Relation between Arrhenius activation energies and excitation functions

Abstract

Analytical expressions are derived which relate the Arrhenius activation energy to the energy dependent reaction cross section or excitation function. Results are presented for reactions which proceed with and without a threshold energy. It is shown that the activation energy for neutral-neutral reactions may display a strong temperature dependence, and that activation energies determined in thermal studies of ion-molecule reactions can commonly be expected to be either positive or negative, and strongly temperature dependent. Particular attention is given to recent rate measurements for the exchange reactions of atomic hydrogen with molecular hydrogen, and an attempt is made to derive excitation functions from these results. Three general formulations of the excitation function are used. These reflect the forms which have been suggested by experiments and by theoretical calculations. In particular one class of functions is found to be able to accurately reproduce the available data on the energy dependence of the reaction cross section for neutral-neutral reactions, and representative data for ion-impact induced fragmentation reactions. A second class of functions is introduced to include the special case of hard spheres which require a critical energy along the line of centers to react, while a final class adequately reproduces data for many ion-molecule processes.

Accurate combined-hyperbolic-inverse-power-representation of ab initio potential energy surface for the hydroperoxyl radical and dynamics study of $\bf O+OH$O+OH reaction

“…With optimized parameters ofà = 30.071 Å 2 K −m ,m = 0.081 andb = 0.010 K −1 , Eq. (9) shows a peak at E tr ∼10 K and decays exponentially onwards, 94 perceptibly in a non-capture manner. We ascribe this to isomerization, since most trajectories form a H-bond complex while transiting to the covalent minima at low energies; see Fig.…”

Determination of Interatomic Potentials for the X0+, A0+, and B1 States of HgKr from Fluorescence and Excitation Spectra

“…However, a recently developed GvNDE-program of LeRoy (36)(37)(38) for fitting vibrational energies to the near-dissociation expansion (NDE) permits the determination of the long-range potential characteristics even when the vibrational transitions close to the dissociation limit are not measured. The program was successfully applied in several cases (37)(38)(39)(40)(41) and showed itself to be a very good tool supplementing the BS and LRB methods. that, in general, very close to the dissociation limit, the BS plot must lose its linearity because the long-range potential is given approximately by the expression…”

“…This should be compared with an erroneously assigned A(v = 0 -9) ← X(v = 0) spectrum ( (7) because the measured E v values are too far from the dissociation limit. The more recent GvNDE program of LeRoy (36,37) can be employed here to determine the long-range characteristics of the A-state potential. Equation (7) representing the LRB method is replaced with more general equations (see Eqs.…”

Extracting Cross Sections from Rate Coefficients: Application to Molecular Gas Dissociation

“…On the contrary, using a much higher energy limit (e.g., 20K B T N T ) introduces spurious results, because the high energy part of the cross section (not contributing significantly to the rate) is left in an undecided state by the minimization procedure. For the test cross section, we choose an empirical LeRoy class II functional form [14] to describe the threshold processes (as also suggested by Martin et al [15]):…”