Approximation of experimental constants of chemical reaction rates in a wide temperature range

This article discusses possible methods of approximation of constants of chemical reaction rates onto a region of values that is beyond the limits of the experimental temperature range. In particular, this work studies direct approximation of constants of chemical reaction rates obtained upon processing of experimental values, approximation based on an analytical simulated dependence of the integral cross section of the process on energy, and approximation based on direct solution of the equation for constants of the chemical reaction rates at an arbitrary dependence of the process integral cross section on energy. The integral equation has been solved using the Tikhonov regularization. It is shown that this approach makes it possible to determine the threshold energy as well as to recover the form of the cross section. A second-order reaction $\mathrm{CH}_4\to\mathrm{CH}_3+\mathrm{H}$ has been considered, the activation energy of which is $44560$ K. Based on the calculation for the temperature range of $10000$–$50000$ K, the following approximation can be recommended: $5.04\times10^{-6} T^{-1.5}\exp(-45377/T)$, $\text{cm}^{-3}/s$. The obtained data can be applied for various calculations, in particular, in problems of hypersound gas dynamics, as well as for filling databases.