Marcus cross relation in the space of H-atom abstraction reactions boosted through off-diagonal thermodynamics

Supplementary Information Marcus Cross Relation in the Space of H-Atom Abstraction Reactions Boosted through Off-diagonal Thermodynamics Jan Kovář,a,b Erik Andris,c Zuzanna Wojdyla,a Jishnu Sai Gopinath,a Jakub Klinkovský,b Radek Fučík,b and Martin Srneca,* aJ. Heyrovský Institute of Physical Chemistry, Czech Academy of Sciences, Dolejškova 3, 18223 Prague, Czech Republic bFaculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 12000 Praha 2, Czech Republic cInstitute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, Flemingovo nám. 2, 16610 Prague, Czech Republic Corresponding Author *E-mail: m[email protected]s.cz Computational Note: Given the large number of reactions examined in this study, we developed an automated pipeline to efficiently identify and eliminate redundant imaginary frequencies in both half-reaction cycle structures and transition states (TSs). In case of redundant imaginary frequencies detected, the resulting geometry is adjusted using the corresponding normal modes rescaled so that the atom with the largest displacement is shifted by x Å. The value of x is initialized by 0.2 Å and the geometry is then re-optimized. In the case that redundant imaginary frequencies are still present, we change the value of x to 0.35, 0.5, 0.65, -0.2, -0.35, -0.5, and -0.65 Å. If the geometry cannot be corrected in this way, the reaction is discarded from the dataset. To balance computational cost with the extensive number of reactions investigated, the more economical def2-SVP basis set was employed throughout the study. Nonetheless, a comparison with the higher-level def2-TZVP basis set was performed, revealing excellent agreement, as illustrated in the figure below. Here, we assess the reliability of the def2-SVP basis set by comparing it with the higher-level def2TZVP for key thermodynamic quantities—namely, the reaction free energy (ΔG⁰), frustration (σ), and asynchronicity (η)—as defined in the main text. For this benchmark, we employed the reaction set A from Figure 3 (main text). The term 𝐶 from eqs (7) and (8) is given as −1 2𝑅𝑇𝑙𝑛(𝐴𝑋𝑋𝐴𝑌𝑌/𝐴𝑋𝑌 2). where the terms 𝐴 are prefactors from eq (4) in the main text. Some basic relations: 1) ∆𝐺0,𝑋𝑌 = 𝐺𝑃,𝑋𝑌 − 𝐺𝑅,𝑋𝑌 (from separated reactants to separated products) 2) Δ𝐺0,𝑋𝑌 𝑅𝐶→𝑃𝐶 = 𝐺𝑃𝐶,𝑋𝑌 − 𝐺𝑅𝐶,𝑋𝑌 3) Δ𝐺0,𝑋𝑌 𝑅𝐶→𝑃𝐶 = ∆𝐺0,𝑋𝑌 + 𝑤𝑃,𝑋𝑌 − 𝑤𝑅,𝑋𝑌 4) ∆𝐺𝑋𝑋 ≠= 𝑤𝑅,𝑋𝑋 +𝜆𝑋𝑋 4= 𝑤𝑅,𝑋𝑋 + ∆𝐺𝑋𝑋 ≠,RC®TS (𝜆𝑋𝑋 – reorganization energy in the self-exchange reaction) 5) ∆𝐺𝑌𝑌 ≠= 𝑤𝑅,𝑌𝑌 +𝜆𝑌𝑌 4= 𝑤𝑅,𝑌𝑌 + ∆𝐺𝑌𝑌 ≠,RC®TS (𝜆𝑌𝑌 – reorganization energy in the self-exchange reaction) Postulated additivity in Marcus cross relations: 𝜆𝑋𝑌 ≈1 2(𝜆𝑋𝑋 + 𝜆𝑌𝑌) The Marcus model of the barrier for the elemementary bimolecular reaction: ∆𝐺𝑋𝑌 ≠= 𝑤𝑅,𝑋𝑌 +(𝜆𝑋𝑌+Δ𝐺0 𝑅𝐶→𝑃𝐶)2 4𝜆𝑋𝑌 that is ∆𝐺𝑋𝑌 ≠= 𝑤𝑅,𝑋𝑌 +𝜆𝑋𝑌 4+Δ𝐺0 𝑅𝐶→𝑃𝐶 2+(Δ𝐺0 𝑅𝐶→𝑃𝐶)2 4𝜆𝑋𝑌 Considering point 3) then ∆𝐺𝑋𝑌 ≠= 𝑤𝑅,𝑋𝑌 +1 2(∆𝐺𝑋𝑋 ≠− 𝑤𝑅,𝑋𝑋 + ∆𝐺𝑌𝑌 ≠− 𝑤𝑅,𝑌𝑌)+Δ𝐺0 𝑅𝐶→𝑃𝐶 2+(Δ𝐺0 𝑅𝐶→𝑃𝐶)2 8(∆𝐺𝑋𝑋 ≠−𝑤𝑅,𝑋𝑋+∆𝐺𝑌𝑌 ≠−𝑤𝑅,𝑌𝑌) that is ∆𝐺𝑋𝑌 ≠=1 2(𝑤𝑅,𝑋𝑌 + 𝑤𝑃,𝑋𝑌)−1 2(𝑤𝑅,𝑋𝑋 + 𝑤𝑃,𝑌𝑌)+∆𝐺0 2+1 2(∆𝐺𝑋𝑋 ≠+ ∆𝐺𝑌𝑌 ≠)+(∆𝐺0+ 𝑤𝑃,𝑋𝑌 − 𝑤𝑅,𝑋𝑌)2 8(∆𝐺𝑋𝑋 ≠+ ∆𝐺𝑌𝑌 ≠− 𝑤𝑅,𝑋𝑋 − 𝑤𝑅,𝑋𝑌) that is ∆𝐺𝑋𝑌 ≠= ∆𝑤 + ∆𝐺0 2+1 2(∆𝐺𝑋𝑋 ≠+ ∆𝐺𝑌𝑌 ≠)+(∆𝐺0+𝑤𝑃,𝑋𝑌−𝑤𝑅,𝑋𝑌)2 8(∆𝐺𝑋𝑋 ≠+∆𝐺𝑌𝑌 ≠−𝑤𝑅,𝑋𝑋−𝑤𝑅,𝑋𝑌) where −1 2𝑅𝑇𝑙𝑛 𝑓 𝑞𝑤 = (∆𝐺0+𝑤𝑃,𝑋𝑌−𝑤𝑅,𝑋𝑌)2 8(∆𝐺𝑋𝑋 ≠+∆𝐺𝑌𝑌 ≠−𝑤𝑅,𝑋𝑋−𝑤𝑅,𝑋𝑌) If the RC/PC formation energies are omitted (𝑤𝑃,𝑋𝑌 = 𝑤𝑅,𝑋𝑌 = 𝑤𝑅,𝑋𝑋 = 𝑤𝑅,𝑋𝑋 = 0) then −1 2𝑅𝑇𝑙𝑛 𝑓 𝑞=1 8 Δ𝐺0,𝑋𝑌 2 Δ𝐺𝑋𝑋 ≠+Δ𝐺𝑌𝑌 ≠ See also the reference: R. A. Marcus and N. Sutin, Electron transfers in chemistry and biology, BBA Reviews On Bioenergetics, 1985, 811, 265–322 Figure S1. The two half-reaction thermodynamic cycles and the associated thermodynamic properties such as: 1) one-electron reduction potential of X·/Y·, 𝐸𝑋/𝑌 ° 2) acidity constant of X·/Y· 𝑝𝐾a,X 3) hydrogenation potential of X·/Y·, 𝐸𝐻,𝑋/𝑌 ° 4) potential disparity of X·/Y· 𝜔X/Y 5) potential duality of X·/Y· 𝜇X/Y and three full-reaction thermodynamic thereof: 1) asynchonicity 𝜂X/Y 2) frustration 𝜎X/Y 3) free energy of reaction Δ𝐺0 The pKa’s and reduction potentials are calculated according to equations specified in Srnec et al, Phys. Chem. Chem. Phys., 2024, 26, 20280–20295. In the equations, the referential values are: 𝐺𝑠𝑜𝑙𝑣(𝐻+) is the free energy of solvation of proton in acetonitrile: -260.2 kcal mol-1. 𝐸𝑎𝑏𝑠 ° is the absolute potential of the ferrocenium/ferrocene reference in acetonitrile: 114.8 kcal mol-1 A4 B4 C2 D2 E Figure S2: The intrinsic reaction coordinates and the important intrinsic bond orbitals (IBOs) of one representative reaction from each set (A4, B4, C2, D2 and E). Table S1. The calculated thermodynamic characteristics of the H-atom acceptors (oxidants) Y• associated with the half-reaction thermodynamic cycle from Figure S2: the acidity constants 𝑝𝐾𝑎,𝑌𝐻 and 𝑝𝐾𝑎,𝑌., one-electron reduction potentials 𝐸°𝑌. and 𝐸°𝑌𝐻, proton-coupled