¹⁵N and ¹H Solid-State NMR Investigation of a Canonical Low-Barrier Hydrogen-Bond Compound: 1,8-bis(dimethylamino) naphthalene

Abstract

Strong or low-barrier hydrogen bonds have been often proposed in proteins to explain enzyme catalysis and proton transfer reactions. So far ¹H chemical shifts and scalar couplings have been used as the main NMR spectroscopic signatures for strong H-bonds. In this work, we report simultaneous measurements of ¹⁵N and ¹H chemical shifts and N-H bond lengths by solid-state NMR in ¹⁵N-labeled 1,8-bis(dimethylamino) naphthalene (DMAN), which contains a well known strong NHN H-bond. We complexed DMAN with three different counter anions to examine the effects of the chemical environment on the H-bond lengths and chemical shifts. All three DMAN compounds exhibit significantly elongated N-H distances compared to the covalent bond length, and the ¹H^N chemical shifts are larger than ~17 ppm, consistent with strong NHN H-bonds in the DMAN cation. However, the ¹⁵N and ¹H chemical shifts and the precise N-H distances differ among the three compounds, and the ¹⁵N chemical shifts show opposite dependences on the proton localization from the general trend in organic compounds, indicating the significant effects of the counter anions on the electronic structure of the H-bond. These data provide useful NMR benchmarks for strong H-bonds, and caution against the sole reliance on chemical shifts for identifying strong H-bonds in proteins, since neighboring sidechains can exert similar influences on chemical shifts as the bulky organic anions in DMAN. Instead, N-H bond lengths should be measured, in conjunction with chemical shifts, as a more fundamental parameter of H-bond strength.

Graphical abstract

Introduction

Hydrogen bonding is ubiquitous in biological systems, and strong hydrogen bonds (H-bonds) have been proposed to play important roles in enzyme catalysis ^1–5 and proton transfer reactions in photoreceptors ^6–9 and ion channels ^10–11. However, the nature and function of strong H-bonds have been the subject of significant debate in the literature. Early NMR spectroscopic studies of the catalytic triad of α-chymotrypsin reported an unusually large ¹H chemical shift of ~18 ppm for the proton bound to Nδ1 of His57 ¹². Combined with subsequent findings of low ¹H/²H fractionation factors and large chemical shift perturbation, these data supported the existence of strong H-bonds in this and other enzymes ^13–15.

The fundamental criterion for classifying H-bond strengths is the potential energy curve (Scheme 1). Strong H-bonds are characterized by the fact that the ground vibrational mode for proton motion lies either near or above the energy barrier for proton transfer ^{12, 16–17}. Two types of strong H-bonds are especially noteworthy: single-well H-bonds, which have no barrier for proton transfer, and low-barrier H-bonds (LBHB), which has a double-well energy minimum (Scheme 1e, f). In both these strong H-bonds, the probability density function for proton position has a single maximum at the center of the two heteroatoms. A rigorous identification of the nature of H-bonds thus requires a study of the system’s electronic and energetic states, which have been conducted largely with computational methods ^18–20.

Scheme 1.

Physical and energetic properties of NHN hydrogen bonds and proposed potentialenergy wells for the DMAN*HX salts studied here.

Since potential energies of H-bonds are difficult to measure experimentally, distances have been used as alternative criteria for classifying H-bonds. For NHN compounds, these are the distance between the donor and acceptor nitrogens, R_NN, and the distances of the proton (H^N) from the donor (R_NH) and acceptor (R_N---H). At one end of the hydrogen bonding spectrum are weak or regular H-bonds (Scheme 1a), in which the ground vibrational energy is much lower than the proton-transfer barrier, thus the probability density function for the proton has two maxima, centered near each heteroatom. Weak NHN H-bonds exhibit a much shorter R_NH than R_N---H, an R_NN distance longer than 3.0 Å, and are primarily electrostatic in nature ^21–22. As the H-bonding strength increases, the H^N moves progressively towards the center of the two nitrogens, and R_NN decreases, making the bond more covalent than electrostatic. Strong NHN H-bonds (Scheme 1c, e, f) have R_NN ≤ 2.65 Å. The degree of covalency of the H-bonds is manifested by the chemical shift of the intervening proton and the two-bond J-couplings between the nitrogens, ^2hJ_NN ^23–27: both the ¹H chemical shift and ^2hJ_NN increase as the proton becomes more delocalized and the H-bond strength increases. For LBHBs (Scheme 1e), the shared proton between the donor and acceptor is expected to have a chemical shift above ~17 ppm ^28–29.

