Hydrogen Bonding Between Ions of Like Charge in Ionic Liquids Characterized by NMR Deuteron Quadrupole Coupling Constants—Comparison with Salt Bridges and Molecular Systems

Abstract We present deuteron quadrupole coupling constants (DQCC) for hydroxyl‐functionalized ionic liquids (ILs) in the crystalline or glassy states characterizing two types of hydrogen bonding: The regular Coulomb‐enhanced hydrogen bonds between cation and anion (c–a), and the unusual hydrogen bonds between cation and cation (c–c), which are present despite repulsive Coulomb forces. We measure these sensitive probes of hydrogen bonding by means of solid‐state NMR spectroscopy. The DQCCs of (c–a) ion pairs and (c–c) H‐bonds are compared to those of salt bridges in supramolecular complexes and those present in molecular liquids. At low temperatures, the (c–c) species successfully compete with the (c–a) ion pairs and dominate the cluster populations. Equilibrium constants obtained from molecular‐dynamics (MD) simulations show van't Hoff behavior with small transition enthalpies between the differently H‐bonded species. We show that cationic‐cluster formation prevents these ILs from crystallizing. With cooling, the (c–c) hydrogen bonds persist, resulting in supercooling and glass formation.


Introduction
Salt bridges play an important role in proteins and supramolecular chemistry. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] They are characterized by the sum of two types of intermolecular interaction:ionic bonding and hydrogen bonding.S alt bridges are very strong because hydrogen bonding adds to the attractive Coulomb forces between the oppositely charged residues.T ypical examples of salt bridges involve the interaction of negatively charged carboxylate groups,a sf ound, for example,i ng lutamic acid and aspartic acid, with positively charged ammonium groups, as present, for example,i nl ysine or arginine.A ni mportant example is the salt bridge between primary ammonium and carboxylate groups in biological structures, + NÀH···O À . [7][8][9][10][11][12][13][14] Theenergetics of salt bridges are typically dominated by the Coulomb interaction between the charge centers,but the total interaction remains directional due to the hydrogen bonds. Thus,salt bridges are crucial for the structure,dynamics,and function of proteins.T his type of Coulomb-enhanced hydrogen bonding is typical for ionic liquids,which consist solely of ions. [15][16][17][18][19] So-called "doubly ionic hydrogen bonds" (DIHB) usually result in the formation of ion pairs. [20][21][22][23][24][25] However,Hbonds in ionic liquids are manifold. They can also be present between ions of like charge. [26][27][28][29][30][31][32][33][34][35][36] This has recently been shown for cation-cation interaction by means of vibrational spectroscopy and neutron diffraction (ND). [37,38] In this case,t he Coulomb forces are repulsive and need to be counterbalanced by hydrogen bonding.F or hydroxyl-functionalized ILs,both types of ionic interaction are present in equilibrium: hydrogen bonding (O À H···O) between oppositely charged ions (c-a) and between like-charged ions,h ere cations (c-c). In principle,s olid-state NMR spectroscopy allows to distinguish between (c-a) and (c-c) interactions if the proton exchange is slow on the NMR time scale. [39][40][41][42] Although very sensitive to the electronic environment and hydrogen bonding, deuteron quadrupole coupling constants (DQCCs) have been rarely used to characterize salt bridges in proteins, supramolecular complexes,a nd the related (c-a) type of interaction in ionic liquids. [43,44] DQCCs of OH groups that are involved in hydrogen bonding to like-charged ions (c-c) are completely unknown. Them ain challenge here is that in the liquid phase,the proton exchange between (c-a)-and (cc)-bound species is usually fast on the NMR time scale, resulting in averaged coupling parameters and prohibiting to distinguish like-charge attraction (c-c) from the regular ion-pair formation (c-a). This situation may change favorably in the supercooled or glassy state of ionic liquids.
