Molecular dynamics simulations for enzymatic hydride-transfer reactions: Defining environmental reaction coordinates to capture transition state diversity

It is now well established that the transition state of a chemical reaction is not a single, static structure but rather a distribution of configurations. However, the implications of this distributed nature remain incompletely characterized, particularly for quantum proton and hydride transfer reactions, where variations in donor-acceptor separations at the transition state are key: they can determine whether or not tunneling contributes to the transfer. Consequently, the transition state's characterization critically depends on the chosen reaction coordinate, and several geometry-based and energy-based coordinates have been proposed for empirical valence bond and hybrid QM/MM molecular dynamics simulations of such reactions. Here, we systematically evaluate these coordinates, using a general analytic model for proton- and hydride-transfer reactions alongside important aspects of the enzymatic hydride transfer in formate dehydrogenase as a case study. Our analysis reveals significant limitations of common geometry-based and vertical energy gap coordinates, which often fail to isolate environmental effects and can bias the description of transition states. To address these issues, we propose an equilibrium energy difference coordinate that excludes the rapid fluctuations of the transferring quantum proton or hydride, focusing instead on the environment's polarization. Additionally, we demonstrate that the broad distribution of transition state configurations implies that key reaction properties, such as rate constants and kinetic isotope effects, may not always report on the same subset of transition state configurations. This insight helps resolve some mechanistic ambiguities and highlights the importance of carefully selecting reaction coordinates for simulating reaction dynamics (especially for quantum particle transfers) in enzymatic and condensed-phase chemistry.