Microcanonical Rate Constants for Unimolecular Reactions in the Low-Pressure Limit

Low-pressure-limit
microcanonical rate constants, κ0(E,J), describe the rate of activating
bath gas collisions in a unimolecular reaction and are calculated
here using classical trajectories and quantized thresholds for reaction.
The resulting semiclassical rate constants are two-dimensional (in
total energy E and total angular momentum J) and are intermediate in complexity between the four-dimensional
state-to-state collisional energy and angular momentum transfer rate
constant, R(E′,J′;E,J), and the highly averaged
thermal rate constant, k0. Results are
presented for CH4 (+M), C2Hx (+M), x = 3–6, and H2O
(+M), where κ0(E,J) is shown generally to be a sensitive function of the bath gas,
temperature, and initial state of the unimolecular reactant. Strong
variations in κ0 with respect to E and J lead to complex trends in relative microcanonical
bath gas efficiencies. This underlying complexity may complicate the
search for simple explanations for observed trends in relative thermal
bath gas efficiencies. A different measure of the microcanonical collision
efficiency that describes the energy range of activating collisions
is introduced that supports the empirical decomposition of collisional
activation into separable translational-to-vibrational and rotational-to-vibrational
activation mechanisms. The two mechanisms depend differently on mass,
temperature, and the J-dependence of the threshold
energy for reaction, with rotational-to-vibrational activation favored
for heavier baths and for reactions with rigid transition states.
Finally, κ0 is used to test the accuracy of several
two-dimensional models for R that were proposed for
use in master equation studies.