Hydrogen Atom Abstraction via Hydride-Coupled Electron Transfer and Its Origin

S1 Supplementary Information Hydrogen atom abstraction via hydride-coupled electron transfer and its origin Zuzanna Wojdyla,a Jishnu Sai Gopinatha and Martin Srneca,* aJ. Heyrovský Institute of Physical Chemistry, Czech Academy of Sciences, Dolejškova 3, 18223 Prague, Czech Republic Corresponding Author *E-mail: m[email protected]s.cz S2 Table of Contents Off-diagonal contributions to HCET expressed in terms of the reduction potentials and hydricities of X–H and Y–H ............ S3 Off-diagonal contributions for HCET expressed in terms of full reaction cycles ....................................................................... S4 Off-diagonal contributions to PCET expressed in terms of the reduction potentials and pKa values of X• and Y• .................... S9 Off-diagonal contributions for PCET expressed in terms of full reaction cycles ....................................................................... S11 Thermodynamic and reactivity data for the substrates and Cu(III)-OH/ Cu(II)-OH complexes ............................................... S14 Oxidants and substrates used in the study ................................................................................................................................... S27 Performance of the three-component model applied to Cu(III)-OH/ Cu(II)-OH reactions ........................................................ S28 Analysis of the reactions based on electronic-structure descriptors ............................................................................................ S30 Intrinsic bond orbital analysis of the HAA reactions ................................................................................................................. S34 HAA involving para substituted phenols .............................................................................................................................. S41 HAA involving the [LNiIIOH] complexes ................................................................................................................................... S45 Intrinsic bond orbital analysis of the OH rebound reaction ......................................................................................................... S48 Structural features of the transition states and adiabaticity of the HAA reaction ....................................................................... S49 S3 Off-diagonal contributions to HCET expressed in terms of the reduction potentials and hydricities of X–H and Y–H Hydricity (Δ𝐺𝑋𝐻 𝐻−) is the free energy of heterolytic X−H bond dissociation to yield a parent species X+ and the hydride anion H−: Δ𝐺𝑋𝐻 𝐻−= 𝐺𝑋++𝐺𝐻−−𝐺𝑋𝐻 (S1) The one-electron reduction potential (𝐸°) is a quantity reflecting Gibbs free energy change upon 1e− reduction of a solute (X−H): 𝐹 ⋅𝐸𝑋𝐻 °= 𝐺𝑜𝑥 −𝐺𝑟𝑒𝑑 −𝐸𝑎𝑏𝑠 °(reference) = 𝐺𝑋𝐻 −𝐺𝑋𝐻•−−𝐸𝑎𝑏𝑠 °(reference) (S2) Note that 𝐸𝑎𝑏𝑠 °(reference) is the absolute potential of the reference electrode. Since this is constant, it can be omitted in derivation of asynchronicity and frustration. Asynchronicity 𝜂 defined in Eq (6) in the main text as: 𝜂𝐻𝐶𝐸𝑇 =1 √2[(Δ𝐺𝑋𝐻 𝑒−−Δ𝐺𝑋𝐻 𝐻−)−(Δ𝐺𝑌𝐻 𝑒−−Δ𝐺𝑌𝐻 𝐻−)] (S3) can be transformed to: 𝜂𝐻𝐶𝐸𝑇 =1 √2[(𝐺𝑋𝐻•−−𝐺𝑋𝐻 −(𝐺𝑋+−𝐺𝑋𝐻))−(𝐺𝑌𝐻•−−𝐺𝑌𝐻 −(𝐺𝑌+−𝐺𝑌𝐻))] (S4) 𝜂𝐻𝐶𝐸𝑇 =1 √2[(−𝐹 ⋅𝐸𝑋𝐻 °−Δ𝐺𝑋𝐻 𝐻−)−(−𝐹 ⋅𝐸𝑌𝐻 °−Δ𝐺𝑌𝐻 𝐻−)] = − 1 √2(𝐹 ⋅Δ𝐸°+ΔΔ𝐺𝐻−), (S5) where Δ𝐸°/ ΔΔ𝐺𝐻− is the difference of reduction potential/hydrictity between electron acceptor (X−H) and electron donor (Y−H). Similarly for 𝜎: 𝜎𝐻𝐶𝐸𝑇 =1 √2[(Δ𝐺𝑋𝐻 𝑒−+Δ𝐺𝑋𝐻 𝐻−)−(Δ𝐺𝑌𝐻 𝑒−+Δ𝐺𝑌𝐻 𝐻−)] (S6) 𝜎𝐻𝐶𝐸𝑇 =1 √2[(𝐺𝑋𝐻•−−𝐺𝑋𝐻 +(𝐺𝑋+−𝐺𝑋𝐻))−(𝐺𝑌𝐻•−−𝐺𝑌𝐻 +(𝐺𝑌+−𝐺𝑌𝐻))] (S7) 𝜎𝐻𝐶𝐸𝑇 =1 √2[(−𝐹 ⋅𝐸𝑋𝐻 °+Δ𝐺𝑋𝐻 𝐻−)−(−𝐹 ⋅𝐸𝑌𝐻 °+Δ𝐺𝑌𝐻 𝐻−)] = − 1 √2(𝐹 ⋅Δ𝐸°−ΔΔ𝐺𝐻−) (S8) S4 Off-diagonal contributions for HCET expressed in terms of full reaction cycles The three-component thermodynamic model presented in the main text is based on the intrinsic thermodynamic properties of individual reactants - the one-electron reduction free energies of X−H and Y−H (Δ𝐺𝑋𝐻/𝑌𝐻 𝑒−) and the free energies of hydride release of X−H and Y−H (hydricities, Δ𝐺𝑋𝐻/𝑌𝐻 𝐻−). Such an approach depicts tug-of-war type competition over electron and hydride between the two species that can act as electron acceptors (and hydride donors at the same time) and gives rise to eqs (6) and (7) in the main text. As an alternative to the tug-of-war view of HCET, HCET can be also depicted in terms of electron and hydride transfers (ET and HT) between X−H and Y•. In such case, the full reaction cycle for HCET can be expressed in terms of the Gibbs free energies of ET (Δ𝐺𝐸𝑇,1and Δ𝐺𝐸𝑇,2) and HT between the two reactants (Δ𝐺𝐻𝑇,1and Δ𝐺𝐻𝑇,2, see Scheme S1). Scheme S1. Full reaction thermodynamic cycle for HCET Based on the full reaction thermodynamic cycle, asynchronicity can be expressed as Δ𝐺𝐸𝑇,1 −Δ𝐺𝐻𝑇,1: 𝜂𝐻𝐶𝐸𝑇 =1 √2(Δ𝐺𝐸𝑇,1 −Δ𝐺𝐻𝑇,1), (S9) where Δ𝐺𝐸𝑇,1 is the difference between the Gibbs free energy of one-electron reduction of X−H (Δ𝐺𝑋𝐻 𝑒−) and the Gibbs free energy of one-electron reduction of Y+ (Δ𝐺𝑌+ 𝑒− as shown in Scheme S2): S5 Δ𝐺𝐸𝑇,1 = Δ𝐺𝑋𝐻 𝑒−−Δ𝐺𝑌+ 𝑒− (S10) and Δ𝐺𝐻𝑇,1is the difference between hydricity of X−H (Δ𝐺𝑋𝐻 𝐻−) and hydricity of Y−H•− (Δ𝐺𝑌𝐻•− 𝐻− as shown in Scheme S2): Δ𝐺𝐻𝑇,1 = Δ𝐺𝑋𝐻 𝐻−−Δ𝐺𝑌𝐻•− 𝐻− (S11) Inserting (S10) and (S11) into (S9) yields: 𝜂𝐻𝐶𝐸𝑇 =1 √2[(Δ𝐺𝑋𝐻 𝑒−−Δ𝐺𝑌+ 𝑒−)−(Δ𝐺𝑋𝐻 𝐻−−Δ𝐺𝑌𝐻•− 𝐻−)], (S12a) which can be rearranged as: 𝜂𝐻𝐶𝐸𝑇 =1 √2[(Δ𝐺𝑋𝐻 𝑒−−Δ𝐺𝑋𝐻 𝐻−)−(Δ𝐺𝑌+ 𝑒−−Δ𝐺𝑌𝐻•− 𝐻−)] (S12b) Eq (S12b) already contains the imbalance between the one-electron reduction and hydride release of/from X−H - (Δ𝐺𝑋𝐻 𝑒− −Δ𝐺𝑋𝐻 𝐻−)- as present in eq (6) in main text. The term describing the H-acceptor species, Y•: −(Δ𝐺𝑌+ 𝑒− −Δ𝐺𝑌𝐻•− 𝐻−) - can be transformed based on the following relationship derived from the thermodynamic cycle for Y• (Scheme S2): Δ𝐺𝑌𝐻 𝑒−+Δ𝐺𝑌𝐻•− 𝐻−= Δ𝐺𝑌𝐻 𝐻−+Δ𝐺𝑌+ 𝑒− (S13a) and consequently: Δ𝐺𝑌+ 𝑒−−Δ𝐺𝑌𝐻•− 𝐻−= Δ𝐺𝑌𝐻 𝑒−−Δ𝐺𝑌𝐻 𝐻− (S13b) Inserting relationship from eq (S13b) into eq (S12b) yields the expression for 𝜂𝐻𝐶𝐸𝑇 introduced in the main text (eq (6)). S6 Scheme S2. Half reaction thermodynamic cycle for electron acceptor Y• in HCET. As a side note, 𝜂𝐻𝐶𝐸𝑇 can be directly expressed through the Gibbs free energies of individual species - eq (S9) can be recast as: 𝜂𝐻𝐶𝐸𝑇 =1 √2[(𝐺𝑋𝐻•−+𝐺𝑌+−(𝐺𝑋𝐻 +𝐺𝑌•))−(𝐺𝑋++𝐺𝑌𝐻•−−(𝐺𝑋𝐻 +𝐺𝑌•))]. (S14) This expression can be simplified to: 𝜂𝐻𝐶𝐸𝑇 =1 √2[(𝐺𝑋𝐻•−+𝐺𝑌+)−(𝐺𝑋++𝐺𝑌𝐻•−)], (S15) which corresponds to the difference in Gibbs free energies between the two off-diagonal states, [X–H•− + Y⁺] and [Y–H•− + X⁺]. Eq (S15) can be similarly obtained from eq (6) in the main text. Similar to (S9), the remaining off-diagonal term - frustration, based on the full-reaction thermodynamic cycle can be expressed as: 𝜎1,𝐻𝐶𝐸𝑇 =1 √2(Δ𝐺𝐸𝑇,1 +Δ𝐺𝐻𝑇,1). (S16) S7 Eq (S16) can be represented in terms of the Gibbs free energies of the individual species as: 𝜎1,𝐻𝐶𝐸𝑇 =1 √2[(𝐺𝑋𝐻•−+𝐺𝑌+−(𝐺𝑋𝐻 +𝐺𝑌•))+(𝐺𝑋++𝐺𝑌𝐻•−−(𝐺𝑋𝐻 +𝐺𝑌•))] (S17) whereas the original 𝜎𝐻𝐶𝐸𝑇 from eq (7) in the main text is represented by the Gibbs free energies of the individual species as: 𝜎𝐻𝐶𝐸𝑇 =1 √2[(𝐺𝑋𝐻•−+𝐺𝑋+−2⋅𝐺𝑋𝐻)−(𝐺𝑌𝐻•−+𝐺𝑌+−2⋅𝐺𝑌𝐻)] (S18) Comparison of eq (S17) with eq (S18) demonstrates that 𝜎1,𝐻𝐶𝐸𝑇 is connected to 𝜎𝐻𝐶𝐸𝑇 through a term that depends on the thermodynamic properties of Y−H/Y•, and is therefore constant for a series of HAA reactions involving a single H-atom acceptor (Y•) and various H-donors (X−H): 𝜎1,𝐻𝐶𝐸𝑇 −𝜎𝐻𝐶𝐸𝑇 =1 √2(2⋅𝐺𝑌+−2⋅𝐺𝑌•+2⋅𝐺𝑌𝐻•−−2⋅𝐺𝑌𝐻), (S19) which based on Scheme S2 can be expressed as: 𝜎1,𝐻𝐶𝐸𝑇 = 𝜎𝐻𝐶𝐸𝑇 +1 √2(Δ𝐺𝑌𝐻 𝐻−−Δ𝐺𝑌𝐻•− 𝐻−+Δ𝐺𝑌𝐻 𝑒−−Δ𝐺𝑌+ 𝑒−) (S20) Alternatively, frustration 𝜎2,𝐻𝐶𝐸𝑇 can be calculated with respect to products of the reaction (X• and Y−H) as 1 √2 (Δ𝐺𝐸𝑇,2 +Δ𝐺𝐻𝑇,2): 𝜎2,𝐻𝐶𝐸𝑇 =1 √2[(𝐺𝑋𝐻•−+𝐺𝑌+−(𝐺𝑋•+𝐺𝑌𝐻))+(𝐺𝑋++𝐺𝑌𝐻•−−(𝐺𝑋•+𝐺𝑌𝐻))] (S21) Comparison of eq (S17) with eq (S21) shows that 𝜎2,𝐻𝐶𝐸𝑇 differs from 𝜎1,𝐻𝐶𝐸𝑇 by the free energy of the reaction: 𝜎1,𝐻𝐶𝐸𝑇 = 𝜎2,𝐻𝐶𝐸𝑇 +√2×Δ𝐺0 (S22) It must be stressed that  is the same in both formulations (one presented in the main text and one presented here), which is not the case of . However, 1 from eq (S16) correlates with  from the main text (eqs (5) and (7)) and thus all conclusions about the joint effect of frustration and asynchronicity on the operative mechanism are independent of the used formulation. Despite this, we favor the formulation presented in the main text as it is associated with the positive range of values for ∆𝐺00 ≠, which is expected as it corresponds S8 to ¼ of the reorganization energy at the synchronous and unfrustrated limit (and the reorganization energy in the Marcus-type model of reactivity is always positive). Note that conversion between 𝜂𝐻𝐶𝐸𝑇/𝜎𝐻𝐶𝐸𝑇 expressed in kcal/mol used in this study and 𝜂𝐻𝐶𝐸𝑇/𝜎𝐻𝐶𝐸𝑇 expressed in Volts involves a change of sign: 𝜂𝐻𝐶𝐸𝑇(kcal mol−1)= −𝐹𝜂𝐻𝐶𝐸𝑇(V) and 𝜎𝐻𝐶𝐸𝑇(kcal mol−1)= −𝐹𝜎𝐻𝐶𝐸𝑇(V) Thus, for instance, both the positive asynchronicity (expressed in Volts) and the negative asynchronicity (expressed in kcal mol⁻¹) equally describe the preference for ET over HT in the HAA reaction. S9 Off-diagonal contributions to PCET expressed in terms of the reduction potentials and pKa values of X• and Y• The acidity constant (𝑝𝐾𝑎,𝑋•) is the free energy of heterolytic X−H bond dissociation of X−H•+ to yield a parent species X• and the proton H+: 𝑅𝑇ln(10)⋅𝑝𝐾𝑎= 𝐺𝑋•−𝐺𝑋−𝐻•+ +𝐺𝑠𝑜𝑙𝑣,𝐻+, (S23) where 𝐺𝑠𝑜𝑙𝑣,𝐻+ is the free energy of solvation of a proton (a constant value which cancels out in derivation of 𝜂𝑃𝐶𝐸𝑇 and 𝜎𝑃𝐶𝐸𝑇). The one-electron reduction potential (𝐸𝑋• °) is a quantity reflecting Gibbs free energy change upon 1e− reduction of a solute (X•): 𝐹 ⋅𝐸𝑋• °= 𝐺𝑋•−𝐺𝑋−−𝐸𝑎𝑏𝑠 ∘(reference) (S24) Asynchronicity 𝜂𝑃𝐶𝐸𝑇, defined in Eq (4) in the main text as: 𝜂𝑃𝐶𝐸𝑇 =1 √2[(Δ𝐺𝑌• 𝑒−−Δ𝐺𝑌• 𝐻+)−(Δ𝐺𝑋• 𝑒−−Δ𝐺𝑋• 𝐻+)] (S25) can be re-expressed using Gibbs free energies of individual species: 𝜂𝑃𝐶𝐸𝑇 =1 √2[(𝐺𝑌−−𝐺𝑌•−(𝐺𝑌𝐻•+ −𝐺𝑌•))−(𝐺𝑋−−𝐺𝑋•−(𝐺𝑋𝐻•+ −𝐺𝑋•))] (S26) and - based on (S23) and (S24) - transformed to: 𝜂𝑃𝐶𝐸𝑇 =1 √2[(−𝐹 ⋅ 𝐸𝑌• °+𝑅𝑇ln(10)⋅𝑝𝐾𝑎,𝑌•)−(−𝐹 ⋅𝐸𝑋• °+𝑅𝑇ln(10)⋅𝑝𝐾𝑎,𝑋•)] = − 1 √2(𝐹 ⋅Δ𝐸∘−𝑅𝑇ln(10)⋅Δ𝑝𝐾𝑎) (S27) where Δ𝐸∘/Δ𝑝𝐾𝑎 is the difference of reduction potential/acidity constant between electron (and