Temperature-Dependent Transitions Between Normal and Inverse Isotope Effects Pertaining to the Interaction of H−H and C−H Bonds with Transition Metal Centers

Abstract

Deuterium kinetic isotope effects (KIEs) serve as versatile tools to infer details about reaction mechanisms and the nature of transition states, while equilibrium isotope effects (EIEs) associated with the site preferences of hydrogen and deuterium enable researchers to study aspects of molecular structure. Researchers typically interpret primary deuterium isotope effects based on two simple guidelines: (i) the KIE for an elementary reaction is normal (k(H)/k(D) > 1) and (ii) the EIE is dictated by deuterium preferring to be located in the site corresponding to the highest frequency oscillator. In this Account, we evaluate the applicability of these rules to the interactions of H-H and C-H bonds with a transition metal center. Significantly, experimental and computational studies question the predictability of primary EIEs in these systems based on the notion that deuterium prefers to occupy the highest frequency oscillator. In particular, the EIEs for (i) formation of sigma-complexes by coordination of H-H and C-H bonds and (ii) oxidative addition of dihydrogen exhibit unusual temperature dependencies, such that the same system may demonstrate both normal (i.e., K(H)/K(D) > 1) and inverse (i.e., K(H)/K(D) < 1) values. The transition between a normal and inverse EIE indicates that these systems do not demonstrate the typical monotonic variation predicted by the van't Hoff relationship. Instead, the calculated EIEs in these systems are 0 at 0 K, increase to a value greater than 1, and then decrease to unity at infinite temperature. This unusual behavior may be rationalized by considering the individual factors that contribute to the EIE. Specifically, the EIE may be expressed in the form EIE = SYM x MMI x EXC x ZPE (where SYM is the symmetry factor, MMI is the mass-moment of inertia term, EXC is the excitation term, and ZPE is the zero-point energy term), and the distinctive temperature profile results from the inverse ZPE (enthalpy) and normal [SYM x MMI x EXC] (entropy) components opposing each other and having different temperature dependencies. At low temperatures, the ZPE component dominates and the EIE is inverse, while at high temperatures, the [SYM x MMI x EXC] component dominates and the EIE is normal. The inverse nature of the ZPE term is a consequence of the rotational and translational degrees of freedom of RH (R = H, CH(3)) becoming low-energy isotopically sensitive vibrations in the product, while the normal nature of the [SYM x MMI x EXC] component results from deuterium substitution having a larger impact on the moment of inertia of the smaller molecule.