We became interested in better understanding H-bonds in biological systems through our studies of the influenza A M2 protein ³⁰. M2 forms a tetrameric proton channel in the virus envelope that is responsible for the acidification of the virion and the subsequent virus uncoating. The proton-selective residue in M2 is a single histidine, His37, in the transmembrane domain ³¹, which contains both a H-bond donor (N-H) and acceptor (N:) in the imidazole ring. Several mechanisms of proton conduction have been proposed. In the shuttle model, the His37 imidazole alternately protonates and deprotonates by proton transfer with water molecules ³². To generate the initial state for the next proton relay, the imidazole was thought to undergo ring flips and tautomerization, both of which have been observed experimentally ^33–34. The H-bonds in this shuttle model are weak NHO H-bonds between histidine and water. A high-resolution crystal structure reported tightly bound water molecules in the vicinity of the H37 tetrad ³⁵, and low-temperature imidazole H^N chemical shifts measured by NMR under conditions where proton transfer is frozen are less than 15 ppm, supporting weak to moderate H-bonds. Moreover, at high temperature when proton exchange is active, the imidazole H^N chemical shifts change to the water ¹H chemical shift value of ~4.9 ppm, indicating that the H-bonding partner of His37 sidechain is water ³⁶. These lines of evidence support the weak water-histidine H-bonded shuttle mechanism. In comparison, an alternative proton-conduction model posits that a neutral imidazole ring of one polypeptide chain forms a strong or low-barrier H-bond with a cationic imidazolium of a neighboring chain at mildly acidic pH, prior to channel activation at lower pH ^10–11. This model was proposed to explain the observations that the first two pK_a’s of the His37 tetrad are significantly elevated (8.2) compared to the typical pK_a of histidines in solution and moreover are unresolved ¹⁰, suggesting that the M2 channel is able to store +2 charges before it becomes conductive. It is thought that a strong or low-barrier imidazole-imidazolium NHN H-bond can provide the mechanism for this charge stabilization. An implication of this LBHB model is that the tetramer consists of two structurally distinct units, or a dimer of dimers. Partial evidence for dimer formation was reported as doubled NMR chemical shifts for many residues in the protein ^37–39; however, this chemical shift doubling was observed at high pH where all histidines are neutral, thus violating the requirement of an imidazole-imidazolium pair in the LBHB model.

These studies of H-bonding in M2 and other complex biological systems inspired us to obtain better and clearer solid-state NMR (SSNMR) signatures of strong H-bonds, to correlate multiple signatures, and to delineate the environmental factors that may affect the H-bond strengths or their manifestations. So far few studies have correlated the readily measureable ¹H and ¹⁵N chemical shifts with the less easily measured but more definitive parameter of R_NH distances. Given vibrational averaging effects and the low electron density of protons, N-H bond lengths obtained from X-ray crystallography are often imprecise and shorter than those measured by neutron diffraction and SSNMR. Thus, it is important to directly measure, in known strong H-bonds, R_NH distances by NMR and correlate them with ¹⁵N and ¹H chemical shifts. In this paper, we report a systematic study of these three NMR observables for the 1,8-bis(dimethylamino)-naphthalene (DMAN) family of strong H-bond compounds. X-ray and neutron diffraction of DMAN salts showed R_NN distances of 2.55 Å – 2.63 Å ^{22, 40–43}. For a small number of these compounds, R_N-H and R_N---H distances have been reported by X-ray crystallography and found to range from equivalent (1.31 Å) to off-center. ¹H NMR chemical shifts of >18 ppm have been reported for DMAN salts containing small inorganic counterions ^{28, 43}, but DMAN cations that are complexed with bulky organic anions, which better mimic protein sidechains, are less studied. We have thus chosen several DMAN compounds with organic counter anions, synthesized them with ¹⁵N and ¹³C labeling, and measured N-H bond lengths, ¹⁵N and ¹H chemical shifts. The results should provide useful NMR fingerprints of strong H-bonds in biological macromolecules.