It is the purpose of this work to show that the DQCCs and the related asymmetry parameters of the electric-field gradients provide valuable information about the strength and directionality of both types of hydrogen bonding present in hydroxyl-functionalized ionic liquids.W ef ind one NMR coupling parameter for ILs exhibiting (c-a) ion pairing, but two if additional (c-c) cationic-cluster formation is present. We measure the first DQCCs describing hydrogen bonding between ions of like charge and show that they are unexpectedly smaller than those in the (c-a) ion pairs. Solid-state NMR spectroscopy allows for counting the (ca)-and (c-c)-bound species and thus providing cluster populations.Overall, we show that cationic-cluster formation in well-suited ILs depends on the polarizability of the cations and the length of the hydroxyalkyl chain. If cationic-cluster formation is present, the ILs cannot be crystallized and form glasses.The solid-state NMR measurements are supported by density functional theory (DFT) calculations,d ifferential scanning calorimetry (DSC) measurements,a nd MD simulations,w hich provide molecular insight into the H-bond patterns and the delicate balance between the two types of ion pairing.

Synthesis and Preparation of Suitable Hydroxyl-Functionalized ILs
We synthesized the ionic liquids 1-(2-hydroxyethyl)-  Information). TheI Ls were prepared in two steps:W e synthesized the OH-functionalized onium halides,w hich were then used for the anion metathesis to create the desired cation/anion combinations.F or the synthesis of the onium salts,wemixed equimolar amounts of the heterocyclic amine and the corresponding w-halide alcohol and heated the mixture up to 110 8 8Cf or 1h.U pon cooling,t he mixture started to crystallize.T he crude products were recrystallized from acetone/acetonitrile mixtures to obtain the colorless crystalline product. Fort he metathesis of the anion (bis(trifluoromethylsulfonyl)imide, [NTf 2 ] À ), we mixed equimolar amounts of the onium halide and lithium-bis(trifluoromethylsulfonyl)imide as aqueous solutions for 1h.T wo phases were obtained. Thel ower phase was washed several times with water until no residual bromine could be detected with silver nitrate solution. Ther esulting colorless ionic liquids were dried for several hours under vacuum at 60 8 8C. For detailed synthesis procedures and analytical data of each ILs see the Supporting Information.
As described, all ILs (I-IV)i nclude the same [NTf 2 ] À counteranion and the same hydroxyl-functional groups at the cations.T his set of hydroxyl-functionalized ILs allows studying cationic-cluster (c-c) formation depending on the polarizability of the cation and the hydroxyalkyl chain lengths (see Scheme 1). Hydrogen/deuterium (H/D) exchange was achieved by mixing the ILs with D 2 Oand removing water several times until nearly 100 %d euteration was reached as confirmed by 1 HNMR. All samples were dried under vacuum (at 3 10 À3 mbar) for several days and the final water concentration (< 15 ppm) was checked by Karl-Fischer titration.

Deuteron Quadrupole Coupling Constants from Solid-State NMR Spectroscopy
Thes olid-state deuterium NMR spectrum is determined by two measurable parameters:t he quadrupole coupling constant DQCC, c D = (e 2 q zz Q/h), and the asymmetry parameter, h = (q xx Àq yy )/q zz ,which describes the principle elements q of the electric-field gradient tensor. [45][46][47] TheD QCC is am easure of the magnitude of the electric-field gradient at the deuterium site,w hile the asymmetry parameter provides information about the shape of the electric-field gradient. For example,a na symmetry parameter of zero suggests ac ylindrical symmetry of the electric-field gradient tensor along the OÀDb ond. [47] We determined the DQCCs from the solidstate deuterium NMR powder patterns for ILs I-IV at 183 K (see Supporting Information).
The 2 HNMR experiments were performed at aL armor frequency of w z /2p = 61.42 MHz on aB ruker Avance-400 spectrometer using ah igh-power probe with a5mm horizontal solenoid coil. All 2 HNMR spectra were obtained by Fourier transformation of the quadrature-detected phasecycled quadrupole echo arising in the pulse sequence (908 8 xt 1 -908 8 y -t 2 -acquisition-t), where t 1 = 20 ms, t 2 = 21 ms, and t is arepetition time of the sequence during the accumulation of the NMR signal. Theduration of the p/2 pulse was 1.6-1.7 ms. Spectra were typically obtained with 50-20 000 scans with arepetition time ranging from 0.5 to 15 s.