H-atom) acceptor (Δ𝐸𝑌• ∘/𝑝𝐾𝑎,𝑌•) and electron (H-atom) donor (Δ𝐸𝑋• ∘/𝑝𝐾𝑎,𝑋•). S16 H-Phe -307.2000097 -306.9664036 -306.7068993 -307.2229195 -306.3239015 -306.5683813 Me-Phe -346.4676865 -346.2460462 -345.974818 -346.4908429 -345.6111161 -345.8398691 NMe2-Phe -441.0173438 -440.8344451 -440.5164912 -441.0367981 -440.2166358 -440.4049291 NO2-Phe -511.5610241 -511.3047177 -511.0919367 -511.6530736 -510.6559101 -510.9214043 OMe-Phe -421.6142306 -421.4044263 -421.1173547 -421.639295 -420.7803448 -420.9921429 TEMPOH -483.7983698 -483.6085652 -483.2765043 -483.8632395 -482.9561975 -483.1950739 G(Cu(II)-OH2) G(Cu(III)-OH2) G(Cu(II)-OH) G(Cu(I)-OH2) G(Cu(IV)-OH) G(Cu(III)-OH) CuIII-OH -3233.659033 -3233.446508 -3233.186894 -3233.774325 -3232.795173 -3233.020498 G(Cu(I)-OH2) G(Cu(II)-OH2) G(Cu(I)-OH) G(Cu(0)-OH2) G(Cu(III)-OH) G(Cu(II)-OH) CuII-OH -3233.774325 -3233.659033 -3233.261305 -3233.825662 -3233.020498 -3233.186894 G([L3-Ni(II)OH2]-) G([L•2Ni(II)OH2]) G([L3-Ni(II)OH]2-) G([L3-Ni(I)OH2]2-) G([L•2-Ni(III)OH]) G([L•2-Ni(II)OH]-) [LNi(II)OH]- -2863.030975 -2862.892238 -2862.558875 -2863.11634 -2862.277165 -2862.437789 G([L•2-Ni(II)OH2]) G([L-Ni(II)OH2]+) G([L•2-Ni(II)OH]-) G([L3-Ni(II)OH2]-) G([LNi(II)OH]+) G([L-Ni(II)OH]) [LNi(II)OH] -2862.892194 -2862.718376 -2862.437787 -2863.029145 -2862.086608 -2862.278816 Table S2. Thermodynamic data for the studied substrates and H-atom acceptors. The values were obtained at the B3LYP(D3)/def2SVP level, with the implicit CPCM solvation model of THF (DMF for TEMPOH/NiII−OH systems) at 298 K. All energies are given in kcal mol-1. substrates ΔG0 (half-reaction) 𝜔𝐻+ 𝜇𝐻+ 𝜔𝐻− 𝜇𝐻− cyclohexane -402.21 141.97 -180.73 -354.29 379.14 cyclohexene -392.60 139.91 -199.88 -361.41 359.07 DHA -386.50 126.50 -213.10 -365.17 336.55 S17 fluorene -391.35 123.89 -231.09 -386.83 343.01 Ph2CH2 -392.88 125.41 -217.09 -373.07 345.14 THF -404.01 145.47 -195.00 -339.90 369.11 toluene -401.97 133.17 -214.46 -380.57 363.75 2,7-di(NMe2)fluorene -392.97 153.43 -250.00 -373.57 347.95 oxetane -405.09 144.19 -203.85 -343.87 367.35 1,3-CHD -383.59 141.00 -208.98 -367.87 332.01 CHD -383.58 133.16 -209.35 -351.60 340.78 CF3-Phe -399.56 103.76 -240.98 -414.57 381.08 Cl-Phe -395.47 114.05 -240.17 -400.58 370.16 H-Phe -396.35 115.15 -238.07 -398.91 378.58 Me-Phe -393.96 120.35 -240.11 -390.35 369.80 NMe2-Phe -384.30 141.08 -240.09 -363.92 346.66 NO2-Phe -401.37 94.41 -245.75 -442.46 360.77 OMe-Phe -390.37 127.38 -238.50 -381.13 358.89 TEMPOH -378.57 147.34 -219.60 -402.47 344.90 H-atom acceptors CuIII-OH -400.69 115.19 -262.86 -434.47 332.15 CuII-OH -368.62 176.48 -242.51 -357.26 311.71 [LNi(II)OH]- -372.23 147.92 -255.37 -372.36 296.60 [LNi(II)OH] -384.90 124.50 -265.58 -418.22 296.68 S18 Table S3. Reactivity data for the Cu(III)-OH/substrate set (singlet). The values were obtained at the B3LYP(D3)/def2-SVP level, with the implicit CPCM solvation model of THF at 298 K. All energies are given in kcal mol-1. substrates ΔG0 ΔG≠ 𝜂𝐻+ 𝜎𝐻+ ∆𝐺𝑜𝑓𝑓𝑑𝑖𝑎𝑔 𝐻+ ∆𝐺𝑡ℎ𝑒𝑟𝑚𝑜 𝐻+ 𝜂𝐻− 𝜎𝐻− ∆𝐺𝑜𝑓𝑓𝑑𝑖𝑎𝑔 𝐻− ∆𝐺𝑡ℎ𝑒𝑟𝑚𝑜 𝐻− cyclohexane 1.52 13.40 -26.78 -82.13 13.84 14.60 80.18 46.99 -8.30 -7.54 cyclohexene -8.09 7.82 -24.72 -62.98 9.57 5.52 73.05 26.92 -11.53 -15.58 DHA -14.18 0.74 -11.31 -49.76 9.61 2.52 69.29 4.39 -16.23 -23.32 fluorene -9.34 5.25 -8.70 -31.77 5.77 1.10 47.63 10.85 -9.20 -13.86 Ph2CH2 -7.81 6.18 -10.21 -45.77 8.89 4.98 61.39 12.99 -12.10 -16.01 THF 3.32 10.41 -30.27 -67.86 9.40 11.06 94.56 36.96 -14.40 -12.74 toluene 1.28 14.34 -17.98 -48.40 7.60 8.24 53.90 31.60 -5.57 -4.94 CF3-Phe -1.13 -9.24 11.43 -21.88 2.61 2.05 19.90 48.93 7.26 6.69 Cl-Phe -5.21 -9.5 1.15 -22.69 5.39 2.78 33.89 38.01 1.03 -1.58 H-Phe -4.33 -8.59 0.05 -24.79 6.18 4.02 35.56 46.43 2.72 0.55 Me-Phe -6.73 -7.08 -5.15 -22.75 4.40 1.04 44.12 37.65 -1.62 -4.98 NMe2-Phe -16.39 --- -25.89 -22.77 -0.78 -8.97 70.55 14.50 -14.01 -22.21 NO2-Phe 0.68 -10.04 20.78 -17.11 -0.92 -0.58 -7.99 28.62 5.16 5.50 OMe-Phe -10.32 -5.63 -12.18 -24.36 3.05 -2.12 53.34 26.73 -6.65 -11.81 S19 Table S4. Reactivity data for the Cu(III)-OH/substrate set (singlet). The values were obtained at the B3LYP(D3)/def2-TZVP level, with the implicit CPCM solvation model of THF at 298 K. All energies are given in kcal mol-1. Δ𝐺0 𝜂𝐻+ 𝜎𝐻+ Δ𝐺𝑜𝑓𝑓𝑑𝑖𝑎𝑔 𝐻+ Δ𝐺𝑡ℎ𝑒𝑟𝑚𝑜 𝐻+ 𝜂𝐻− 𝜎𝐻− Δ𝐺𝑜𝑓𝑓𝑑𝑖𝑎𝑔 𝐻− Δ𝐺𝑡ℎ𝑒𝑟𝑚𝑜 𝐻− cyclohexane 5.49 -26.11 -73.28 11.79 14.54 72.01 40.46 -7.89 -5.14 cyclohexene -3.94 -25.00 -56.75 7.94 5.97 68.62 24.79 -10.96 -12.93 DHA -9.68 -13.37 -45.54 8.04 3.21 66.49 4.47 -15.50 -20.34 fluorene -5.04 -11.62 -27.48 3.97 1.45 45.75 11.33 -8.61 -11.13 Ph2CH2 -3.55 -12.63 -41.53 7.22 5.45 58.81 12.97 -11.46 -13.23 THF 7.97 -27.22 -59.81 8.15 12.13 85.36 31.67 -13.42 -9.44 toluene 5.14 -18.73 -42.80 6.02 8.59 50.49 30.26 -5.06 -2.49 Table S5. Reactivity data for the Cu(II)-OH/substrate set (doublet). The values were obtained at the B3LYP(D3)/def2-SVP level, with the implicit CPCM solvation model of THF at 298 K. All energies are given in kcal mol -1. substrates ΔG0 ΔG≠ 𝜂𝐻+ 𝜎𝐻+ ∆𝐺𝑜𝑓𝑓𝑑𝑖𝑎𝑔 𝐻+ ∆𝐺𝑡ℎ𝑒𝑟𝑚𝑜 𝐻+ 𝜂𝐻− 𝜎𝐻− ∆𝐺𝑜𝑓𝑓𝑑𝑖𝑎𝑔 𝐻− ∆𝐺𝑡ℎ𝑒𝑟𝑚𝑜 𝐻− cyclohexane 33.59 34.79 34.51 -61.78 6.82 23.61 2.98 67.44 16.12 32.91 cyclohexene 23.98 23.55 36.57 -42.63 1.52 13.51 -4.15 47.37 10.80 22.80 DHA 17.88 8.72* 49.98 -29.41 -5.14 3.80 -7.91 24.84 4.23 13.17 fluorene 22.73 5.52 52.59 -11.42 -10.29 1.07 -29.57 31.30 0.43 11.80 Ph2CH2 24.26 --- 51.07 -25.42 -6.41 5.72 -15.81 33.44 4.41 16.53 THF 35.39 32.98 31.01 -47.51 4.12 21.82 17.36 57.40 10.01 27.71 toluene 33.35 --- 43.31 -28.05 -3.81 12.86 -23.30 52.05 7.19 23.86 2,7-di(NMe2)fluorene 24.35 8.05 23.05 7.49 -3.89 8.28 -16.31 36.23 4.98 17.16 oxetane 36.47 31.47 32.29 -38.66 1.59 19.83 13.40 55.64 10.56 28.80 1,3-CHD 14.97 16.73 35.48 -33.54 -0.49 7.00 -10.60 20.30 2.42 9.91 S20 CHD 14.96 8.64 43.32 -33.16 -2.54 4.94 5.67 29.07 5.85 13.33 *an estimate based on unfinished TS optimization Table S6. Reactivity data for the Ni(II)-OH/complexes. The values were obtained at the B3LYP(D3)/def2-SVP level, with the implicit CPCM solvation of DMF at 298 K. All energies are given in kcal mol -1. The values for the H→ −e← − ⁄ cycle are calculated using S=1 TEMPO+ as the off-diagonal state in line with the mechanism observed in IBO analysis; values in parentheses are calculated using the ground state S=0 TEMPO+. system ΔG0 ΔG≠ 𝜂𝐻+ 𝜎𝐻+ ∆𝐺𝑜𝑓𝑓𝑑𝑖𝑎𝑔 𝐻+ ∆𝐺𝑡ℎ𝑒𝑟𝑚𝑜 𝐻+ 𝜂𝐻− 𝜎𝐻− ∆𝐺𝑜𝑓𝑓𝑑𝑖𝑎𝑔 𝐻− ∆𝐺𝑡ℎ𝑒𝑟𝑚𝑜 𝐻− TEMPOH / [LNi(II)OH]− 6.34 -1.47 0.58 -35.77 8.80 11.97 -30.11 (-6.10) 48.30 (24.29) 4.55 (4.55) 7.72 (7.72) TEMPOH / [LNi(II)OH] S=0 -6.33 -6.85 -22.84 -45.97 5.78 2.62 14.86 (39.76) 47.32 (24.21) 8.12 (-3.89) 4.95 (-7.05) TEMPOH / [LNi(II)OH] S=1 -11.65 -8.79 -28.03 -48.31 5.07 -.075 15.75 (38.86) 48.22 (23.31) 8.12 (-3.89) 2.29 (-9.71) Table S7. Charges and volumes (at isodensity surface 0.002) of the H-atom, H-atom