reduction potential 𝐸°𝐻,𝑌, potential disparity 𝜔, potential duality 𝜇. The free-energy barrier in going from separated reactants to TS for self-exchange YY HAA reaction Δ𝐺𝑌𝑌 ≠ as well as the free energy of the reactant complex formed by two YY, 𝑤𝑅,𝑌𝑌, are also provided. Labels for Y in the first column are defined in Figure 3 in the main text. Y 𝑝𝐾𝑎,𝑌𝐻 [−] 𝑝𝐾𝑎,𝑌. [−] E°𝑌.[𝑉] 𝐸°𝑌𝐻[𝑉] 𝐸°𝐻,𝑌[𝑉] 𝜔[𝑉] 𝜇[𝑉] Δ𝐺𝑌𝑌 ≠[𝑘𝑐𝑎𝑙 𝑚𝑜𝑙−1] 𝑤𝑅,𝑌𝑌[𝑘𝑐𝑎𝑙 𝑚𝑜𝑙−1] A1 56.4 -5.4 -2.332 1.325 1.008 -1.424 -1.873 20.5 5.2 A2 18.7 -8.8 -0.334 1.293 0.772 0.132 -0.605 12.9 5.8 A3 31.8 -1.2 -1.033 0.919 0.845 -0.678 -0.782 7.3 0.0 A4 76.4 -23.5 -3.377 2.534 1.145 -1.406 -3.370 17.4 5.9 A5 79.4 14.0 -3.758 0.111 0.937 -3.241 -2.073 19.0 4.2 A6 55.1 -11.1 -2.427 1.491 0.832 -1.250 -2.182 21.0 4.6 A7 20.0 -27.8 0.189 3.017 1.370 1.298 -1.031 23.3 8.9 A8 15.6 -11.4 0.370 1.972 1.295 0.740 -0.217 8.5 5.7 B1 56.4 -5.4 -2.332 1.325 1.008 -1.424 -1.873 20.5 5.2 B2 76.4 -23.5 -3.377 2.534 1.145 -1.406 -3.370 17.4 5.9 B3 79.4 14.0 -3.758 0.111 0.937 -3.241 -2.073 19.0 4.2 B4 55.1 -11.1 -2.427 1.491 0.832 -1.250 -2.182 21.0 4.6 B5 56.9 -10.1 -2.632 1.332 0.735 -1.439 -2.284 20.4 4.9 C1 31.8 -1.2 -1.033 0.919 0.845 -0.678 -0.782 7.3 0.0 C2 18.7 -8.8 -0.334 1.293 0.772 0.132 -0.605 12.8 5.8 D1 31.8 -1.2 -1.033 0.919 0.845 -0.678 -0.782 7.3 0.0 D2 35.2 12.4 -0.917 0.431 1.163 -1.166 -0.131 8.4 1.1 E1 31.8 -1.2 -1.033 0.919 0.845 -0.678 -0.782 7.3 -0.2 SO₂H A3 18.8 4.0 5.9 19.5 2.9 1.7 0.1 0.0 2.1 COCl A3 19.5 3.1 -6.8 17.9 2.9 2.6 0.0 0.0 2.0 H A4 17.0 -3.2 0.4 -34.5 5.3 5.8 0.0 0.0 0.0 F A4 17.3 -3.0 2.3 -34.9 5.8 5.8 0.0 0.0 0.5 Br A4 16.9 -3.2 -0.6 -38.4 4.8 5.3 0.0 0.0 0.3 COOMe A4 16.2 -3.6 -12.9 -39.2 3.7 4.9 0.0 0.0 0.7 NO₂ A4 14.9 -3.5 -25.8 -40.9 3.6 4.9 0.0 0.0 0.0 CONH₂ A4 16.5 -3.2 -6.9 -40.3 4.7 4.7 0.0 0.0 0.5 SH A4 16.7 -3.9 9.4 -46.5 4.6 4.9 0.1 0.1 0.2 SO₂H A4 16.5 -2.9 -10.9 -40.2 2.3 4.2 0.0 0.0 0.1 COCl A4 15.3 -3.8 -23.6 -41.7 3.1 5.0 0.1 0.0 0.4 tBu A5 17.5 1.2 -36.2 -7.3 4.6 2.9 0.0 0.0 -0.4 Me A5 18.1 1.1 -35.7 -7.1 5.0 5.4 0.0 0.0 0.4 OPh A5 18.5 1.7 -32.2 -14.4 5.6 4.4 0.0 0.0 1.8 Ph A5 17.1 0.9 -36.1 -16.6 5.1 2.9 0.0 0.0 0.7 H A5 18.0 1.6 -41.9 -4.6 5.0 5.1 0.0 0.0 0.4 F A5 18.0 1.8 -40.0 -5.0 5.5 4.2 0.0 0.0 0.4 Cl A5 17.2 1.5 -42.3 -7.5 5.2 3.3 0.0 0.0 0.5 Br A5 17.6 1.6 -42.9 -8.5 4.4 4.9 0.0 0.0 0.7 COOMe A5 15.6 1.2 -55.2 -9.3 4.5 2.8 0.0 0.0 0.9 CH₂OMe A5 18.2 1.6 -39.2 -8.7 5.6 2.8 0.0 