Rigidity Analysis of Hydride Tunneling-Ready States From Secondary Kinetic Isotope Effects and Hammett Correlations: Relating to the Temperature Dependence of Kinetic Isotope Effects

Recent study on the effects of enzyme mutations on the primary kinetic isotope effects (1° KIEs) of H-tunneling reactions revealed that a more rigid system results in a weaker temperature dependence of KIEs, indicated by a smaller isotopic activation energy difference (∆E_a = E_aD − E_aH). In literature, a more rigid system has been defined by the presence of shorter, more densely populated hydrogen donor-acceptor distances (DADs) in both the productive reactant complexes (PRCs) and the tunneling-ready states (TRSs). Studying the relationship between DAD_PRC/DAD_TRS and ∆E_a can help validate existing H-tunneling models or guide the development of new theories. In a previous publication, we employed Hammett correlations on hydride acceptors (NAD⁺ analogues) to propose TRS electronic structures for qualitative analysis of DAD_TRS order. In this paper, we selected a pair of such systems and used secondary (2°) KIEs on the hydride donor (NADH analogue) to obtain quantitative DAD_TRS information at the molecular level. TRS structures were computed, and the corresponding 2° KIEs were calculated and fitted to the observed values to extract DAD_TRS data. PRC structures were also computed. The DAD_PRC/DAD_TRS information aligns with the rigidity order derived from Hammett correlation analysis, and the correlation between DAD_PRC/DAD_TRS and ∆E_a is consistent with observations in enzyme systems.