Hydrogen—Deuterium Kinetic Isotope Effect, an Experimental and Theoretical Study over a Wide Range of Temperature

An experimental study of the kinetic isotope effect for the reaction $${\mathrm{CF}}_3+{\mathrm{CHD}}_3–|\begin{array}{c}\to {\mathrm{F}}_3\mathrm{C}–\mathrm{H}–{\mathrm{CD}}_3\to {\mathrm{F}}_3\mathrm{CH}\mathrm{+···}\\ \\ \to {\mathrm{F}}_3\mathrm{C}–\mathrm{D}–{\mathrm{CHD}}_2\to {\mathrm{F}}_3\mathrm{CD}\mathrm{+···}\end{array}$$ has been carried out between 300° and 700°K, and also the Arrhenius parameters k=A exp (—E/RT) were obtained for the individual reactions. An especial effort was made to avoid systematic errors, and the precision obtained was good. These data were combined with those of Tschuikow‐Roux who studied the essentially same reaction between 1000° and 1800°K, and a detailed test was made of activated complex theory utilizing the method of London—Polanyi—Eyring—Sato with corrections for quantum mechanical tunneling. Sato's parameter was evaluated from activation energy of an analogous reaction so that k_H/k_D and A provided an unambiguous, nonadjustable test of theory. Because reactants were identical for both reactions, all the kinetic isotope effect depended on differences in the two activated complexes. The vibrational frequencies of the two nine‐atom models of the complex were evaluated by a computer, programmed to E. B. Wilson's FG‐matrix methods, and the effect of replacing the full nine‐atom model by simpler five‐, four‐, or three‐atom models was tested. The Arrhenius A factor was enormously sensitive (factor of 10³) to number of atoms assigned to the model; the three‐ or four‐atom models gave A factors much too high, but the five‐ or nine‐atom models with tunneling corrections were in fairly good agreement with experiment from 300° to 1800°K. It is judged that if one evaluates a potential‐energy surface, carries out a full vibrational analysis, and applies a reasonable tunneling correction, then one has in activated complex theory an expression analogous in logic and in usefulness to the perfect‐gas theory; that is, broad over‐all predictions can be made (in spite of readily identified conceptual flaws) but fine points will always be missed. Any quantitative value in the simplified versions of the theory is open to grave doubt.