0.0 0.0 CN A5 15.0 1.4 -58.7 -8.3 5.3 4.5 0.0 0.0 0.9 NO₂ A5 12.2 1.3 -68.1 -10.9 1.5 3.7 0.0 0.0 -0.8 CONH₂ A5 16.8 1.6 -49.2 -10.4 5.1 4.8 0.0 0.0 1.6 SH A5 17.5 0.8 -32.9 -16.6 5.1 3.3 0.0 0.0 0.5 N(Me)CHO A5 16.1 1.0 -32.9 -16.2 3.2 3.3 0.0 0.0 1.5 CF₃ A5 16.1 1.7 -54.0 -4.8 4.3 5.0 0.0 0.0 0.6 SO₂H A5 15.6 1.9 -53.2 -10.3 4.5 3.1 0.0 0.0 1.4 COCl A5 12.8 1.0 -65.9 -11.8 4.4 2.8 0.0 0.0 0.8 tBu A6 22.0 3.6 9.7 -9.9 4.2 3.7 0.0 0.0 -0.4 Me A6 22.4 3.5 10.2 -9.6 4.3 4.3 0.0 0.0 -0.7 OPh A6 22.1 4.1 13.7 -16.9 4.9 3.5 0.1 0.0 0.8 Ph A6 22.3 3.4 9.8 -19.1 3.4 2.8 0.0 0.0 -0.3 H A6 22.5 4.0 4.0 -7.1 4.8 4.4 0.0 0.1 -0.3 F A6 22.8 4.2 5.9 -7.5 4.1 3.8 0.1 0.1 -0.7 Cl A6 22.4 3.9 3.7 -10.0 3.4 3.3 0.0 0.1 -0.6 Br A6 22.4 4.0 3.0 -11.0 3.3 3.4 0.0 0.1 -0.7 COOMe A6 22.0 3.6 -9.3 -11.9 2.3 2.5 0.0 0.1 -0.5 CH₂OMe A6 23.1 4.1 6.8 -11.2 4.0 3.8 0.1 0.1 -0.4 CN A6 22.0 3.8 -12.8 -10.8 3.6 3.1 0.0 0.0 -0.8 NO₂ A6 21.3 3.7 -22.2 -13.5 2.5 2.4 0.0 0.0 -1.2 CONH₂ A6 22.1 4.0 -3.3 -13.0 3.2 2.7 0.0 0.0 -0.6 SH A6 22.2 3.3 13.0 -19.1 3.6 4.1 0.0 0.1 0.0 N(Me)CHO A6 20.3 3.4 13.1 -18.7 1.9 2.5 0.0 0.1 0.3 CF₃ A6 21.9 4.1 -8.1 -7.3 4.2 4.2 0.1 0.1 0.0 SO₂H A6 22.2 4.3 -7.3 -12.8 2.0 2.1 0.1 0.1 -0.5 COCl A6 21.2 3.4 -20.0 -14.3 2.3 2.1 0.0 0.0 -0.8 tBu A7 7.5 -8.8 68.5 16.7 1.8 3.6 0.2 0.2 -3.8 Me A7 7.2 -8.9 69.0 17.0 2.2 3.8 0.2 0.2 -4.2 OPh A7 7.4 -8.3 72.5 9.6 2.1 4.0 0.2 0.2 -2.5 Ph A7 7.9 -9.0 68.5 7.4 2.4 4.1 0.2 0.2 -2.4 H A7 8.4 -8.4 62.8 19.4 2.8 3.9 0.2 0.2 -3.7 Cl A7 8.8 -8.5 62.4 16.5 3.4 4.4 0.2 0.2 -2.2 Br A7 9.3 -8.4 61.8 15.5 3.5 4.7 0.2 0.2 -2.2 COOMe A7 10.2 -8.8 49.4 14.7 2.4 5.1 0.2 0.1 -1.3 CH₂OMe A7 8.3 -8.3 65.5 15.3 0.9 0.8 0.2 0.3 -5.6 CN A7 11.1 -8.6 46.0 15.7 4.5 5.6 0.2 0.2 -1.3 NO₂ A7 11.9 -8.7 36.6 13.1 4.0 5.9 0.2 0.2 -0.8 CONH₂ A7 9.6 -8.4 55.4 13.6 0.8 4.4 0.2 0.1 -3.1 SH A7 6.3 -9.1 71.8 7.4 1.5 3.8 0.2 0.2 -3.4 N(Me)CHO A7 5.6 -9.0 71.8 7.8 0.7 2.5 0.3 0.2 -2.5 CF₃ A7 10.6 -8.3 50.7 19.3 3.0 4.4 0.2 0.2 -2.7 SO₂H A7 10.4 -8.1 51.4 13.8 2.1 5.2 0.2 0.1 -1.0 COCl A7 11.4 -9.0 38.8 12.2 3.2 5.8 0.2 0.2 -0.7 tBu A8 8.4 -7.0 55.6 35.4 2.8 2.3 0.2 0.4 -2.3 Me A8 7.9 -7.1 56.1 35.7 2.8 3.5 0.2 0.3 -2.4 OPh A8 8.0 -6.6 59.6 28.4 2.5 3.3 0.2 0.2 -1.0 Ph A8 8.5 -7.3 55.7 26.2 3.5 3.6 0.3 0.3 -0.5 H A8 9.4 -6.6 49.9 38.2 3.8 3.7 0.2 0.3 -1.7 F A8 9.7 -6.4 51.8 37.8 4.3 4.1 0.2 0.3 -1.0 Cl A8 10.0 -6.7 49.6 35.3 3.6 4.0 0.2 0.3 -0.7 Br A8 10.3 -6.7 48.9 34.3 3.9 3.9 0.2 0.3 -0.8 