donor (substrate) and H-atom acceptor calculated for stationary points (RC and TS) obtained for HAAs from the the C−H substrates by the Cu(III)-OH complex. TS q (e) V (a.u.3) substrates H substrate H-atom acceptor H substrate H-atom acceptor cyclohexane 0.295 0.062 -0.360 19.4 761.0 3879.6 cyclohexene 0.288 0.075 -0.366 20.6 713.8 3890.3 DHA 0.303 -0.018 -0.326 20.0 1354.3 3894.8 fluorene 0.363 -0.086 -0.279 18.0 1236.1 3895.6 S21 Ph2CH2 0.322 0.010 -0.335 19.0 1307.1 3888.7 THF 0.279 0.110 -0.392 20.5 561.2 3890.1 toluene 0.343 0.024 -0.369 18.9 753.4 3891.5 RC H substrate H-atom acceptor H substrate H-atom acceptor cyclohexane -0.037 0.018 0.018 42.4 759.9 3887.1 cyclohexene 0.008 -0.020 0.010 38.8 717.0 3881.3 DHA 0.047 -0.056 0.008 35.2 1355.6 3889.7 fluorene 0.033 -0.016 -0.018 39.1 1231.4 3898.6 Ph2CH2 0.037 -0.047 0.006 36.3 1318.3 3886.7 THF 0.039 -0.052 0.012 36.7 563.5 3867.7 toluene 0.014 -0.006 -0.009 40.4 756.0 3891.8 Table S8. Charges and volumes (at isodensity surface 0.002) of the H-atom, H-atom donor (substrate) and H-atom acceptor calculated for stationary points (RC and TS) obtained for HAAs from the the C−H substrates by the Cu(II)-OH complex. TS q (e) V (a.u.3) substrates H substrate H-atom acceptor H Substrate H-atom acceptor cyclohexane 0.538 -0.132 -1.406 14.0 772.8 3922.1 cyclohexene 0.558 -0.336 -1.224 13.8 736.5 3929.7 DHA 0.553 -0.700 -0.855 14.1 1380.6 3912.2 fluorene 0.472 -0.640 -0.835 15.7 1261.2 3916.8 S22 THF 0.536 -0.092 -1.446 14.2 571.9 3925.4 2,7-di(NMe2)fluorene 0.512 -0.668 -0.846 15.0 1955.4 3916.3 oxetane 0.556 -0.107 -1.449 13.9 451.7 3922.7 1,3-CHD 0.516 -0.543 -0.974 15.1 702.8 3938.0 CHD 0.557 -0.534 -1.025 14.2 703.3 3935.2 RC H substrate H-atom acceptor H Substrate H-atom acceptor cyclohexane -0.008 -0.031 -0.964 36.0 760.3 3928.2 cyclohexene 0.042 -0.064 -0.979 34.7 717.3 3931.4 DHA 0.080 -0.110 -0.970 34.2 1357.4 3937.5 fluorene 0.118 -0.167 -0.973 30.5 1231.9 3928.4 THF 0.029 -0.053 -1.073 35.0 564.4 3936.1 2,7-di(NMe2)fluorene 0.085 -0.114 -0.975 32.6 1925.5 3931.3 oxetane 0.023 -0.051 -0.975 35.6 444.1 3913.5 1,3-CHD 0.051 -0.062 -0.990 35.4 672.2 3935.3 CHD -0.032 0.025 -0.994 40.9 668.8 3937.1 Table S9. Charges and volumes (at isodensity surface 0.002) of the H-atom, H-atom donor (substrate) and H-atom acceptor calculated for stationary points (TS) obtained for HAAs from the the para-substituted phenols by the Cu(III)-OH complex. TS q (e) V (a.u.3) substrates H substrate H-atom acceptor H substrate H-atom acceptor CF3-Phe 0.653 -0.527 0.444 8.70 904.51 3736.23 S23 Cl-Phe 0.655 -0.769 0.689 8.77 824.07 3726.82 H-Phe 0.661 -0.457 0.414 8.54 684.91 3738.85 Me-Phe 0.668 -0.431 0.379 8.31 820.75 3745.24 NMe2-Phe --- --- --- --- --- --- NO2-Phe 0.654 -0.648 0.620 8.73 861.46 3732.89 OMe-Phe 0.660 -0.312 0.271 9.15 871.45 3749.74 Table S10. Charges and volumes (at isodensity surface 0.002) of the H-atom, H-atom donor (substrate) and H-atom acceptor calculated for stationary points (TS) obtained for HAA reactions between Ni(II)-OH and TEMPOH. TS q (e) V (a.u.3) H substrate H-atom acceptor H substrate H-atom acceptor TEMPOH/ [LNi(II)OH]− 0.630 -0.436 -1.197 9.01 1292.840 3074.640 TEMPOH/ [LNi(II)OH] 0.638 -0.270 -0.370 9.01 1287.029 3058.395 Table S11. Charges and volumes of the H-atom and the donor/acceptor in self-exchange reactions q (e) V (a.u.3) substrates