Test of Transition-State Theory Using the Experimentally Determined Rate Constant Ratio for the Reactions H+H2 and H+D2

Abstract

The rate constant ratio $k_1{\mathrm{\hspace{0.17em}/\hspace{0.17em}k}}_4$ for the hydrogen‐exchange reactions $$\mathrm{H}+{\mathrm{H}}_2\to {\mathrm{H}}_2+\mathrm{H}$$ and $$\mathrm{H}+{\mathrm{D}}_2\to \mathrm{HD}+\mathrm{D}$$ has been measured in the temperature range 290 to 690°K. Reactions [1] and [4] were carried out simultaneously, and $k_1{\mathrm{\hspace{0.17em}/\hspace{0.17em}k}}_4$ was determined directly using only concentration ratios of stable molecules. The precision of the results was ± 10% or better and it is believed that this also represents the accuracy. The experimental results were compared with the theoretical values of $k_1{\mathrm{\hspace{0.17em}/\hspace{0.17em}k}}_4$ given by transition‐state theory with quantum‐mechanical tunneling, using the most recent ab initio potential surface of Shavitt, Stevens, Minn, and Karplus. The one‐dimensional tunneling correction was calculated numerically using the minimum energy path on the surface. Good agreement between experiment and theory was found only when tunneling was included; scaling of the one‐dimensional barrier, as suggested by the correlation work of Shavitt, improved the agreement. It is concluded that transition‐state theory, as applied, leads to results for the hydrogen‐exchange reactions which are not inconsistent with experiment.