COOMe A8 10.7 -7.0 36.6 33.4 4.0 3.8 0.2 0.3 0.4 CH₂OMe A8 9.3 -6.6 52.7 34.0 4.0 2.0 0.2 0.5 -1.9 CN A8 12.2 -6.9 33.1 34.5 4.7 4.9 0.2 0.3 0.0 NO₂ A8 13.0 -7.0 23.7 31.8 4.8 4.8 0.2 0.3 0.7 CONH₂ A8 10.8 -6.7 42.6 32.3 1.8 2.6 0.2 0.2 -1.9 SH A8 6.8 -7.4 58.9 26.2 2.8 2.8 0.2 0.4 -1.7 N(Me)CHO A8 6.3 -7.2 59.0 26.6 1.3 2.1 0.3 0.3 -0.8 SO₂H A8 12.3 -6.4 38.6 32.5 2.8 3.2 0.2 0.2 -0.1 COCl A8 12.6 -7.3 25.9 31.0 4.8 4.7 0.3 0.4 1.2 B: X (R) Y Δ𝐺𝑋𝑌 ≠ Δ𝐺0,𝑋𝑌 𝜂𝑋𝑌 𝜎𝑋𝑌 𝑤𝑅,𝑋𝑌 𝑤𝑃,𝑋𝑌 −1 2RTln(fq) −1 2RTln(fqw) Δ𝑤 H B1 15.2 -3.7 -17.2 -25.2 4.6 4.2 0.1 0.1 1.8 NO₂ B1 16.3 2.0 -36.2 -32.7 3.5 2.2 0.0 0.0 -0.3 Me B1 14.6 -6.1 -12.1 -25.2 4.8 3.7 0.2 0.3 1.7 OMe B1 12.8 -10.0 -5.3 -24.8 4.3 3.8 0.5 0.6 1.8 Cl B1 14.8 -4.3 -18.1 -26.9 4.1 3.2 0.1 0.2 0.9 Br B1 14.9 -3.8 -18.8 -27.8 4.0 3.2 0.1 0.1 0.9 NH₂ B1 10.7 -16.2 5.7 -24.1 4.6 4.2 1.3 1.6 2.5 CN B1 16.0 0.1 -30.3 -30.6 4.0 2.9 0.0 0.0 0.5 CH₂OMe B1 15.9 -1.0 -26.5 -30.5 4.0 2.7 0.0 0.0 0.5 CONH₂ B1 15.8 -1.8 -23.1 -29.5 4.2 3.1 0.0 0.0 0.9 F B1 14.5 -5.2 -16.5 -24.4 4.4 3.5 0.1 0.2 1.3 SH B1 13.9 -8.1 -10.0 -29.2 4.3 3.5 0.3 0.5 1.7 N(Me)CHO B1 14.0 -6.8 -11.1 -30.3 4.2 3.5 0.2 0.3 1.5 COOMe B1 16.0 -0.7 -26.6 -30.2 3.2 2.7 0.0 0.0 0.0 SO₂H B1 15.3 -0.4 -26.8 -30.1 3.7 1.6 0.0 0.0 -0.6 COCl B1 16.5 1.8 -34.4 -33.6 2.9 2.2 0.0 0.0 -0.6 NMe₂ B1 10.0 -16.6 8.1 -25.6 4.5 2.8 1.5 2.0 2.0 H B2 12.4 -6.9 -16.8 -59.7 4.0 5.5 0.2 0.2 1.8 NO₂ B2 14.0 -1.2 -35.8 -67.2 4.0 5.9 0.0 0.0 1.4 Me B2 12.0 -9.3 -11.7 -59.7 4.1 5.2 0.4 0.5 1.8 OMe B2 10.7 -13.2 -4.9 -59.3 4.6 5.6 0.9 1.0 2.4 Cl B2 12.2 -7.4 -17.7 -61.4 4.3 5.6 0.3 0.3 1.9 Br B2 12.4 -7.0 -18.4 -62.3 4.4 5.7 0.2 0.2 2.0 NH₂ B2 9.3 -19.4 6.1 -58.6 4.0 5.6 2.2 2.4 2.6 CN B2 13.5 -3.1 -29.9 -65.1 4.0 5.8 0.0 0.0 1.6 CH₂OMe B2 13.5 -4.2 -26.1 -65.0 3.9 5.5 0.1 0.0 1.5 CONH₂ B2 13.1 -5.0 -22.7 -64.0 4.3 4.7 0.1 0.1 1.4 F B2 11.8 -8.4 -16.1 -58.9 4.1 5.8 0.4 0.3 1.9 SH B2 11.6 -11.3 -9.6 -63.7 4.4 5.4 0.7 0.8 2.3 N(Me)CHO B2 12.1 -9.9 -10.7 -64.8 4.3 5.5 0.5 0.5 2.2 COOMe B2 13.6 -3.9 -26.1 -64.7 4.4 5.7 0.1 0.0 1.7 COCl B2 14.5 -1.3 -34.0 -68.1 4.0 5.9 0.0 0.0 1.5 NMe₂ B2 8.9 -19.8 8.5 -60.1 4.6 5.5 2.4 2.7 3.1 H B3 9.4 -2.1 -59.1 -29.8 1.7 5.7 0.0 0.0 1.6 Me B3 4.8 -4.5 -54.0 -29.8 0.1 3.9 0.1 0.0 0.0 OMe B3 6.0 -8.4 -47.2 -29.4 1.9 4.2 0.4 0.2 1.2 Cl B3 4.2 -2.6 -60.0 -31.4 -0.2 2.5 0.0 0.0 -1.1 Br B3 3.9 -2.2 -60.7 -32.3 -0.1 2.4 0.0 0.0 -1.1 NH₂ B3 4.0 -14.6 -36.2 -28.7 1.3 4.4 1.2 0.8 1.5 CN