Radical ligand transfer: mechanism and reactivity governed by three-component thermodynamics

Abstract

Here, we demonstrate that the relationship between reactivity and thermodynamics in radical ligand transfer chemistry can be understood if this chemistry is dissected as concerted ion-electron transfer (cIET). Namely, we investigate radical ligand transfer reactions from the perspective of thermodynamic contributions to the reaction barrier: the diagonal effect of the free energy of the reaction, and the off-diagonal effect resulting from asynchronicity and frustration, which we originally derived from the thermodynamic cycle for concerted proton-electron transfer (cPET). This study on the OH transfer reaction shows that the three-component thermodynamic model goes beyond cPET chemistry, successfully capturing the changes in radical ligand transfer reactivity in a series of model Fe^III-OH⋯(diflouro)cyclohexadienyl systems. We also reveal the decisive role of the off-diagonal thermodynamics in determining the reaction mechanism. Two possible OH transfer mechanisms, in which electron transfer is coupled with either OH^- and OH⁺ transfer, are associated with two competing thermodynamic cycles. Consequently, the operative mechanism is dictated by the cycle yielding a more favorable off-diagonal effect on the barrier. In line with this thermodynamic link to the mechanism, the transferred OH group in OH^-/electron transfer retains its anionic character and slightly changes its volume in going from the reactant to the transition state. In contrast, OH⁺/electron transfer develops an electron deficiency on OH, which is evidenced by an increase in charge and a simultaneous decrease in volume. In addition, the observations in the study suggest that an OH⁺/electron transfer reaction can be classified as an adiabatic radical transfer, and the OH^-/electron transfer reaction as a less adiabatic ion-coupled electron transfer.

Scheme 1. Examples of radical ligand transfers in biological and synthetic chemistry.

Scheme 2. The canonical concerted proton-electron transfer between the oxidant and the substrate (top) along with the associated half-reaction thermodynamic cycles (panels in blue and green, left). The full-reaction thermodynamic cycle results from the combination of two half-reaction cycles (bottom left). The key thermodynamic quantities associated with two off-diagonal branches of these cycles are the free energy of reduction ΔG^e− (horizontal arrows) and the free energy of protonation ΔG^H+(vertical arrows) of the oxidant and the substrate radical. The combination of ΔG^e−and ΔG^H+, corresponding to a π/4 rotation of the [ΔG^e−; ΔG^H+] coordinate system, gives rise to two composite variables, potential duality μ and potential disparity ω (bottom right). The difference in μ and in ω between the oxidant and the substrate yields two off-diagonal thermodynamic reaction characteristics – frustration and asynchronicity (σ and η), which together with the free energy of the reaction ΔG₀ form the three-component thermodynamic basis, shaping cPET reactivity.

Fig. 1. (A) Reaction between the tetramethylcyclam (TMC)-supported, axial-ligand (L)-perturbed Fe^III–OH systems and the substrates CHD˙ and 3,3-diflouroCHD˙ used in the study. Note that for Fe^III–OH complexes with L marked with an asterisk, we calculated the free-energy barriers ΔG^≠ only for the 2F-CHD-based systems, as we were not able to optimize the respective transition states of the CHD-based systems in the appropriate spin state (i.e. S = 5/2 Fe^III–OH complex coupled antiferromagnetically with the substrate radical). (B) The difference between off-diagonal energetics (ΔG^≠_offdiag from eq (7)): negative values indicate preference for the OH⁻ cycle (blue), positive – for OH⁺ (red).

Scheme 3. Top: two mechanistic scenarios for radical ligand transfers between the R˙ donor (D–R) and acceptor (A˙): one involving concerted and co-directional transfer of R⁺ and the electron denoted as R⁺_→/e⁻_→ transfer, and one with concerted contra-directional transfer of R⁻ and the electron denoted as R⁻_→/e⁻_← (left and right, respectively). The group R˙ corresponds to OH˙ in this study. Bottom: the full-reaction thermodynamic cycles associated with the two R⁺_→/e⁻_→ transfer and R⁻_→/e⁻_← transfer mechanisms (left and right, respectively) are depicted together with their constituent blocks – half-reaction thermodynamic cycles (color coded in the figure). For each half-reaction thermodynamic cycle, three key free energy quantities are shown. Their meaning and importance are explained in the main text. Note the left scenario is fully analogous to cPET presented in Scheme 2. The half-reaction cycles are presented in Fig. S2.

Fig. 2. ΔG^≠vs. linear free energy relationship (LFER) (left); LFER with the effect of asynchronicity (middle); LFER together with the complete off-diagonal term (right) for the OH⁻ (top) and OH⁺ (bottom) sets. The quality of correlations is assessed by using the squared Pearson's coefficient (R²). For the plot with the points labeled according to the axial ligand of the (L)(TMC)Fe^III–OH complex see ESI – Fig. S3, and the detailed decomposition of the barriers into the non-thermodynamic and thermodynamic (diagonal and off-diagonal) components is shown in Fig. S4. The barriers and thermodynamic descriptors are given in Tables S1–S3. For the details on all systems investigated in this work see Fig. S5–S7 and Tables S4–S10. Further details on the performance of the models are presented in Tables S11 and S12.

Fig. 3. Characterization of the OH rebound reaction by change in volume and charge on the transferred OH group upon the RC → TS transition. The points are colored and shaded from dark blue (favored OH⁻) to dark red (favored OH⁺) to reflect the difference in off-diagonal thermodynamic contributions to the barrier (ΔG^≠_offdiag) originating from the OH⁻ and OH⁺ cycles. The HOMO for the OH⁻ and OH⁺ cycle driven reaction is shown in the inset. For the plot with the points labeled according to the axial ligand of the (L)(TMC)Fe^III–OH complex see Fig. S10, and the AIM charges and volumes of the studied systems are listed in Tables S16–S17.

Fig. 4. ΔG^≠₀₀vs. asynchronicity for radical ligand transfers linked to the OH⁻ (blue) and OH⁺ (red) thermodynamic cycles. For the OH⁻/OH⁺ sets, the η_R⁻ and η_R⁺ from eqn (3) and (4) were employed, respectively. For the plot with the points labeled according to the axial ligand of the (L)(TMC)Fe^III–OH complex see Fig. S22A.