All spectra show purely Pake-powder patterns. [39,40] We obtained the DQCCs and the asymmetry parameters from aproper line-shape analysis.T he deconvoluted spectra result from ap arameter optimization guided by visual inspection. Them easured, analyzed, and modelled spectra are shown in Figure 1. Thee xperimental accuracy of c D and h is AE 3kHz and AE 0.01, respectively,f or the dominant component, and AE 5kHz and AE 0.02, respectively,for the second component of the Pake spectra. ForI LI we observed as ingle Pakespectrum with c D = 220 kHz and h = 0.08 (see Figure 1a). In contrast, we could deconvolute the measured spectrum of IL II into two Pake patterns.O ne deconvoluted spectrum exhibits almost the same NMR parameters as IL I (c D = 221 kHz; h = 0.09), obviously describing the same type of O À D···O interaction in both ILs.H owever,t he second deconvoluted spectrum is clearly different and shows asmaller DQCC and asymmetry parameter,n amely c D = 180 kHz and h = 0.05 (see Figure 1b). Smaller DQCCs suggest that the OÀ D···O interaction is stronger.W ek now from recent IR and ND experiments that (c-c) hydrogen bonds are stronger than the (c-a) ones,resulting in significant IR red-shifts of the OH/ OD stretching frequencies,lengthening of the R(O À H) bonds and shortening of the intermolecular R(OÀH···O) and R(O···O) distances. [37,38] Thus,w ec onclude that the larger DQCC in both ILs of about 220 kHz can be related to the conventional (c-a) ion pairs,w hereas the smaller DQCC of about 180 kHz characterizes the (c-c) interaction in cationic clusters.T he smaller asymmetry parameter, 0.05 vs.0 .09, indicates that the hydrogen bond is more linear in (c-c) than in (c-a) hydrogen bonds,ina ccord with the above finding of stronger H-bonds in the cationic clusters.T he fact that IL I shows (c-a) interactions only,w hereas IL II includes both types of H-bond interaction, (c-a) and (c-c), is related to the different polarizabilities of the piperidinium and pyridinium cations.T he pyridinium cation is highly polarizable and thus interacts favorably with the [NTf 2 ] À anion, leaving the hydroxyl group free to interact with other OH bonds by forming cationic clusters.Incontrast, the "hard" piperidinium cation in ILs I and III interacts less favorably with the counteranion, which is then available for interacting with the OH group of the cation, resulting in typical H-bond enhanced (c-a) ion pairs.
If we increase the hydroxyalkyl chain length from ethyl to propyl for both types of ILs,w em easure two DQCCs with c D = 230 kHz and c D = 205 kHz for IL III,a nd c D = 215 kHz and c D = 165 kHz for IL IV.A gain, the larger values c D = 230 kHz and c D = 215 kHz can be assigned to (c-a) interactions,w hereas the smaller values c D = 205 kHz and c D = 165 kHz reflect stronger (c-c) cationic interactions.T he fact that both ILs form cationic clusters despite the differently favorable cations is related to the increasing distance between the positively charged ring systems and the OH functional groups within the cations.T he longer tethers allow for enhanced cationic-cluster formation (see Scheme 1). All DQCCs are shown in Figure 2, and values measured for salt bridges in supramolecular complexes or proteins are compared to (c-a) IL interactions and those measured for molecular liquids mimicking the (c-c) interaction in the ILs. Although the (c-c) DQCCs are slightly lower than those observed for solid methanol, ethanol, and tert-butanol, the (ca) DQCCs range between the values of ice and liquid water. [48][49][50][51][52][53][54][55][56][57] The(c-a) DQCCs are significantly larger than the measured values for salt bridges,w hich range from 156 to 171 kHz, indicating that the H-bond-enhanced Coulomb interaction in (c-a) ion pairs of these ILs is weak. The molecular ions have low surface charge densities,resulting in strongly attenuated Coulomb attraction and DQCCs similar to those in H-bonded liquids.Itshould be noted that the (c-a) DQCCs in the hydroxyl-functionalized ILs considered in this study are about 30 kHz higher than those measured for the protic IL triethylammonium bis(trifluoromethylsulfonyl)imide [Et 3 NH][NTf 2 ]due to weaker hydrogen bonding. [58] Why Are (c-c) Hydrogen Bonds Stronger Than (c-a) Hydrogen Bonds?