B3 3.4 1.7 -72.2 -35.2 -0.9 -0.4 0.0 0.0 -3.1 CH₂OMe B3 4.0 0.6 -68.5 -35.1 -0.5 0.7 0.0 0.0 -2.2 F B3 4.2 -3.6 -58.4 -29.0 -0.2 3.0 0.1 0.0 -0.8 SH B3 4.1 -6.5 -51.9 -33.8 0.0 3.7 0.2 0.0 0.0 N(Me)CHO B3 4.2 -5.1 -53.1 -34.9 0.1 3.8 0.1 0.0 0.1 SO₂H B3 3.8 1.3 -68.7 -34.7 -0.6 0.0 0.0 0.0 -3.0 COCl B3 3.4 3.5 -76.3 -38.2 -0.9 -2.0 0.1 0.0 -4.2 NMe₂ B3 3.8 -15.0 -33.8 -30.2 1.3 3.4 1.3 1.0 1.2 H B4 18.1 0.3 -13.2 -32.3 4.7 3.6 0.0 0.0 1.9 NO₂ B4 19.5 6.0 -32.2 -39.8 2.6 2.1 0.2 0.2 -0.5 Me B4 17.4 -2.1 -8.1 -32.3 3.7 3.4 0.0 0.0 1.4 OMe B4 15.6 -6.0 -1.3 -31.9 3.6 2.6 0.2 0.3 1.1 Cl B4 17.8 -0.2 -14.1 -34.0 3.0 2.9 0.0 0.0 0.6 Br B4 17.9 0.2 -14.8 -34.9 3.7 2.1 0.0 0.0 0.4 NH₂ B4 13.3 -12.2 9.7 -31.2 4.4 3.7 0.7 0.9 2.5 CN B4 19.2 4.2 -26.3 -37.7 3.1 2.3 0.1 0.1 0.0 CH₂OMe B4 19.0 3.0 -22.5 -37.6 3.1 2.6 0.0 0.0 0.3 CONH₂ B4 18.9 2.2 -19.1 -36.6 2.9 1.9 0.0 0.0 0.0 F B4 17.3 -1.2 -12.5 -31.5 4.0 3.5 0.0 0.0 1.4 COOMe B4 19.3 3.3 -22.6 -37.3 2.6 1.9 0.0 0.0 -0.5 SO₂H B4 18.8 3.7 -22.8 -37.2 1.8 1.1 0.1 0.0 -1.5 NMe₂ B4 12.6 -12.6 12.1 -32.7 4.5 2.9 0.8 1.2 2.4 H B5 18.2 2.5 -17.5 -34.6 3.8 4.6 0.0 0.1 1.8 NO₂ B5 19.0 8.3 -36.5 -42.2 1.7 2.4 0.3 0.4 -1.0 Me B5 17.5 0.2 -12.4 -34.6 3.7 3.1 0.0 0.0 1.1 OMe B5 18.3 -3.7 -5.6 -34.3 3.7 5.0 0.1 0.0 2.2 Cl B5 17.6 2.0 -18.5 -36.3 3.3 3.1 0.0 0.0 0.7 Br B5 17.8 2.5 -19.1 -37.2 3.4 3.2 0.0 0.0 0.7 NH₂ B5 13.5 -9.9 5.3 -33.6 4.3 4.6 0.5 0.5 2.8 CN B5 18.9 6.4 -30.6 -40.1 3.1 3.5 0.2 0.3 0.5 CH₂OMe B5 18.6 5.3 -26.9 -40.0 2.2 3.0 0.1 0.2 -0.1 CONH₂ B5 18.6 4.5 -23.4 -38.9 2.8 2.8 0.1 0.1 0.2 SH B5 16.8 -1.8 -10.4 -38.7 3.5 3.6 0.0 0.0 1.4 N(Me)CHO B5 19.7 -0.5 -11.5 -39.8 2.8 4.7 0.0 0.0 1.6 COOMe B5 21.5 5.5 -26.9 -39.6 4.4 3.1 0.1 0.1 0.9 SO₂H B5 18.8 5.9 -27.2 -39.6 1.3 2.3 0.2 0.3 -1.2 COCl B5 19.2 8.1 -34.7 -43.1 1.6 2.3 0.3 0.4 -1.1 NMe₂ B5 15.4 -10.3 7.8 -35.0 3.9 4.6 0.6 0.6 2.8 C: X (R) Y Δ𝐺𝑋𝑌 ≠ Δ𝐺0,𝑋𝑌 𝜂𝑋𝑌 𝜎𝑋𝑌 𝑤𝑅,𝑋𝑌 𝑤𝑃,𝑋𝑌 −1 2RTln(fq) −1 2RTln(fqw) Δ𝑤 H C1 7.3 0.0 0.0 0.0 0.0 -0.1 0.0 0.0 0.0 NO₂ C1 8.8 5.7 -19.0 -7.6 -0.8 1.5 0.3 0.6 -0.2 Me C1 5.8 -2.4 5.1 0.0 0.1 -0.5 0.0 0.1 -0.1 OMe C1 2.6 -6.3 11.9 0.4 0.2 -1.1 0.4 0.5 -0.1 Cl C1 7.0 -0.5 -0.9 -1.7 -0.1 0.1 0.0 0.0 -0.1 Br C1 7.1 -0.1 -1.6 -2.6 -0.1 0.3 0.0 0.0 0.0 CN C1 8.4 3.9 -13.1 -5.5 -0.7 1.1 0.1 0.3 -0.2 CH₂OMe C1 8.2 2.7 -9.4 -5.4 -0.3 0.8 0.1 0.1 0.0 CONH₂ C1 7.9 1.9 -5.9 -4.3 -0.3 0.6 0.0 0.1 0.0 F C1 6.5 -1.5 0.7 0.8 -0.1 0.1 0.0 0.0 -0.1 SH C1 3.6 -4.4 7.2 -4.1 0.0 -0.9 