# Bimolecular Recombination Reactions: *K*‑Adiabatic and *K*‑Active Forms of RRKM
Theory, Nonstatistical Aspects, Low-Pressure Rates, and Time-Dependent
Survival Probabilities with Application to Ozone. 2

journal contribution

posted on 06.11.2014, 00:00 by Nima Ghaderi, R. A. MarcusWe consider for bimolecular
recombination reactions the

*K*-adiabatic versus the*K*-active forms of RRKM theory, where*K*is the component of the total angular momentum along the axis of least moment of inertia of the recombination product. When that product is approximately a prolate symmetric top, with two moments of inertia of the product substantially larger than the third,*K*becomes a dynamically slowly varying quantity and the*K*-adiabatic form of RRKM theory is the appropriate version to use. Using classical trajectory results for the rate constant for ozone formation in the low-pressure region as an example, excellent agreement for the recombination rate constant*k*_{rec}with the*K*-adiabatic RRKM theory is observed. Use of a two transition state (inner, outer TS) formalism also obviates any need for assessing recrossings in the exit channel. In contrast, the*K*-active form of RRKM theory for this system disagrees with the trajectory results by a factor of about 2.5. In this study we also consider the distribution of the (*E*,*J*) resolved time-dependent survival probabilities*P*(*E*,*J*,*t*) of the intermediate O_{3}^{*}formed from O + O_{2}. It is calculated using classical trajectories. The initial conditions for classical trajectories were selected using action-angle variables and a total*J*representation for (*E*,*J*) resolved systems, as described in Part I. The difference between*K*-active and*K*-adiabatic treatments is reflected also in a difference of the*K*-active RRKM survival probability*P*(*E*,*J*,*t*) from its trajectory-based value and from its often non-single-exponential decay. It is shown analytically that*k*_{rec}(*K*-active) ≥*k*_{rec}(*K*-adiabatic), independent of the details of the TS (e.g., variational or fixed RRKM theory, 1-TS or 2-TS). Nonstatistical effects for O_{3}^{*}formation include a small initial recrossing of the transition state, a slow (several picoseconds) equipartitioning of energy among the two O–O bonds of the newly formed O_{3}^{*}, and a small nondissociation (a quasi-periodicity) of some trajectories originating in O_{3}^{*}(∼10%) and so, by microscopic reversibility, are not accessible from O + O_{2}. An apparently new feature of the present results is the comparison of classical trajectories with*K*-adiabatic and*K*-active theories for rate constants of bimolecular recombinations. The quantum mechanical counterpart of classical*K*-adiabatic RRKM theory is also given, and its comparison with the experimental*k*_{rec}for O_{3}is given elsewhere.