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Figure 1. O·O hydrogen bonds follow a linear relationship with donor and acceptor ΔpKa (ΔpKa = pKa Donor −pKa Acceptor). (A) As the donor/ acceptor ΔpKa increases from 0.0 (green) to 8.2 (red), the O·O hydrogen bond distance also increases (see footnote c). Lengths are reported from small molecule neutron diffraction structures (CSD IDs of NAHMAL01 and SUCACBO3 for green and red, respectively). (B) O·O hydrogen bonds in small molecule neutron diffraction structures. Reproduced from ref 26. Copyright 2015 American Chemical Society.

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Figure 2. 1H chemical shifts have a strong inverse correlation with hydrogen bond O·O distances. (A) As the hydrogen bond shortens, the 1H chemical shift of the hydrogen-bonded proton increases. This increase in chemical shift is due to deshielding of the hydrogen- bonded proton, which arises from the lengthening of the covalent O− H bond that accompanies shorter O·O (rO·O) and H·O (rO·H) distances, as has been widely discussed.27,69,115,116 (B) Correlation of O·O hydrogen bond distances from X-ray crystal structures of diverse small molecules with 1H chemical shifts from solid-state NMR of the same compound. Panel B is reproduced from ref 117. Copyright 1999 John Wiley & Sons, Inc. Data are from ref 118. The empirical fit of the data in panel B (black line) has been used extensively in the literature to estimate hydrogen bond lengths from chemical shift data.117−125

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Figure 3. Substituted salicylates have the same hydrogen bond lengths in nonpolar solvents and water.26 (A) Substituted salicylates used by Sigala et al. and their donor and acceptor ΔpKa values. (B) 1H NMR spectra of substituted salicylates in chloroform, acetone, and water at 4 °C. (C) 1H chemical shifts and estimated hydrogen bond lengths vs ΔpKa (slopes = 0.8−1.0 ppm/pKa unit; R2 = 0.82−0.92 and 0.027−0.032 Å/pKa unit; R2 = 0.82−0.93). (D) 1H NMR spectra for the hydrogen-bonded proton of 2-hydroxyphenylacetate in chloroform and in a 10% water/90% acetone mixture. (E) One-dimensional potential energy curve for displacement of the hydrogen-bonded proton between the donor and acceptor oxygen atoms of the water−hydroxide dimer. Calculations were performed at the B3LYP level using the 6-311++G(d,p) basis set. Panels B−E are reproduced from ref 26. Copyright 2015 American Chemical Society.

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Figure 4. Hydrogen bond distances derived from 1H NMR of small molecules follow a linear relationship with donor/acceptor ΔpKa for (A) O·O, (B) N·O, and (C) N·N hydrogen bonds. Hydrogen bond lengths were estimated from 1H chemical shifts of the hydrogen-bonded proton using the empirical correlation function from Figure 2A for O·O hydrogen bonds.117 N·O and N·N hydrogen bonds from small molecule crystal structures in the Cambridge Structural Database are, on average, 0.13 and 0.30 Å longer than O·O hydrogen bonds, respectively, reflecting the larger van der Waals radius of nitrogen (S. Alvarez, personal communication; see also footnote g). To account for this difference, N·O and N·N hydrogen bond distances predicted from 1H NMR chemical shifts were uniformly corrected by the factors mentioned above, consistent with a previous analysis from ref 126 of N·O hydrogen bonds (see also Text S3 in ref 50). This correction does not influence the scale of the length vs ΔpKa relationship and thus does not change the conclusions herein. The origin of the steeper relationship between O·O hydrogen bond lengths and ΔpKa from 1H NMR remains to be determined. One factor that may contribute to this difference is potential inaccuracies in converting 1H NMR chemical shifts to hydrogen bond lengths due to the scatter in the empirical relationship in Figure 2B. Values are reported in Tables S1−S5 and Table S1 of ref 26. Slopes are reported in Table 1.

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Figure 6. Linear relationship between hydrogen bond distance and ΔpKa that accounts for 86, 74, and 69% of the observed difference in hydrogen bond lengths for O·O, N·O, and N·N hydrogen bonds, respectively (R2 = 0.86, 0.74, and 0.69 for panels A−C, respectively). However, there remains variation that is beyond experimental error in neutron diffraction structures.48,49 In neutron diffraction structures of 3,5-dinitrosailcylate, the intramolecular hydrogen bond length varies on the order of 0.1 Å (A, green) despite standard uncertainties of these structures of 0.001−0.010 Å.50

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Figure 5. Hydrogen bond distances derived from 1H NMR and ultra-high-resolution (≤1.0 Å) X-ray crystal structures of proteins (cyan points) also follow a linear relationship with donor and acceptor ΔpKa for (A) O·O, (B) N·O, and (C) N·N hydrogen bonds. Dark and light gray points are for small molecule hydrogen bonds from neutron diffraction and 1H NMR, respectively. Hydrogen bond lengths from 1H NMR were, again, estimated using the empirical correlation function from Figure 2B, and lengths of N·O and N·N hydrogen bonds derived from this relationship were corrected by 0.13 and 0.30 Å, respectively, as in Figure 4. Values are reported in Tables S6 and S7. Slopes are reported in Table 1.