So far,w es howed that deuterons involved in (c-c) Hbonds exhibit smaller DQCCs than those bound in (c-a) species,i ndicating stronger binding.T hese results are in accord with stronger red-shifted IR bands and downfieldshifted NMR proton chemical shifts for hydrogen bonding between ions of like charge as observed experimentally. [36][37][38] At afirst glance,itseems to be counterintuitive that the (c-c) hydrogen bonds are stronger than the (c-a) hydrogen bonds, although the first are weakened by repulsive,a nd the latter are enhanced by attractive Coulomb forces.T ou nderstand why hydrogen bonding is stronger in (c-c) than (c-a) clusters, we employed B3LYP-D3/6-31 + G* calculations performed with the Gaussian 09 program and analyzed with the NBO 6.0 program. [59][60][61][62][63][64] To calculate the (c-a) and (c-c) clusters using the same method, we have used the well-balanced but small 6-31 + G* basis set. It includes polarization as well as diffuse functions,a nd has been shown to be suitable for calculating hydrogen-bonded clusters of like-charged ions. [31,32,65,66] The 6-31 + G* basis set is also chosen for better comparison with earlier studies of molecular and ionic clusters. [17,[67][68][69] We also show that the salient properties of these clusters can be robustly calculated with both smaller und larger basis sets. (see Supporting Information). Firstly,w efully optimized the cationic clusters of the IL IV,[ HOC 3 Py][NTf 2 ], up to cyclic tetramers.T he calculated vibrational frequencies were all positive,s howing that we calculated at least local minimum structures.A dditionally,w ec alculated the DQCC, c D ,f or each deuteron present in the (c-a) and (c-c) configurations. TheD QCC describes the coupling between the nuclear quadrupole moment, eQ,and the principle component of the electric-field gradient tensor, eq zz ,atthe deuteron nucleus.It could be shown that the relation between c D and eq zz is given by the equation where the factor 2.3496 converts between the units.I n principle,t he DQCC can be obtained by multiplying the calculated principle component of the electric-field gradient tensor, eq zz ,ofthe OD hydroxyl groups in the (c-a) and (c-c) clusters of IL IV with ac alibrated nuclear quadrupole moment, eQ. Thec alibrated eQ is obtained by plotting the measured gas-phase quadrupole coupling constants from microwave spectroscopy vs.t he calculated electric-field gradients for small molecules,s uch as H 2 O, CH 3 OH, or formic acid, as described by Huber et al. [45,46,70] Thes lope gives ar easonable value of eQ = 295.5 fm 2 ,w hich should be used for calculating DQCCs with the B3LYP-D3/6-31 + G*

b) Comparison of the (c-c) hydrogen-bond
DQCCs with those for water,methanol, ethanol, and tert-butanol in the liquid and solid phases as well as in phenols. [49][50][51][52][53][54][55][56][57] The DQCCs for the (c-a) hydrogen bonds are related to those of salt bridges in proteins. [13,[43][44] method. Forthis set of molecules,itcould also be shown that the principal axis of the deuteron electric-field gradient is nearly axially symmetric and lies along the direction of the O À Dbonds. [25] We cannot expect that the calculated DQCCs of (c-a) and (c-c) clusters represent the measured NMR values in the crystalline or glassy state of IL IV.Thus,wefocus on the differences of the c D values in (c-c) clusters relative to those obtained for the (c-a) clusters,which can be compared to Dc D ((c-a)À(c-c)) obtained from the NMR experiment. These spectroscopic features can be rationalized in the framework of natural bond orbital (NBO) analysis. [63,64] NBO analysis of the same (c-a) and (c-c) clusters shows at ypical strong n o !s* OH donor-acceptor interaction with corresponding second-order stabilization energies DE (2) n!s* and estimated total charge transfers of q CT for OH···O hydrogen bonds.