Experimental

Synthesis of ¹⁵N, ¹³C-labeled DMAN

DMAN was synthesized using modified literature procedures outlined in Scheme 2 ^44–47. Naphthalene (783 mg, 6.12 mmol), NH₄ ¹⁵NO₃ (1 g, 12.3 mmol, 2.01 eq) and chloroform (6 mL) were added to a 50 mL round bottom flask and the mixture stirred. An addition funnel was added to the top of the flask and the whole system placed under N₂ gas. Trifluoroacetic anhydride (5 mL, 35.4 mmol, 5.8 eq) was added to the addition funnel and introduced to the reaction flask via slow drip over 1.5 hours. The solution became homogeneous and changed from colorless to rose to yellow during the addition. The reaction was stirred overnight under N₂. The resulting heterogeneous reaction mixture was then put on ice and 10 mL of H₂O was slowly added to the flask by addition funnel to quench excess TFAA. The contents were poured into a separatory funnel containing 60 mL H₂O and 20 mL CHCl₃. The organic layer was extracted three more times with 20 mL CHCl₃ and the combined organic fractions were dried over MgSO₄, filtered and the solvent removed on a rotary evaporator to yield an orange-yellow crude mixture consisting of a 3 : 1 mixture of ¹⁵N₂-1,8-dinitronaphthalene and ¹⁵N₂-1,5-dinitronaphthalene (1.25 g, 93%). The 1,8 isomer was purified first with a basic Al₂O₃ column and eluted with benzene (1,8 isomer: Rf = 0.4; 1,5 isomer: Rf = 0.76). The 1,8-rich fractions were collected and recrystallized three times with EtOAc. The supernatant of each crystallization was collected and the solvent removed under reduced pressure. The resulting solid was again recrystallized with EtOAc. The recrystallization process was repeated one more time to give a total of 608 mg (65% recovery, 49% overall yield) ¹⁵N₂-1,8-dinitronaphthalene as yellow plates. ¹H NMR (400 MHz, CDCl₃): δ 7.75 (t, ³J_HH = 7.9 Hz, 2H), 8.24 (d, ³J_HH = 8.3 Hz, 2H), 8.30 (dd, ³J_HH = 7.6 Hz, ³J_NH = 2 Hz, 2H).

Scheme 2.

Synthetic route to DMAN.

¹⁵N₂-labeled 1,8-dinitronaphthalene (604 mg, 2.74 mmol), FeCl₃ hexahydrate (22 mg, 3 mol%) and 45 mg Nuchar SA activated carbon were combined in a 25 mL round bottom flask equipped with a stir bar and reflux condenser. MeOH (6 mL) and 50–60% N₂H₄ (464 μL, 5.45 eq) were added, the reaction stirred and heated to 65 °C. After 5.5 hrs an aliquot was removed and the reaction progress was checked by ¹H NMR. There was 7% remaining starting material so two drops of hydrazine were added and stirred for another hour, after which no more starting material was observed. The reaction was cooled to room temperature, filtered over Celite and the filter cake-washed with MeOH. The filtrate was removed under reduced pressure to yield a crude oil (430 mg, 98%), which was the pure ¹⁵N₂-1,8-diaminonaphthalene compound as verified by NMR. ¹⁵N₂-1,8-diaminonaphthalene was used without purification for the next step. ¹H NMR (400 MHz, CDCl₃): δ 4.62 (bs, 4H, ¹⁵NH₂), 6.60 (d, ³J_HH = 7 Hz, 2H), 7.15–7.22 (m, 4H).

¹⁵N₂-1,8-diaminonaphthalene (430 mg, 2.68 mmol) was added to a 10 mL round bottom flask equipped with a stir bar and placed under N₂ gas. Anhydrous DMSO (4 mL) was quickly added, the contents stirred and then KOH (775 mg, 5.15 eq) was quickly added. The flask was placed in a room-temperature water bath, to which ¹³CHI (950 μL, 5.6 eq) was slowly added and stirred for 2.25 hrs. The temperature was then raised to 100 °C over 1 hr, at which point KOH (320 mg, 2.1 eq) was added. The reaction was stirred at 100 °C for another 40 minutes and then cooled to 50 °C. The reaction contents were quickly poured into a separatory funnel containing 150 mL 2 M NaOH and 50 mL Et₂O. The organic layer was washed 3 × 50 mL 2 M NaOH and then collected. The combined aqueous layers were extracted with 2 × 50 mL Et₂O. The combined organic layers were dried with MgSO₄, filtered and the solvent removed under reduced pressure, resulting in a red oil (532 mg, 2.42 mmol, 90%) that crystallized into needles upon refrigerating and was pure by ¹H NMR. δ 2.83 (dd, ¹J_CH = 138.7 Hz, ²J_NH = 4.1 Hz, 12H), 6.96 (broad d, ³J_HH = 7.4 Hz, 2H), 7.33 (t, ³J_HH = 7.6 Hz, 2H), 7.38 (d, ³J_HH = 7.7 Hz, 2H).