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Figure 8. Intramolecular hydrogen bonds are generally shorter than intermolecular hydrogen bonds of similar ΔpKa.18 (A−C) Comparison of intermolecular (black) and intramolecular (red) (A) O·O, (B) N·O, and (C) N·N hydrogen bond lengths from small molecule neutron diffraction structures.

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Figure 7. Common coupling relationship observed between oxyanion hole hydrogen bonds in pKSI, tKSI, and PYP. (A) Hydrogen bond networks in the active sites of two variants of ketosteroid isomerase (KSI) and photoactive yellow protein (PYP). Perturbations made to each residue are shown in parentheses. (B) Coupled changes in oxyanion hole hydrogen bond lengths follow a single correlation line with a slope of −0.30 ± 0.03. The “1° H-Bond” is the oxyanion hole hydrogen bond most directly affected by the perturbation (e.g., the Asp103·phenolate hydrogen bond for an Asp103Asn mutation in pKSI), and the “2° H-Bond” is the other oxyanion hole hydrogen bond (in this example the Tyr16·phenolate). N·O hydrogen bonds from small molecule crystal structures in the Cambridge Structural Database are, on average, 0.13 Å longer than O·O hydrogen bonds, reflecting the larger van der Waals radius of nitrogen (S. Alvarez, personal communication). To account for this, distances for N·O hydrogen bonds were corrected by 0.13 Å for direct comparison to O·O distances. This correction does not alter the interpretation of these results. Data are from ref 50.

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Figure 10. Crystal structures of pKSI D40N bound to 2,6- difluorophenolate (pKa = 7.1; orange; Protein Data Bank entry 2INX) and phenolate (pKa = 10.0; blue; Protein Data Bank entry 2PZV). (A) Overlay of pKSI·2,6-difluorophenolate (orange) and pKSI·phenolate (blue) structures. (B) Side view of the overlay in panel A highlighting the ∼15° rotation of 2,6-difluorophenolate relative to the phenolate ligand.54 This reorientation is consistent with repulsion that is partially relieved by the rotation. The 2,6-difluorophenolate hydrogen bond is longer than that for phenolates of the same pKa (not shown).54

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Figure 9. Intermolecular hydrogen bonds have angles of ∼180°, whereas intramolecular hydrogen bonds of similar lengths generally have bent hydrogen bonds. (A) Intermolecular and intramolecular O− H·O hydrogen bond lengths and angles from selected small molecule neutron diffraction structures (CSD IDs are UROXAL01, SUCAB03, LIHPAL01-02, and DHNAPH17, from top right). (B) O·O hydrogen bond lengths vs O−H·O angles for inter- and intramolecular hydrogen bonds from small molecule neutron diffraction structures collected in ref 27. Slopes in panel B are −133°/Å and −28°/Å for intra- and intermolecular hydrogen bonds, respectively.

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Figure 12. Thermodynamic framework for dissecting hydrogen bond energetics in different environments. Equilibria for hydrogen bond formation (ΔGf HB, horizontal lines) are depicted in water (front, blue) and a nonpolar solvent (back, tan) for a ground state (top line, ΔGf,GS HB ) and a transition state (bottom line, ΔGf,TS HB ). Equilibria for transfer between water and a nonpolar solvent (ΔEnvironment) are depicted for non-hydrogen-bonded (left) and hydrogen-bonded (right) ground state (ΔGGS,−HB Tx and ΔGGS,+HB Tx , top line) and transition state (ΔGTS,−HB Tx and ΔGTS,+HB Tx , bottom line) species. Finally, a schematic reaction from ground state to transition state (vertical “Reaction” coordinate) is depicted in water (front) or a nonpolar solvent (back) without (ΔGW,−HB ⧧ and ΔGNP,−HB ⧧ , left) and with (ΔGW,+HB ⧧ and ΔGNP,+HB ⧧ , right) hydrogen bond formation.

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Figure 11. Hydrogen bond formation (ΔGHB) between an acid [A (blue) or A′ (red)] and a base [B (blue) or B′ (red)], where ΔGHB′ (red) is more favorable than ΔGHB (blue).

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