Thefact that the + OH···OH + structural motif of the (c-c) species exhibits smaller DQCCs results from significant charge transfer from the non-bonding electron pair of the oxygen into the + OH anti-bonding orbital, leading to strong IR red-shifts of n OH ,e nhanced downfield NMR chemical shifts, d 1 H, and, in our case,s maller deuteron quadrupole coupling constants, c D .T his charge transfer is stronger than the one between cation and anion in the structural motif + OH···O À .T his is true in particular for hydrophobic anions such as [NTf 2 ] À ,where the negative charge is distributed over the entire molecule,significantly reducing the surface charge density and thus the proton-acceptor ability of the anion. The results are summarized in Figure 3. Thec alculated secondorder stabilization energies, DE (2) n!s* ,a nd the transferred charges, q CT ,f or the (c-c) clusters are plotted vs.t he differences Dc D ((c-c)À(c-a)) with zero indicating the average DQCC calculated for (c-a) clusters.F igure 3shows that both NBO parameters increase almost linearly with decreasing DQCCs for (c-c) hydrogen bonding,i ndicated by an egative Dc D ((c-c)À(c-a)). Obviously,b oth properties characterize hydrogen bonding and cooperativity in as imilar way.T he largest stabilization energies, DE (2) n!s* ,a nd most intensive charge transfer, q CT ,isobserved for the (c-c) cyclic tetramers due to cooperative effects. [64,65,[67][68][69] Charge from the nonbonding electron-pair orbital of the oxygen of afirst cation is donated into the OH anti-bonding orbital of asecond cation. Thel arger negative charge at the OH oxygen at the second cation can now be transferred into the OH anti-bond of another cation, further enhancing hydrogen bonding.T his process leads to stronger cooperativity in the (c-c) trimers and tetramers.T his way,t he short-range donor-acceptor covalencyforces can overcome the strong long-range electrostatic repulsive forces,asexpected for ions of like charge.The enhanced (c-c) hydrogen bonds are even stronger than those in (c-a) ion pairs despite the additional attractive Coulomb forces in the latter. Thus,cooperative stabilization energy and enhanced charge transfer lead to smaller DQCCs for (c-c) clusters.I nF igure 3, we also show the experimentally measured Dc D ((c-c)À(c-a)) for IL IV.Adifference of 50 kHz between the (c-c) and (c-a) DQCCs suggests that the fraction of (c-c) clusters consists of significant amounts of (c-c) trimers and tetramers at least in the glassy state.  [38] Inspired by the solid-state NMR experiments,w ea lso performed MD simulations using ar ecently improved version of the force field introduced by Kçddermann et al. [71] Therefined dihedral potentials for the [NTf 2 ] À anion are based on extensive ab initio calculations and are leading to ab etter representation of the conformational space of the anion. [72] In detail, we performed NpT molecular-dynamics simulation using Gromacs 5.0.6 [73][74][75][76][77] at temperatures of 300 K, 320 K, 340 K, 360 K, 380 K, and 400 Ka nd ap ressure of p = 1bar.T he ILs were represented by ac ubic simulation box containing 512 ion pairs.T he box was first equilibrated for 2nsa tT = 500 K employing the Berendsen thermostat as well as the Berendsen barostat [78] with coupling times of t T = t p = 0.5 ps.A fter that, another equilibration run for 2nsatthe desired temperature followed. Production runs of 100 ns length utilizing the NosØ-Hoover thermostat [79,80] with t T = 1psa nd the Rahman-Parrinello barostat [81,82] with t p = 2psw ere performed for each temperature.A ll simulations were done with a2 .0 fs time step employing periodic boundary conditions and the LINCS algorithm [83] for fixed bond lengths.T he smooth particle-mesh Ewald summation [84] was applied with am esh spacing of 0.12 nm, ar eal-space cutoff 0.9 nm and fourthorder interpolation. Ther elative accuracy of the Ewald sum was set to 10 À5 corresponding to aconvergence factor of a = 3.38 nm À1 .

