Strong Short‐Range Cooperativity in Hydrogen‐Bond Chains

Abstract Chains of hydrogen bonds such as those found in water and proteins are often presumed to be more stable than the sum of the individual H bonds. However, the energetics of cooperativity are complicated by solvent effects and the dynamics of intermolecular interactions, meaning that information on cooperativity typically is derived from theory or indirect structural data. Herein, we present direct measurements of energetic cooperativity in an experimental system in which the geometry and the number of H bonds in a chain were systematically controlled. Strikingly, we found that adding a second H‐bond donor to form a chain can almost double the strength of the terminal H bond, while further extensions have little effect. The experimental observations add weight to computations which have suggested that strong, but short‐range cooperative effects may occur in H‐bond chains.


Measurement of Conformational Free Energies of Molecular Balances
NMR spectra were recorded using either a Bruker Ultrashield 400 MHz, heteronuclear, or a Bruker Ascend 500 MHz with Prodigy cryoprobe, heteronuclear. Conformational free energies of the molecular balances were determined by 19 F NMR spectroscopy. Samples of molecular balances were prepared at the concentrations specified in dried solvent (see host-guest binding studies) and the conformer integral ratio determined by 19 F NMR (2048 scans). The integral ratio of the conformers was used to determine the conformational equilibrium constant, K. Conformational free energies were then calculated using the equation ΔG = −RTlnK, where K is defined according to the equilibrium shown in Figure 1. Synthesis, characterization and experimental data for the 0X series of compounds were reported in references. 1,2 Conformers were assigned as detailed in the Synthesis and Characterization section below. A conservative integration error estimate of ±0.025 in the minor conformer NMR peak integration when the major conformer relative integral was set to 1.000 (i.e. the integration ratio was [∫ major conformer = 1]/ [∫ minor conformer ± 0.025] ) was applied, resulting in asymmetric ΔG exp error margins as listed in Table S2 and plotted on figures. An example of determination of extreme conformer ratios is shown on page S35.
n.d. = not determined due to peak overlap in NMR spectra.

Dilution of 1H in CDCl 3
It was anticipated that balances containing both H-bond acceptors and donors might dimerize in apolar

Van't Hoff Analyses of compounds 1H, 2H and 3H.
Van't Hoff analysis was carried out on 1 mM samples of compounds 1H, 2H and 3H in dried CDCl 3 .
Samples were prepared and placed in an air-tight Wilmad-cap NMR tube. Spectra were obtained at a minimum of seven temperatures, beginning with the coldest. Samples were equilibrated at each temperature for 30 minutes within the spectrometer. Results are shown in Tables S4-S5       S14 Figure S16. Version of main text Figure 2 with error bars. Error bars (± 0.2 kJ mol −1 ) for 0X series (grey dots) lie within the points.

Computational Methods and Data
Molecular torsion balance equilibrium geometries and energies were calculated in the gas-phase using Spartan '14 at the levels of theory specified. Starting geometries for full minimizations of molecular balances were determined using an unconstrained equilibrium conformer search. Local minima of the unfolded conformer (without the internal CO … HO bond) were determined by taking this structure, rotating the formyl C-N bond by 180°, and performing a second equilibrium conformer search subject to this dihedral-angle constraint. The resulting structures in each formyl conformer were then re-subjected to an unconstrained equilibrium geometry calculation to obtain the local minimum geometry at the relevant level of theory. ΔE was determined as the difference in energy between the conformers in which the formyl oxygen (O conf, major) vs. formyl proton (H conf, minor) laid over the X-substituted ring.
Calculations were confirmed to represent energy minima by an absence of imaginary vibrational frequencies.
S15  Figure   OH groups were flipped 180° to create the specified number of H-bonds in a chain to the formamide (Fig. 3) S19 Table S10. Calculated gas-phase conformational energies for molecular balances minimized with a terminal intermolecular phenol molecule acting as a H-bond donor. Data are plotted in Figure 3C in the main text.

BSSE (Counterpoise) Corrected Interaction Energies for Complexes
BSSE (Counterpoise) corrected interaction energies were calculated using Gaussian '09 3 at the B3LYP level of theory. Initially, the complex of trimethylphosphine oxide with each compound/chain was subjected to a geometry minimization using the specified basis set. The interaction energy between the phosphine oxide and the rest of each of the complexes (i.e. an input where all atoms of the phenol derivative = fragment 1 and all atoms of trimethylphosphine oxide = fragment 2) was then determined using the counterpoise method to account for basis set superposition errors (BSSE), and the values are listed in Table S11. All calculations were determined to be minima by the lack of imaginary vibrational frequencies.

Synthesis and Compound Characterization
General NMR spectra were recorded using the following instruments: Bruker Ultrashield 400 MHz, heteronuclear; Bruker Ascend 500 MHz equipped with a DCH cryoprobe and 13  High-resolution mass spectroscopy was carried out using a Bruker micrOTOF II. Logan Mackay (University of Edinburgh) is thanked for this service.
Unless otherwise specified, the term "ether" relates to diethyl ether, "petroleum ether" relates to the 40-60 °C boiling point range grade and "dppf" refers to 1,1'-bis(diphenylphosphino)ferrocene. Where 'anhydrous' solvents (THF, toluene, DCM, ether) are specified these were purified using a "Glass Contour" brand solvent purification system (SPS). 'Anhydrous' DMF was purchased as such from Sigma-Aldrich or Acros organics and used as supplied. Glassware was dried overnight in an oven (130-140 °C). Reactions were carried out in septum-sealed vessels under an atmosphere of nitrogen. Solvents for other reactions, purification, etc. were purchased from commercial suppliers and used as supplied unless stated otherwise. Degassing was carried out by sonication whilst bubbling nitrogen through the solvent for 30 minutes. All reagents were purchased from commercial suppliers and used as supplied unless specified otherwise. Flash chromatography was carried out using Geduran silica gel 60. Analytical TLC was carried out using Merck silica gel 60 F254 plates. Visualization was carried out using UV light and/or "Goofy's dip", an aqueous solution containing molybdic acid, cerium sulfate and sulfuric acid.
The reaction mixture was added dropwise to water (75 mL) at 0 °C. Additional DCM (100 mL) was added and organics separated. The aqueous layer was then re-extracted with DCM (2 x 100 mL).

1D NMRS (full 2D assignments are given in the Conformer Assignment section below)
1 H NMR (CD3CN) 13 C NMR