Effects of variations in reaction coordinate eigenvalue on heavy-atom kinetic isotope effects: Eigenvectors consisting of one and two nonzero elements

Abstract

The pentatomic formic acid molecule is used as a model for the survey of the influence on calculated heavy atom kinetic isotope effects of curvature of the potential energy surface (ν1‡ = 0–800i cm−1) along the reaction coordinate at the transition state. Restrictions employed are: invariant geometry and basis diagonal force field; light species reaction coordinate eigenvector consisting of one or two nonzero elements only. The temperature independent factor TIF = (ν1‡/ν1′ ‡) in the rate constant ratio k/k′ generally falls as ν1‡ is increased, but the effect is small. The effect for two-element reaction coordinates of this restricted type is likely the largest such, therefore the influence of barrier curvature on ν1‡/ν1′ ‡ is negligible for practical reaction modeling purposes. The remaining part of k/k′, the temperature dependent factor TDF, arising in isotopic shifts of genuine vibrations, can be strongly affected by barrier curvature. In a few cases, TDF rises slightly as ν1‡ is increased; usually it falls, sometimes so rapidly that the sign of ln(k/k′) is reversed. Since ν1‡ is not an experimental variable, its significance to reaction modeling lies in the fact that graphs of ln(k/k′) vs (1/T) for various reaction coordinates with various ν1‡ do not often intersect at large angles; adjustment of ν1‡ can therefore assist in reducing the redundancy of results of calculations based on a variety of models being compared with experimental results. The barrier curvature and reaction coordinate complexity problem are discussed in terms of the first-order high temperature approximation, ``cut-off procedures,'' and other approaches to the simplification and rationalization of ab initio calculations of kinetic isotope effects.