Recently there have been several experimental demonstrations of how concerted proton electron transfer (CPET) reaction rates are affected by off-diagonal energies, namely the stepwise thermodynamic parameters ΔG°PT and ΔG°ET. Semiclassical structure-activity relationships have been invoked to rationalize these linear free energy relationships despite the widely acknowledged importance of quantum effects such as nonadiabaticity and tunneling in CPET reactions. Here we report variable temperature kinetic isotope effect data for the asynchronous reactivity of a terminal Co-oxo complex with C–H bonds and find evidence of substantial quantum tunneling which is inconsistent with semiclassical models even when including tunneling corrections. This indicates substantial nonadiabatic tunneling in the CPET reactivity of this Co-oxo complex and further motivates the need for a quantum mechanical justification for the influence of ΔG°PT and ΔG°ET on reactivity. We include ΔG°PT and ΔG°ET in nonadiabatic models of CPET by modeling how they influence the anharmonicity and depth of proton potential energy surfaces, which we approximate with a four-state model. With this model we independently reproduce a dominant trend with ΔG°PT + ΔG°ET as well as a more subtle effect of ΔG°PT − ΔG°ET (equivalently η) in a nonadiabatic framework. The primary route through which these off-diagonal energies influence rates is through vibronic coupling. Our results reconcile predictions from semiclassical transition state theory with models that treat proton transfer quantum mechanically in CPET reactivity and suggest that similar treatments may be possible for other reactions with significant nuclear tunneling.
Additional spectra, data, and simulations.
Python code for simulations.