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

Abstract

We 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.1 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.