The ¹⁵N, ¹³C-labeled DMANH⁺ salts were recrystallized with three counterions: perchlorate (HClO₄), 4,5-dichlorophthalic acid (DCPA), and furan-3,4-dicarboxylic acid (FDCA). DMAN*HClO₄ was formed by dissolving DMAN in diethyl ether, stirring the solution and adding concentrated aq. HClO₄ dropwise. DMAN*HClO₄ precipitated as a brown material, and the addition of HClO₄ was ceased when no more precipitate formed. The stirring was then stopped, the supernatant pipetted out, the precipitate washed three times with diethyl ether and then dried under vacuum. The resulting goo was recrystallized twice from a minimal amount of boiling acetonitrile. DMAN*DCPA and DMAN*FDCA were formed by adding DMAN and the respective acid as solids into a 1.5 mL HPLC vial, dissolving them in a minimal amount of hot acetonitrile and then letting the solution cool. Afterwards, the DMAN*DCPA and DMAN*FDCA solutions were allowed to evaporate slowly at room temperature. The resulting crystals were recrystallized once more, washed with a very small amount of cold acetonitrile, and dried. The structures of DMAN*HClO₄ and DMAN*FDCA were solved using X-ray diffraction, since no structure existed for DMAN*HClO₄ and, despite multiple attempts, the exact unit cell obtained by Wozniak for DMAN*FDCA could not be reproduced.⁴² Instead, a unique unit cell with the same molecular composition (DMAN + FDCA + water) was obtained. The unit cell of DMAN*DCPA matched the literature unit cell and no further X-ray analysis was performed.

Solid-state NMR spectroscopy

All experiments were conducted using Bruker 400 and 600 MHz solid-state NMR spectrometers equipped with 4 mm or 3.2 mm magic-angle-spinning (MAS) probes. Typical radiofrequency (rf) field strengths were 40–50 kHz for ¹⁵N and 80 – 100 kHz for ¹H. The experiments were conducted at both ambient temperature and 95 K to investigate the degree of proton dynamics at ambient temperature. ¹⁵N cross-polarization (CP) spectra were measured under an MAS frequency of 7.58 kHz, while ¹H spectra were measured under 15 kHz MAS. ¹⁵N chemical shifts were externally referenced to the N-acetyl-valine ¹⁵N chemical shift of 122.0 ppm on the liquid ammonium scale. ¹H chemical shifts were referenced to the published values of the tripeptide formyl-MLF-OH ⁴⁸. N-H bond lengths were measured using the dipolar-doubled 2D ¹⁵N-¹H dipolar chemical-shift (DIPSHIFT) correlation experiment ⁴⁹ under 3.79 kHz MAS. ¹H homonuclear decoupling was conducted using the FSLG sequence ⁵⁰, which has a theoretical scaling factor of 0.577. The experimental scaling factor was measured using formyl-MLF-OH ^51–52 and found to be 0.577 at ambient temperature and 0.610 at 95 K. 2D ¹⁵N-¹H HETCOR spectra were measured under 7.58 kHz MAS. Lee-Goldburg (LG) CP ^53–54 with a 1 ms contact time and a 50 kHz effective spin-lock field was used to transfer the ¹H polarization to ¹⁵N without ¹H spin diffusion. ¹H homonuclear decoupling during the t₁ evolution period was carried out using the FSLG sequence with a transverse field strength of 80 kHz.