H donor/acceptor H donor/acceptor cyclohexane 0.111 -0.055 25.0 752.8 cyclohexene 0.109 -0.054 25.5 707.3 DHA 0.123 -0.061 24.6 1342.1 fluorene 0.129 -0.065 24.1 1215.1 Ph2CH2 0.118 -0.067 23.7 1296.4 S24 THF 0.131 -0.066 25.4 559.5 toluene 0.124 -0.062 25.3 745.0 2,7-di(NMe2)fluorene 0.134 -0.067 24.3 1907.7 oxetane 0.143 -0.076 24.8 436.4 1,3-CHD 0.103 -0.051 24.1 662.7 CHD 0.118 -0.059 24.9 662.3 CF3-Phe 0.650 -0.325 8.565 897.7 Cl-Phe 0.648 -0.324 8.583 799.6 H-Phe 0.648 -0.324 8.575 680.7 Me-Phe 0.647 -0.323 8.590 809.6 NO2-Phe 0.653 -0.326 8.573 848.4 OMe-Phe 0.646 -0.323 8.600 869.1 TEMPOH 0.608 -0.304 9.735 1294.5 Cu(III)-OH / Cu(II)-OH 0.647 -0.385/-0.243 8.892 1462.1/1457.0 Cu(II)-OH / Cu(I)-OH 0.637 -1.320 9.157 1511.1 [L•2-Ni(II)OH]- / [L3-Ni(II)OH2]- 0.641 -1.320 9.087 2305.6 [L-Ni(II)OH] / [L•2-Ni(II)OH2] 0.634 -0.317 8.428 2265.7 Table S12. Change of charge, Δq, and volume, ΔV, on the H-atom, the substrate fragment and the H-atom acceptor upon RC-to-TS transition during the HAA reactions with Cu(III)-OH and Cu(II)-OH. For q and V, see eqs (S43) and (S44). Δq (e) ΔV (a.u.3) Cu(III)-OH H substrate H-atom acceptor H substrate H-atom acceptor cyclohexane 0.332 0.044 -0.378 -23.0 1.1 -7.5 S25 cyclohexene 0.279 0.095 -0.376 -18.2 -3.2 9.0 DHA 0.255 0.038 -0.334 -15.2 -1.3 5.1 fluorene 0.330 -0.070 -0.261 -21.1 4.7 -3.0 Ph2CH2 0.285 0.057 -0.341 -17.3 -11.1 2.0 THF 0.240 0.162 -0.403 -16.2 -2.3 22.4 toluene 0.329 0.030 -0.360 -21.6 -2.5 -0.3 Cu(II)-OH H substrate H-atom acceptor H substrate H-atom acceptor cyclohexane 0.546 -0.101 -0.442 -22.1 12.5 -6.1 cyclohexene 0.516 -0.272 -0.246 -20.9 19.1 -1.6 DHA 0.473 -0.590 0.115 -20.0 23.3 -25.4 fluorene 0.355 -0.473 0.138 -14.7 29.3 -11.6 THF 0.507 -0.039 -0.373 -20.8 7.5 -10.8 2,7-di(NMe2)fluorene 0.427 -0.554 0.130 -17.7 29.9 -14.9 oxetane 0.533 -0.057 -0.474 -21.7 7.6 9.2 1,3-CHD 0.465 -0.481 0.016 -20.3 30.7 2.8 CHD 0.589 -0.559 -0.031 -26.8 34.5 -1.9 S32 Figure S5. Volume and charge of the transferred H moiety at the TS relative to the volume and charge at RC (eqs (S43) and eqs (44)). The points are colored and shaded from dark blue (favored H→ −e← − ⁄) to dark red (favored H→ +e→ − ⁄) to reflect the difference in off-diagonal thermodynamic contributions to the barrier, which originates from the two different H→ −e← − ⁄ and H→ +e→ − ⁄ cycles presented in Figure 3 in the main text. S33 Figure S6. Correlations between η obtained from the nonoperative (left) and the operative thermodynamic cycle (right) and the deviation of charge on the transferred H atom at the TS calculated with respect to: the average of self-exchange reactions (top) or the RC (bottom). The points are colored to reflect the preference towards one of the thermodynamic cycles (as measured by the ∆𝐺𝑜𝑓𝑓𝑑𝑖𝑎𝑔 ≠ originating from the H→ −e← − ⁄ and H→ +e→ − ⁄ cycles) - in blue (favored H→ −e← − ⁄, the Cu(III)−OH set) and red (favored H→ +e→ − ⁄, the Cu(II)−OH set). S34 (a) (b) Figure S7. The evolution of IBOs initially describing the -orbital electron pair of the C−H bond along the IRC for (a) Cu(III)−OH with cyclohexane and (b) Cu(II)−OH with cyclohexane. S35 (a) S36 (b) S37 (c) S38 (d) Figure S8. The intrinsic reaction coordinates (IRCs) and the important IBOs and their evolutions along the respective IRCs in the Cu(III)−OH-based reaction set. (a) Cyclohexane (b) Cyclohexene (c) DHA and (d) Toluene. For Toluene and DHA the transient (“bouncing”) electron transfer occurs before the TS. S39 (a) S40 (b) Figure S9. The intrinsic reaction coordinates (IRCs) and the important IBOs and their evolutions along the respective IRCs in the Cu(II)−OH-based reaction set. (a) 1,3-CHD and (b) THF. Exhibiting a normal PCET behaviour. S41 HAA involving para substituted phenols Figure S10. a) The difference between the off-diagonal contributions (Δ𝐺𝑜𝑓𝑓𝑖𝑑𝑖𝑎𝑔 ≠ from eq (3)) associated with PCET and HCET thermodynamic cycles for the para-substituted phenols undergoing HAA with CuIII−OH: negative values indicate preference for the PCET cycle (red), positive – for HCET (blue). b) Charge and volume of the transferred H moiety at the TS relative to the referential self-exchange values, as given by eqs (8) and (9) in the main text for all investigated systems: the C−H substrates and para-substituted phenols in HAA reactions with CuIII−OH as well as the C−H substrates in HAA reactions with CuII−OH; the reactions with parasubstituted phenols are labeled according to the substituent. The points are colored and shaded from dark blue (favored H→ −e← − ⁄) to dark red (favored H→ +e→ − ⁄) to reflect the difference in off-diagonal thermodynamic contributions to the barrier, which originates from the two different H→ −e← − ⁄ and H→ +e→ − ⁄ cycles presented in Figure 3. S48 IBO analysis of the OH rebound reaction Figure S13. The IRC and the important IBOs and their evolutions along the IRC in the Fe(III)−OH-based rebound reaction with cyclohexadiene radical. Showing a hydroxide coupled electron transfer. S49 Structural features of the transition states and adiabaticity of the reaction. Comparison of geometries of the transition states for CuIII−OH and CuII−OH systems reveals that, as it can be expected for CuII−OH, the strongly hindered, endoergic reactions feature late TSs, with an elongated C−H bond and a short O−H bond (nearly formed). From a mechanistic perspective, the geometry of the transition state is somewhat reflective of the asynchronicity of the reaction, as reactions more asynchronous towards H+ transfer feature more elongated C−H bond and a shorter H−O distance. On the other hand, in the CuIII−OH set, the H atom is located at the midpoint between the donor (C atom) and the acceptor (O of CuIII−OH). This characteristic is in line with lower ∆𝐺0 and ∆𝐺≠ values for the reactions but also indicates that H−/e− transfer features stronger interactions between the substrates and the H-atom acceptor, possibly reflecting a larger adiabatic coupling. Stronger interactions are evidenced by the shorter sum of C−H and H−O bond lengths at the respective TSs as shown in Figure S14. S50 Figure S14. The crucial C−H and H−O distances at the TS, the points are colored and shaded from grey to dark blue to reflect the asynchronicity of the H→ −e← − ⁄ reaction the and from grey to red to reflect asynchronicity of the H→ +e→ − ⁄ reaction. S51 References in SI: (S1) Wojdyla, Z.; Maldonado-Domínguez, M.; Bharadwaz, P.; Culka, M.; Srnec, M. Elucidation of Factors Shaping Reactivity of 5′- Deoxyadenosyl – a Prominent Organic Radical in Biology. Phys. Chem. Chem. Phys. 2024, 26 (30), 20280–20295. (S2) Novak, I.; Harrison, L. J.; Kovač, B.; Pratt, L. M. Electronic Structure of Persistent Radicals: Nitroxides. J. Org. Chem. 2004, 69 (22), 7628–7634.