K-adiabatic and K-active bimolecular master equations, separately, for a single and multiple potential wells and reaction channels, where K is the component of the total angular momentum J along the axis of least moment of inertia of the recombination products at a given energy E. The analytic approach provides the functional dependence of the population of molecules on its K-active or K-adiabatic dissociation, association rate constants and the intermolecular energy transfer, where the approach may complement the usual numerical approaches for reactions of interest. Our previous work, Part I, considered the solutions for a single potential well, whereby an assumption utilized there is presently obviated in the derivation of the exact solutions and farther discussed. At the high-pressure limit, the K-adiabatic and K-active bimolecular master equations may each reduce, respectively, to the K-adiabatic and K-active bimolecular Rice-Ramsperger-Kassel-Marcus theory (high-pressure limit expressions) for bimolecular recombination rate constant, for a single potential well, and augmented by isomerization terms when multiple potential wells are present. In the low-pressure limit, the expression for population above the dissociation limit, associated with a single potential well, becomes equivalent to the usual presumed detailed balance between the association and dissociation rate constants, where the multiple well case is also considered. When the collision frequency of energy transfer, Z LJ, between the chemical intermediate and bath gas is sufficiently less than the dissociation rate constant k d(E′J′K′) for postcollision (E′J′K), then the solution for population, g(EJK)+, above the critical energy further simplifies such that depending on Z LJ, the dissociation and association rate constant k r(EJK), as g(EJK)+ = k r(EJK)A·BC/[Z LJ+k d(EJK)], where A and BC are the reactants, for example, relevant for O3 formation from O + O2 + Ar up to ∼100 bar; otherwise, additional contributions from postcollision are present and especially relevant at high pressures. In the aforementioned regime Z LJ < k d(E′J′K) the physical connection of recombination rate constants, k rec based on either utilizing population from the master equation approach or a collision based bimolecular RRKM theory is traced and elucidated analytically that the rate constants are equal. Recombination rate constants, k rec, based on t |
|---|---|
| ISSN: | 1089-5639 1520-5215 |
| DOI: | 10.1021/acs.jpca.7b09244 |