Populations of (c-a) and (c-c) Clusters from Solid-State NMR and MD Simulations
Theforce field of the [NTf 2 ] À anion has been published in refs. [71,85].T he pyridinium force fields were derived from the OPLS force field for pyridine from Jorgensen et al. [86,87] Thedihedral potentials of the hydroxyalkyl chain were fitted to ab initio calculations employing second-order Møller-Plesset perturbation theory using the cc-pVTZ basis set. Thep oint charges were derived from the electrostatic potential according to the CHelpG scheme. [88] TheL ennard-Jones parameters for the cations can be found in Table 1 ]between 300 and 400 Ktoshow the temperature dependence of the cluster populations.A lthough we obtained the cluster populations from NMR (183 K) and ND (303 K) measurements only at single temperatures,and those from MD simulations only above room temperature,w ec an clearly conclude:a )longer hydroxyalkyl chain lengths significantly enhance the formation of (c-c) cationic clusters; b) for longer alkyl chain lengths,t he polarizability of the cation is less important;c)the temperature dependence of (cc)-cluster formation in the liquid phase between 300 and 400 Kcan be described by vantHoff plots.T he ratios for the (c-c) and the (c-a) hydrogen-bonded species vs.t he inverse temperature obtained from MD-simulation data result in transition enthalpies from (c-c) to (c-a) of about 31.24 kJ mol À1 (II), 9.42 kJ mol À1 (IV), and 3.75 kJ mol À1 (for [HOC 4 Py][NTf 2 ]). Thes maller transition enthalpy suggests that cationic clusters already exist at room temperature.

Crystallization or Supercooling-(c-c) Cluster Formation Prevents Crystallization
TheDSC traces of ILs I-IV as shown in Figure 5strongly support the interpretation of the NMR spectra at low temperatures (see also the Supporting Information). Thermograms were recorded during cooling (373-193 K) and heating (193-373 K) at cooling and heating rates of 1, 5, and 10 Kmin À1 .T he glass-transition temperature (T g ,m iddle point of the heat capacity change), crystallization temperature (T c ), and melting temperature (T fus )w ere determined from DSC thermograms during the heating scans.T he summary of phase transitions is given in Table 2.
During cooling from 373 to 193 Ka t5and 10 Kmin À1 cooling rates,o nly ah eat-capacity change corresponding to glass transitions (T g )could be observed in the DSC profiles of ILs II (200 K), III (206 K), and IV (200 K). Thes upercooled state of the (c-c) cluster-forming ILs is obviously fairly stable. In contrast, the phase-transition behavior is complex for IL I, including melting (T fus = 276.2 K) and solid/solid phase transitions (T ss = 266.2 Ka nd T ss = 251.6 K). Fort he crystalline state of IL I at 183 K, we observed only one Pake pattern, indicating pure (c-a) hydrogen bonding.T he strong formation of cationic clusters in ILs II, III and IV results in supercooling and glass transition. From the combined NMR and DSC experiments,w eh ave clear evidence that the formation of cationic clusters prevents the ILs from crystallization and liquid/solid phase transition. Ther esulting material is ag lass. [89] Our findings suggest that the phase with n = 2-4 from MD simulationsfor the liquid phase between 300 and 400 K. The filled symbols show the cluster distribution obtained from the crystalline-and glassy-state NMR at 183 K(this study) and neutron diffraction (ND) experiments at 303 K. [38]  behavior of this type of ILs can be controlled by cationiccluster formation.

Conclusion
We measured DQCCs of hydroxyl-functionalized ionic liquids in the crystalline and glassy states.W eo bserved two Pake patterns for deuterons involved in normal (c-a) Coulomb-enhanced hydrogen bonds,a nd in unusual (c-c) Coulomb-weakened hydrogen bonds between cations.T he DQCCs in the (c-c) cationic clusters are smaller than in (c-a) ion-pairs,i ndicating stronger hydrogen bonding in accord with observed redshifts in IR spectra. These DQCCs are close to values for molecular liquids but larger than those known for salt bridges of supramolecular complexes.T he (c-a) DQCCs are surprisingly large despite the additional attractive Coulomb forces.Depending on the polarizability of the cation and the alkyl chain length, the (c-c) clusters can be more strongly populated than the (c-a) ion pairs at low temperatures.T he DSC traces clearly show that the ILs which form substantial amounts of (c-c) clusters do not tend to crystallize and rather form glasses. Figure 5. DSC traces for the ILs I-IV:F or IL I we observe liquid/solid and several solid/solid phase transitions. [33] Fort he crystalline state at 183 K, we found asingle Pake pattern indicating (c-a) hydrogenbonded ion pairs only (see Figure 1). ForILs II-IV we observe supercooling and finally glass transition below 200 K. These ILs exhibit substantial cationic-cluster formation characterizedb ytwo distinguished Pake patterns. Obviously,cationic-cluster formation prevents the ILs from crystallizing.