Results

X-ray diffraction data of selected DMAN compounds

We chose three compounds from the many known DMAN salts using two criteria ^{40, 42, 55–57}. First, each recrystrallization should give a single crystalline form, since bulk separation of polymorphic crystals is often incomplete, which would complicate spectral interpretation. Second, DMAN salts with a highly delocalized proton as well as more localized protons are needed to compare the chemical shifts and bond lengths for different strengths of H-bonds. Based on the literature, we chose DMAN*DCPA and DMAN*FDCA as examples of salts with bulky organic counter anions (Fig. 1) ⁴² that contain partly localized H^N protons and DMAN*HClO₄ as a potential model system with a delocalized H^N.

Figure 1.

Structures of the DMAN salts used in this study. (a) Chemical structures. (b–d) X-ray crystal structures. (b) DMAN*HClO₄. (c) DMAN*DCPA. (d) DMAN*FDCA. Hydrogen atoms are omitted for clarity. The structure for DMAN*DCPA is reproduced from reference ⁴².

We first verified the structures of the recrystallized DMAN salts by X-ray diffraction (Fig. 1). DMAN*HClO₄ has not been previously characterized by X-ray diffraction, thus a full atomic structure was determined. The unit cell for DMAN*DCPA matched the literature result while the unit cell of DMAN*FDCA differed significantly from the literature ⁴² (Table 1). Upon obtaining a full data set, we found that the FDCA in our crystal has a different spatial arrangement with respect to the DMAN cation. In addition, there is one equivalent of water in the DMAN*FDCA unit cell, which is absent in the other two salts, but the water molecule has a different position in our crystal from that of the literature.

Table 1.

Unit cell parameters of the crystal structures of the three DMAN salts used in this study.

Crystal Group	DMAN*HClO4	DMAN*DCPA	DMAN*FDCA
	Fdd2	P1	P21/n
α (°)	90.00	75.13	90.00
β (°)	90.00	71.23	91.65
γ (°)	90.00	70.62	90.00
a (Å)	12.55	9.30	11.24
b (Å)	46.88	9.63	10.28
c (Å)	10.24	13.03	16.69
Volume (Å3)	6022.69	1027.63	1928.04

Comparison of the three DMAN crystal structures reveals small but important differences. First, despite the common cation, the R_NN distance differs among the three compounds. The distance is the shortest for DMAN*HClO₄ (2.55 Å) and increases to 2.59 Å for DMAN*DCPA and 2.62 Å for DMAN*FDCA. Second, the inorganic perchlorate anion rests proximally above the NHN H-bond, roughly equidistant to the two dimethylamino groups, whereas the organic DCPA and FDCA anions lie on one side of the NHN H-bond. The nearest heavy-atom distance between the nitrogen donor/acceptors and the counter anion is 3.30 Å for DMAN*HClO₄, 3.85 Å for DMAN*DCPA, and 3.64 Å for DMAN*FDCA. The proximity and orientation of the anion to the NHN H-bond and the differences in R_NN may affect the localization of the proton by changing the chemical environment at the nitrogen donors and acceptors.

¹⁵N chemical shifts and N-H distances of DMAN salts

Fig. 2 shows the ¹⁵N CP-MAS spectra of the three DMAN compounds at 283 K and 95 K. Consistent with the crystal structure, the compound with the shortest R_NN distance and the highest unit cell symmetry, DMAN*HClO₄, exhibits a single ¹⁵N peak at 35.4 ppm. In comparison, DMAN*DCPA and DMAN*FDCA display two ¹⁵N chemical shifts: 37.8 ppm and 31.2 ppm for the DCPA salt and 39.5 ppm and 29.3 ppm for the FDCA salt, suggesting that the proton is located asymmetrically between the two nitrogens. DMAN*DCPA has a smaller ¹⁵N chemical shift difference (6.6 ppm) than DMAN*FDCA (10.2 ppm), but the average of the two ¹⁵N chemical shifts, 34.4 ppm, is close to the single ¹⁵N chemical shift of DMAN*HClO₄.

Figure 2.

¹⁵N CPMAS spectra of DMAN salts at 283 K and 95 K. (a) DMAN*HClO₄. (b) DMAN*DCPA. (c) DMAN*FDCA. The N-H and N^…H assignment is based on the DIPSHIFT data in Fig. 3.

