Effects of variations in reaction coordinate eigenvalue on heavy-atom kinetic isotope effects: Comparison of two methods for curving the potential barrier

Abstract

The formic acid molecule is used as a model for a computational comparison of the Willi-Wolfsberg curvature parameter (K) method (Type K calculations) and the Johnston-Bonner-Wilson method (Type II calculations), both including bond order (N) and barrier curvature (ν1‡ ≠ 0) effects, for calculation of 13C kinetic isotope effects involving reaction coordinate eigenvectors consisting nominally of two nonzero elements. Results obtained by the two methods cover similar ranges of value of calculated k12C/k13C. Reaction coordinate eigenvectors (uncontaminated for Type II results) may involve as much as 20% extraneous displacement in Type K results when ν1‡ ≅ 800 i cm−1; however, the effect on (ν1‡/ν′1‡), the temperature independent factor (TIF) in k12C/k13C, is so small as to be of limited practical significance. The remainder (TDF) of the isotopic rate constant ratio for various combinations of K and N (Type K) or of ν1‡ and N (Type II) can be arranged well into magnitude sequence by invocation of details of the input F and G matrices in the first order high temperature approximation. But, Type K and Type II results similar only with respect to barrier curvature (as indicated by value of ν1‡) may be very different. The Type K approach (at least for two-element reaction coordinates) seems the more serviceable for data matching and may be conceptually the simpler. The Type II approach, however, seems the more instructive concerning the influence of specific internal coordinate displacements on values of the kinetic isotope effect.