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-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.

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

“…The origin of the unclear and shallow correlations in these data is not immediately apparent. 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 . Despite the complicated trends between the observed kinetics and computed thermodynamic parameters, there are several key conclusions that can be drawn from this data.…”

The role of basicity in selective C–H bond activation by transition metal-oxidos

“…In addition, Anderson has explored imbalanced transition states in the context of his complexes that includes a theoretical treatment of asynchronous mechanisms involving metal–oxido C–H bond. 20,25…”

“…However, a growing area of interest in inorganic chemistry are mechanisms of C-H bond activation that fall between these limits off the diagonal often referred to as "asynchronous", "nonsynchronous", or "imbalanced" PCET. [18][19][20][21][22][23][24][25][26][27][28][29][30] These types of reactions are still considered concerted, as compared to stepwise, because a thermodynamically stable intermediate is not formed during the transfer process but differ from balanced CPET as the degree of charge transfer or delocalization of either the proton or electron lags behind the other (Fig. 2).…”

“…Effects like nonadiabatic couplings, multiconfigurational interactions, and tunneling can alter the mechanisms and therefore rates of both the proton and electron transfer. 14,25,32 The necessity of including these effects depends on the nature of the mechanism or identity of the transition state (i.e., whether it is concerted or imbalanced) because the degree of nonadiabaticity and tunneling will directly depend on the proximity of the two potential energy surfaces near their crossing point. The closer the passage through the transition state is to a conical intersection, the more nonadiabatic it becomes.…”

“…The role of nonadiabatic couplings in PCET and C-H bond activation specifically have been extensively theoretically Dalton Transactions Frontier treated. 13,14,[25][26][27]32 However, unambiguous delineation of these mechanisms experimentally is challenging as they are controlled by factors that are hard to isolate and systematically control such as the symmetry and energy differences between the ground and excited states of the reactants and products.…”