In general, ¹⁵N chemical shifts of organic compounds follow the trend that larger (downfield) shifts correspond to more deprotonated nitrogens with longer R_NH bond lengths, while smaller (upfield) chemical shifts indicate more protonated nitrogens with shorter R_NH bond lengths. Interestingly, direct measurement of the N-H distance in the three DMAN compounds shows deviations from this rule. We used the dipolar-doubled DIPSHIFT experiment to measure the ¹⁵N-¹H dipolar coupling and R_NH distances (Fig. 3). Motion in these rigid organic crystals is negligible, thus the measured coupling constant directly indicates the internuclear distance. At ambient temperature, the single ¹⁵N peak of the perchlorate compound exhibits a ¹⁵N-¹H dipolar coupling of 5.39 kHz, which translates to an R_NH of 1.32 Å. This distance is in good agreement with the R_NH of 1.31 Å in the crystal structure of DMAN salts that contain an equally shared proton, such as DMAN*HBr ⁵⁶ and DMAN*tetrazole ⁴⁰. In DMAN*DCPA, the downfield peak has a 6.50 kHz coupling, corresponding to an R_NH of 1.24 Å, while the upfield ¹⁵N peak has a longer R_NH of 1.47 Å. For DMAN*FDCA, the downfield ¹⁵N peak has an R_NH distance of 1.23 Å while the upfield ¹⁵N peak has an R_NH of 1.49 Å. Thus, for the DCPA and FDCA salts, the more deshielded (or downfield) ¹⁵N resonance has a stronger ¹⁵N-¹H dipolar coupling or a shorter R_NH bond length than the upfield ¹⁵N peak, opposite the general trend, suggesting that the two nitrogens’ spectroscopic signatures are significantly perturbed by the counter anions.

Figure 3.

¹⁵N-¹H doubled-DIPSHIFT data of DMAN salts at 293 K (top) and 95 K (bottom). (a) DMAN*HClO₄. (b) DMAN*DCPA. (c) DMAN*FDCA. The data were obtained under 3.79 kHz MAS. Solid lines are best-fit simulations. The listed N-H dipolar coupling strengths are true values after taking into account the experimental FSLG scaling factor and the doubling factor. The ¹⁵N chemical shift and the N-H distances are also indicated.

We repeated the ¹⁵N CP-MAS and N-H DIPSHIFT experiments at 95 K to determine if there is noticeable proton dynamics at ambient temperature and if the H^N proton becomes more localized to one of the two nitrogens at low temperature. The ¹⁵N chemical shift showed negligible changes with temperature, but the linewidth broadened significantly for DMAN*HClO₄, from 55 Hz at ambient temperature to 109 Hz at 95 K. In comparison, the DMAN*DCPA and DMAN*FDCA ¹⁵N peaks show only minor line broadening of ~10 Hz. The ¹⁵N-¹H dipolar couplings remain unchanged within experimental uncertainty from 293 K to 95 K, indicating that the H^N position is insensitive to temperature in this range.

¹H^N chemical shifts of DMAN salts

We next measured the acidic proton’s chemical shift to correlate with the ¹⁵N chemical shift and R_NH bond lengths. The chemical shift differences between the H^N and aliphatic protons are sufficiently large that 1D ¹H MAS spectra are already effective in resolving them (Fig. 4). At 600 MHz under 15 kHz MAS, the 1D ¹H spectra show sufficient resolution at both 283 K and 95 K. For DMAN*HClO₄, the NHN⁺ proton resonates at 18.9 ppm while the methyl protons resonate at 3.50 ppm and 1.70 ppm, in good agreement with literature values ⁴³. In addition, two resonances at 6.87 ppm and 5.48 ppm were observed and assigned to aromatic protons.

Figure 4.

¹H MAS spectra of DMAN salts at 283 K (black) and 95 K (red) under 15 kHz MAS. Assignment is based on the general chemical shift trends of aromatic, H^N, and aliphatic protons. Asterisks indicate spinning sidebands.

The ¹H spectrum of DMAN*DCPA shows more resolved peaks. Two large ¹H chemical shifts at 20.76 ppm and 17.52 ppm are detected and likely correspond to the OHO⁻ proton of the DCPA anion and the NHN⁺ proton of the DMAN cation, respectively. The 8.59 ppm and 6.52 ppm peaks can be assigned to the naphthalene ring protons, while the 3.70 ppm and 1.41 ppm peaks are assigned to the N-methyl groups. DMAN*FDCA exhibited a single downfield ¹H peak at 17.26 ppm, despite having a similar OHO⁻ proton as in DMAN*DCPA. We attribute this to coincidental overlap of the NHN⁺ and OHO⁻ chemical shifts, which is consistent with the high intensity of this peak compared to the aromatic and aliphatic signals. Similar to DMAN*DCPA, the aromatic ¹H resonances are well resolved at 8.25 ppm and the methyl ¹H signals span from 3.63 ppm to −0.47 ppm. The −0.47 ppm resonance likely results from the methyl group that is flanked by the π-cloud of the FDCA anion and the naphthalene ring of a neighboring DMANH⁺ cation in the crystal lattice, which causes additional shielding from the aromatic electrons.