0.2 0.3 -0.1 N(Me)CHO C1 5.0 -3.0 6.0 -5.1 0.2 -0.6 0.1 0.1 0.1 COOMe C1 7.9 3.0 -9.4 -5.0 -0.2 0.9 0.1 0.1 -0.1 SO₂H C1 9.1 3.4 -9.6 -4.9 -0.2 0.9 0.1 0.2 -0.2 COCl C1 8.9 5.6 -17.2 -8.4 -0.6 1.4 0.3 0.5 -0.1 H C2 10.3 1.7 18.7 4.1 4.4 -0.7 0.0 0.1 -1.0 NO₂ C2 15.3 7.4 -0.3 -3.5 5.4 1.8 0.3 0.1 0.1 Me C2 7.9 -0.7 23.8 4.1 5.4 -1.2 0.0 0.5 -0.8 Cl C2 10.2 1.2 17.8 2.4 4.8 -0.1 0.0 0.1 -0.7 Br C2 10.4 1.6 17.1 1.5 5.6 0.0 0.0 0.1 -0.3 CN C2 14.1 5.5 5.6 -1.4 5.3 0.9 0.2 0.0 -0.2 CH₂OMe C2 12.9 4.4 9.3 -1.3 5.6 0.3 0.1 0.0 -0.2 CONH₂ C2 12.5 3.6 12.8 -0.2 5.2 0.2 0.1 0.0 -0.4 F C2 9.5 0.2 19.4 4.9 5.5 -0.2 0.0 0.3 -0.4 COOMe C2 13.3 4.7 9.3 -0.9 5.2 0.7 0.1 0.0 -0.3 SO₂H C2 13.7 5.1 9.1 -0.8 5.3 0.9 0.2 0.0 -0.4 COCl C2 15.4 7.3 1.5 -4.3 5.6 1.3 0.3 0.1 -0.1 D: X (R1, R2) Y Δ𝐺𝑋𝑌 ≠ Δ𝐺0,𝑋𝑌 𝜂𝑋𝑌 𝜎𝑋𝑌 𝑤𝑅,𝑋𝑌 𝑤𝑃,𝑋𝑌 −1 2RTln(fq) −1 2RTln(fqw) Δ𝑤 H, H D1 4.4 0.7 21.2 -7.6 1.6 -2.9 0.0 0.1 -0.7 H, Me D1 3.6 -0.4 23.7 -7.5 2.2 -2.7 0.0 0.2 -0.7 H, tBu D1 4.0 -0.2 23.6 -7.7 1.1 -2.7 0.0 0.1 -1.5 H, F D1 4.5 0.0 21.1 -7.1 2.1 -2.5 0.0 0.2 -0.6 H, Cl D1 5.1 0.6 19.4 -8.0 2.2 -2.2 0.0 0.1 -0.6 H, Br D1 5.5 1.0 18.9 -8.5 2.1 -2.1 0.0 0.1 -0.8 H, COOMe D1 7.2 2.5 14.3 -10.7 1.9 -1.7 0.0 0.0 -0.4 H, CH₂OMe D1 4.0 -0.7 22.3 -7.3 2.3 -1.8 0.0 0.2 -0.4 H, CN D1 8.0 2.9 11.8 -11.2 1.8 -1.4 0.1 0.0 -0.3 H, NO₂ D1 9.2 4.0 7.7 -13.6 1.8 -1.1 0.1 0.0 -0.2 H, CONH₂ D1 6.8 2.2 16.3 -10.0 2.3 -2.0 0.0 0.0 -0.5 H, SH D1 3.6 -0.8 23.3 -9.4 1.3 -2.6 0.0 0.2 -0.9 H, N(Me)COH D1 2.3 -0.9 23.2 -9.7 -0.7 -3.7 0.0 0.1 -2.1 H, COCl D1 9.3 4.0 8.3 -13.5 1.9 -1.3 0.1 0.0 -0.3 Me, H D1 4.1 -0.4 23.7 -7.5 1.5 -2.7 0.0 0.2 -1.0 Me, F D1 3.8 -1.2 23.7 -6.5 1.2 -2.2 0.0 0.2 -1.1 Me, Cl D1 4.0 -0.8 22.0 -7.6 3.2 -2.0 0.0 0.3 -0.1 Me, COOMe D1 5.8 1.1 16.9 -10.4 1.9 -2.0 0.0 0.1 -0.9 Me, CONH₂ D1 5.2 1.0 18.4 -9.9 2.1 -2.6 0.0 0.1 -0.6 Me, SH D1 3.5 -1.5 25.1 -8.8 1.0 -2.6 0.0 0.2 -1.2 Me, N(Me)COH D1 1.4 -1.8 25.0 -9.1 -0.9 -4.2 0.0 0.2 -2.5 Me, COCl D1 8.0 3.1 10.8 -13.7 1.8 -1.4 0.1 0.0 -0.5 tBu, H D1 4.1 -0.2 23.6 -7.7 1.1 -2.7 0.0 0.1 -1.1 tBu, F D1 4.0 -0.6 23.4 -6.9 1.2 -2.5 0.0 0.1 -0.9 tBu, Cl D1 3.9 -0.3 21.7 -7.9 1.3 -2.3 0.0 0.1 -1.2 tBu, Br D1 4.4 0.0 21.1 -8.3 1.3 -2.2 0.0 0.1 -1.2 tBu, NO₂ D1 8.5 3.0 10.1 -13.8 1.5 -1.4 0.1 0.0 0.1 H, H D2 3.0 -6.7 10.0 7.4 0.5 -0.6 0.3 0.4 -0.7 H, Me D2 1.8 -7.7 12.5 7.5 1.1 0.2 0.4 0.5 -0.3 H, tBu D2 2.5 -7.5 12.4 7.4 1.4 0.4 0.4 0.5 -0.3 H, F D2 3.1 -7.4 9.9 7.9 1.1 0.7 0.4 0.4 -0.1 