Reconciling Imbalanced Transition State Effects with Nonadiabatic CPET Reactions

Abstract

Recently there have been several experimental demonstrations of how concerted proton electron transfer (CPET) reaction rates are affected by off-main-diagonal energies, namely the stepwise thermodynamic parameters ΔG°PT and ΔG°ET. Semi-classical structure-activity relationships have been invoked to rationalize these asynchronous linear free energy relation-ships 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 semi-classical 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 in-fluence of ΔG°PT and ΔG°ET on reactivity. To reconcile this dichotomy, we include ΔG°PT and ΔG°ET in nonadiabatic models of CPET by having them influence the anharmonicity and depth of the proton potential energy surfaces, which we approximate as Morse potentials. With this model we independently reproduce the dominant trend with ΔG°PT + ΔG°ET as well as the subtle effect of ΔG°PT − ΔG°ET (or 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 nonadiabatic processes.

Testing the Limits of Imbalanced CPET Reactivity: Mechanistic Crossover in H-Atom Abstraction by Co(III)–Oxo Complexes

“…It is possible that cross-correlations between the energetics of CPET and PT, significant tunneling effects as we have observed with C−H substrates, hydrogen bonding effects, or some combination of these factors convolute reactivity trends. 88 Despite the complicated trends between the observed kinetics and computed thermodynamic parameters, there are several key conclusions that can be drawn from this data. First, the correlation between k obs,PT for the stepwise substrates and ΔG PT1 can be used to assess the possible agency of similar stepwise PTET mechanisms for the apparently concerted substrates.…”