For DMAN*DCPA, the 1D ¹H MAS spectrum alone cannot unambiguously determine which of the two downfield signals belongs to the NHN⁺ H-bond. Thus, we measured 2D ¹⁵N-¹H HETCOR spectra to make a definitive assignment. Fig. 5 shows two ¹H-¹⁵N cross peaks at (17.4 ppm, 37.8 ppm) and (17.4 ppm, 31.2 ppm), thus confirming the assignment of the NHN⁺ proton to 17.4 ppm. The OHO⁻ proton then resonates at 20.76 ppm, consistent with the fact that it lies in a very short and strong H-bond. The 2D HETCOR spectra of the other two DMAN compounds (not shown) also confirmed the ¹H chemical shift assignment in the 1D ¹H spectra.

Figure 5.

2D ¹⁵N-¹H HETCOR spectrum of DMAN*DCPA at 293 K under 7.58 kHz MAS. The ¹H chemical shift is the true value after taking into account the FLSG scaling factor of 0.577.

Discussion

While hydrogen bonding has undisputed importance in biological and synthetic compounds, rigorous studies of the NMR signatures of hydrogen bonding in the solid state are relatively scarce. McDermott and coworkers investigated NHN H-bonds in imidazole - imidazolium complexes with different counterions by measuring temperature-dependent ¹⁵N chemical shifts and correlating these with crystallographically determined R_NN distances ⁵⁸. The R_NN were 2.65 – 2.68 Å, which are slightly longer than the cutoff for strong H-bonds. Their NMR data revealed the presence of fast proton exchange in some of the salts from 200 to 280 K, and the population of the two protonation states is strongly dependent on temperature and counter anions. At 210 K, these workers measured an R_NH distance of 1.10 Å, which is close to the covalent bond length of R_NH = 1.05 Å in imidazole ²². The temperature-dependent ¹⁵N chemical shifts, near-covalent R_NH bond lengths, and the modest R_NN distances, together indicate that the imidazole – imidazolium complexes contain weak to moderate H-bonds.

The intramolecular strong H-bonds formed by DMAN differ qualitatively from the intermolecular weak H-bonds in imidazoles. Fig. 6 summarizes the measured chemical shifts and R_NH distances in our DMAN compounds. All three compounds show ¹H^N chemical shifts larger than ~17 ppm, which is generally accepted as the lower limit for strong H-bonds ^27–29. Despite this large ¹H chemical shift, the nitrogens in DMAN*DCPA and DMAN*FDCA are not chemically equivalent, as seen by two resolved ¹⁵N chemical shifts (Fig. 2). This is caused by the fact that the bulky organic DCPA and FDCA anions are positioned asymmetrically with respect to the DMANH⁺ cation, creating different chemical environments for the two nitrogens. In comparison, smaller counter anions, such as mineral acids, perchlorate, and tetrafluoroborate, do not exert as large an effect on the ¹⁵N chemical environment, as seen from X-ray and ¹⁵N NMR studies of Limbach and coworkers ⁴¹.

Figure 6.

Summary of the ¹H and ¹⁵N NMR chemical shifts (green), N-H bond lengths (red), and crystallographically determined N---N distances (blue) of the three DMAN salts. DMAN*HClO₄ shows the most delocalized H^N or the strongest H-bond, the largest ¹H chemical shift and equivalent ¹⁵N chemical shifts. The two DMAN salts with bulky organic counter anions have different R_NH’s, inequivalent ¹⁵N chemical shifts, and smaller ¹H chemical shifts.