H, Cl D2 3.8 -6.7 8.2 7.0 0.9 0.8 0.3 0.3 -0.3 H, Br D2 4.2 -6.4 7.7 6.6 1.1 0.9 0.3 0.3 -0.3 H, COOMe D2 5.9 -4.8 3.0 4.3 0.8 1.2 0.1 0.1 -0.1 H, CH₂OMe D2 2.8 -8.0 11.0 7.7 1.1 0.8 0.4 0.6 -0.3 H, CN D2 6.4 -4.4 0.5 3.9 0.5 1.0 0.1 0.1 -0.3 H, NO₂ D2 7.1 -3.3 -3.6 1.4 0.2 1.5 0.1 0.0 -0.2 H, CONH₂ D2 5.5 -5.2 5.0 5.0 0.9 0.3 0.2 0.2 -0.6 H, SH D2 1.8 -8.1 12.1 5.7 0.9 0.5 0.5 0.6 -0.1 H, N(Me)COH D2 0.7 -8.2 12.0 5.4 -0.9 -0.6 0.5 0.5 -1.2 H, COCl D2 7.1 -3.3 -2.9 1.5 0.6 1.2 0.1 0.1 -0.3 Me, H D2 1.8 -7.7 12.5 7.5 1.1 0.3 0.4 0.5 -0.3 Me, tBu D2 1.2 -8.6 14.6 8.0 1.3 0.9 0.5 0.6 0.3 Me, F D2 2.0 -8.5 12.4 8.6 1.0 0.6 0.5 0.7 -0.3 Me, Cl D2 2.5 -8.1 10.8 7.4 1.1 1.0 0.4 0.5 -0.1 Me, COOMe D2 4.4 -6.2 5.6 4.6 0.8 1.2 0.3 0.3 -0.3 Me, CH₂OMe D2 1.5 -8.2 13.3 6.9 1.3 -0.2 0.4 0.7 -0.5 tBu, H D2 2.5 -7.5 12.4 7.4 1.4 0.4 0.4 0.5 0.0 tBu, Me D2 1.7 -8.6 14.6 8.0 1.5 0.3 0.5 0.7 0.1 tBu, F D2 2.5 -7.9 12.2 8.1 1.6 0.4 0.4 0.6 0.2 tBu, Cl D2 2.6 -7.6 10.5 7.1 1.1 0.5 0.4 0.5 -0.5 tBu, Br D2 3.1 -7.4 9.8 6.8 1.1 0.6 0.4 0.5 -0.5 tBu, NO₂ D2 6.0 -4.3 -1.2 1.2 0.4 1.1 0.1 0.1 0.1 E: X (R1, R2) Y Δ𝐺𝑋𝑌 ≠ Δ𝐺0,𝑋𝑌 𝜂𝑋𝑌 𝜎𝑋𝑌 𝑤𝑅,𝑋𝑌 𝑤𝑃,𝑋𝑌 −1 2RTln(fq) −1 2RTln(fqw) Δ𝑤 H, H E1 10.9 7.3 11.2 -15.0 2.0 -2.1 0.4 0.1 -0.5 H, Me E1 9.7 5.9 13.8 -14.7 2.8 -1.6 0.3 0.0 -0.4 H, Cl E1 11.4 7.3 9.4 -15.8 2.2 -1.5 0.4 0.1 -0.6 H, Br E1 11.8 7.6 8.9 -16.2 2.3 -1.1 0.4 0.1 -0.3 H, COOMe E1 13.1 9.3 5.7 -17.6 2.4 -1.2 0.6 0.3 -0.5 H, NO₂ E1 14.0 11.0 0.1 -19.6 2.1 -0.9 0.9 0.5 -0.4 H, CONH₂ E1 12.5 8.5 7.5 -16.9 2.4 -0.8 0.5 0.2 -0.2 H, SH E1 8.6 5.1 14.7 -17.0 2.4 -2.4 0.2 0.0 -0.8 H, N(Me)COH E1 7.7 5.2 15.2 -16.5 0.2 -3.3 0.3 0.0 -0.5 H, COCl E1 14.1 10.9 1.0 -19.7 2.2 -0.8 0.9 0.5 -0.4 Me, H E1 9.7 5.9 13.8 -14.7 2.8 -1.7 0.3 0.0 -0.4 Me, Me E1 8.5 4.6 15.9 -14.1 2.6 -2.0 0.2 0.0 -0.7 Me, Cl E1 10.1 5.9 11.7 -15.3 2.3 -1.6 0.3 0.0 -0.6 Me, Br E1 10.3 6.2 11.2 -15.6 2.4 -1.7 0.3 0.0 -0.5 Me, CH₂OMe E1 8.8 5.0 14.7 -15.0 2.7 -1.8 0.2 0.0 -0.6 Me, NO₂ E1 12.6 9.2 3.5 -19.7 2.3 -1.1 0.7 0.3 -0.4 Me, CONH₂ E1 11.2 7.2 10.1 -16.8 2.6 -1.8 0.4 0.1 -0.8 Me, SH E1 7.3 4.0 16.1 -16.1 2.6 -1.4 0.1 0.0 -0.2 Me, COCl E1 12.3 9.0 4.3 -19.6 1.8 -0.7 0.6 0.3 -0.2 tBu, Cl E1 10.2 5.9 11.9 -15.2 2.3 -1.2 0.3 0.1 -0.3 tBu, CH₂OMe E1 9.2 5.3 14.6 -14.8 2.9 -1.6 0.2 0.0 -0.7 tBu, NO₂ E1 12.8 9.2 3.4 -19.5 2.2 -0.7 0.7 0.4 -0.4 tBu, CONH₂ E1 11.4 7.5 9.8 -16.9 2.6 -1.6 0.4 0.1 -0.6 tBu, COCl E1 13.0 9.2 4.1 -19.6 2.9 -0.8 0.7 0.3 0.1