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

Abstract

Low-pressure-limit microcanonical rate constants, κ 0 (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 twodimensional (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, k 0 . Results are presented for CH 4 (+M), C 2 H x (+M), x = 3−6, and H 2 O (+M), where κ 0 (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 κ 0 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, κ 0 is used to test the accuracy of several two-dimensional models for R that were proposed for use in master equation studies.

“Third‐body” collision parameters for hydrocarbons, alcohols, and hydroperoxides and an effective internal rotor approach for estimating them

“…Detailed models for the collisional energy transfer function 22,38 have been shown to enable a priori kinetics predictions with errors of just 25%, 22,69 whereas simpler models that incorporate fewer physical details, such as the “single‐exponential‐down” model 17,45 that is often used in energy‐resolved master equation calculations, 70–72 have a priori accuracies of closer to a factor of two 69,73–75 . Again, in an effort to be most directly useful for constructing extensive chemical kinetics tabulations, we restrict attention to models where collision outcomes are controlled by the single parameter α = ⟨Δ E d ⟩, which is the average energy transferred in deactivating collisions.…”

“…Once the outcomes of an appropriately prepared trajectory ensemble are computed, one can generate any number of different energy and angular‐momentum transfer averages as required for parameterizing more detailed higher accuracy models for energy transfer, 22,69 but this is not pursued here. Instead we analyze trends in the single moment α computed for a large number of systems.…”

Semiclassical transition state theory/master equation kinetics of HO + CO: Performance evaluation

“…Although such treatments were first demonstrated decades ago [39][40][41][42][43] and exist in improved forms today, [39][40][41][42][43][44][45][46] they require input parameters that involve extensive additional calculations. 47 Instead of an explicit 2DME, most practical ME calculations utilize various methods for reducing the 2DME to one dimension. 48,49 We consider three versions of the simpler 1D master equations, which are the most widely used theoretical means for predicting pressure-dependent rate constants.…”

“…The 2DME includes a kernel for collisional energy transfer transitions that depends on both variables. Although such treatments were first demonstrated decades ago 39‐43 and exist in improved forms today, 39‐46 they require input parameters that involve extensive additional calculations 47 . Instead of an explicit 2DME, most practical ME calculations utilize various methods for reducing the 2DME to one dimension 48,49 .…”

Microcanonical Tunneling Rates from Density-of-States Instanton Theory

“…1,2 However, cases are also provided by reaction schemes which proceed via one or more intermediates or pre-reactive complexes. [3][4][5][6][7][8] In a low-pressure environment the reaction will not thermalize at each step and thus thermal rate theories such as transition-state theory (TST) would not be valid. However, assuming that the reaction is statistically well-behaved, the total rate constant can be computed by averaging over an appropriate distribution of reaction energies using a microcanonical framework for each step.…”