The distinct nitrogen environments affect the basicity of the nitrogen lone-pair electron and in turn the proton localization ²⁷. Both DMAN*DCPA and DMAN*FDCA show a partially localized proton based on the measured R_NH distances, and this proton localization correlates with a decrease in the ¹H chemical shift (Fig. 6). This correlation is understandable, since a more covalently bonded proton is more shielded by the heteroatom’s electrons. Similar correlations between ¹H chemical shifts and R_NH have been observed for DMAN salts formed from mineral acids and organic acids ⁴³. The mineral acids caused more equally shared H^N protons, and the resulting H^N chemical shifts ranged from 20.7 ppm to 18.8 ppm, whereas the organic acids caused more localized protons, and the ¹H chemical shifts ranged from 18.6 to 16.9 ppm. The large effects of the counter anion on the charge density profiles of the DMAN cation have been previously observed in DMAN salts such as DMAN*picrate ⁴¹ and DMAN*PF₆ ^{42–43, 55, 59–60}, and even minor polarization differences in the nitrogen lone pair have been shown to cause modest to large changes in R_NH and R_N---H.

While the two R_NH distances in DMAN*DCPA and DMAN*FDCA are not equivalent, both distances are much longer than the covalent bond length of 1.1 Å, and both compounds also have relatively short R_NN distances. These results indicate that DMAN complexed with DCPA and FDCA contain a strong NHN⁺ H-bond with an asymmetric double-well potential (Scheme 1d). In comparison, the NHN⁺ H-bond in DMAN*HClO₄ has a symmetric double-well potential with a low barrier (Scheme 1e), because a single ¹⁵N peak and a single ¹H^N peak was observed at both high and low temperatures. Proton motion in this LBHB is instantaneous but over a very small distance, thus making the two R_NH distances indistinguishable. That the DMAN*HClO₄ potential energy curve still has a barrier, rather than being barrier-less (Scheme 1f), is manifested by the fact that the ¹⁵N and ¹H peaks are both broadened at low temperature, while a barrier-less single-well potential should exhibit no temperature-dependent linewidths or chemical shifts.

In conclusion, the proton position along the H-bond and the strength of the H-bond in DMAN compounds are extremely sensitive to the distant effects of the anion. This sensitivity calls into question the likelihood of establishing and preserving strong H-bonds in complex macromolecules such as proteins. While strong and low-barrier H-bonds have been proposed in proteins such as chymotrypsin, ketosteroid isomerases and M2, the necessary distances are rarely measured. Instead, a large downfield ¹H chemical shift is often used as proof of strong H-bonds. However, a large ¹H chemical shift is not definitive proof of a strong H-bond, since sidechains and charged residues in close proximity to the H-bond of interest can exert significant influences on the ¹H chemical shift. For example, the π-bond node of aromatic sidechains and electrostatic interactions between a downfield proton such as in carboxylic acids (around 12–14 ppm) and another group can cause large downfield ¹H chemical shifts. On the other hand, small ¹H chemical shifts can rule out the existence of strong H-bonds. In other words, large ¹H chemical shifts are a necessary but not sufficient condition for strong or low-barrier H-bonds. For a strong H-bond to exist, the donor - acceptor distance must be significantly shorter than the sum of the van der Waals radii while the proton distance to the two heteroatoms must be significantly longer than the covalent bond length. While the heavy-atom distances can be readily measured by crystallography, the N-H or O-H distance cannot, thus NMR spectroscopy is an important tool for identifying strong H-bonds. In a true low-barrier H-bond, the proton in the H-bond should be equidistant between the donor and acceptor; in other words, the pK_a of the donor and acceptor heteroatoms should be matched. Finally, as well documented in the literature, if the protein of interest functions in solution, then water further reduces the likelihood of LBHBs compared to the solid state because water oxygen can compete with the heteroatoms while the water hydrogen can compete for the lone pairs in the LBHB ⁶¹. For example, Yamaguchi recently reported crystallographic evidence for a LBHB between para-coumaric acid and Glu46 in the photoactive yellow protein; but in solution a small ¹H chemical shift of 15.2 ppm was found for the OHO⁻ proton, and computational modeling further supported a regular H-bond ^{5, 8–9}. Thus, transient interactions between water and biomolecules substantially decrease the likelihood of LBHBs in solution. These considerations argue against the presence of LBHBs between the proton-selective histidines in the water-filled pore of the influenza M2 channel, in addition to the experimental evidence of imidazole H^N chemical shifts near the water frequency and the X-ray crystal structure of a water cluster at the histidine tetrad.