Computing the frequency-dependent NMR relaxation of 1H nuclei in liquid water.

We present a computational framework for reliably determining the frequency-dependent intermolecular and intramolecular nuclear magnetic resonance (NMR) dipole-dipole relaxation rates of spin 1/2 nuclei from Molecular Dynamics (MD) simulations. This approach avoids the alterations caused by the well-known finite-size effects of translational diffusion. Moreover, a procedure is derived to control and correct for effects caused by fixed distance-sampling cutoffs and periodic boundary conditions. By construction, this approach is capable of accurately predicting the correct low-frequency scaling behavior of the intermolecular NMR dipole-dipole relaxation rate and thus allows for the reliable calculation of the frequency-dependent relaxation rate over many orders of magnitude. Our approach is based on the utilization of the theory of Hwang and Freed for the intermolecular dipole-dipole correlation function and its corresponding spectral density [L.-P. Hwang and J. H. Freed, J. Chem. Phys. 63, 4017-4025 (1975)] and its combination with data from MD simulations. The deviations from the Hwang and Freed theory caused by periodic boundary conditions and sampling distance cutoffs are quantified by means of random walker Monte Carlo simulations. An expression based on the Hwang and Freed theory is also suggested for correcting those effects. As a proof of principle, our approach is demonstrated by computing the frequency-dependent intermolecular and intramolecular dipolar NMR relaxation rates of 1H nuclei in liquid water at 273 and 298 K based on the simulations of the TIP4P/2005 model. Our calculations are suggesting that the intermolecular contribution to the 1H NMR relaxation rate of the TIP4P/2005 model in the extreme narrowing limit has previously been substantially underestimated.

Three in One: The Versatility of Hydrogen Bonding Interaction in Halide Salts with Hydroxy-Functionalized Pyridinium Cations.

The paradigm of supramolecular chemistry relies on the delicate balance of noncovalent forces. Here we present a systematic approach for controlling the structural versatility of halide salts by the nature of hydrogen bonding interactions. We synthesized halide salts with hydroxy-functionalized pyridinium cations [HOCn Py]+ (n=2, 3, 4) and chloride, bromide and iodide anions, which are typically used as precursor material for synthesizing ionic liquids by anion metathesis reaction. The X-ray structures of these omnium halides show two types of hydrogen bonding: 'intra-ionic' H-bonds, wherein the anion interacts with the hydroxy group and the positively charged ring at the same cation, and 'inter-ionic' H-bonds, wherein the anion also interacts with the hydroxy group and the ring system but of different cations. We show that hydrogen bonding is controllable by the length of the hydroxyalkyl chain and the interaction strength of the anion. Some molten halide salts exhibit a third type of hydrogen bonding. IR spectra reveal elusive H-bonds between the OH groups of cations, showing interaction between ions of like charge. They are formed despite the repulsive interaction between the like-charged ions and compete with the favored cation-anion H-bonds. All types of H-bonding are analyzed by quantum chemical methods and the natural bond orbital approach, emphasizing the importance of charge transfer in these interactions. For simple omnium salts, we evidenced three distinct types of hydrogen bonds: Three in one!

Controlling "like-likes-like" charge attraction in hydroxy-functionalized ionic liquids by polarizability of the cations, interaction strength of the anions and varying alkyl chain length.

We provide comprehensive understanding of "like-likes-like" charge attraction in hydroxy-functionalized ionic liquids (ILs) by means of infrared spectroscopy (IR), quantum chemistry and differential scanning calorimetry (DSC). We show that hydrogen bonding between cation and cation (c-c) is possible despite the repulsive forces between ions of like charge. Already at room temperature, the (c-c) hydrogen bonds can compete with the regular Coulomb-enhanced hydrogen bonds between cation and anion (c-a). For a large set of well-selected ILs, we show that "like-charge attraction" between the OH-functionalized cations is controllable by the polarizability of the cation, the interaction strength of the anion and the length of the hydroxyalkyl chain. In particular, we clarify whether tethering the OH group away from the positive charge center of the cationic ring with longer hydroxyalkyl chains compensates for unfavourable cation/anion combinations with respect to (c-c) cluster formation. For that purpose, we synthesized and characterized twelve ionic liquids including the differently polarizable cations, 1-(n-hydroxyalkyl)-1-methylpiperidinium [HOCnMPip]+ and 1-(n-hydroxyalkyl)-pyridinium [HOCnPy]+, as well as the weakly and strongly interacting anions, bis(trifluoromethanesulfonyl)imide [NTf2]- and methanesulfonate [OMs]-, respectively. On top, we varied the hydroxyalkyl chain length (HOCn) (n = 2-5). We systematically show how these three molecular ion parameters affect like-charge attraction. The use of polarizable cations, weakly interacting anions, and long alkyl chain tethers results in (c-c) clustering already at room temperature. Kinetic trapping is not a prerequisite for the existence of (c-c) cluster species in ILs. Moreover, we demonstrate that micro structuring affects macroscopic behavior of this type of ILs. We observed that substantial (c-c) interaction prevents ILs from crystallizing. Instead, these ILs supercool and finally form a glass.

Counting cations involved in cationic clusters of hydroxy-functionalized ionic liquids by means of infrared and solid-state NMR spectroscopy.

In hydroxy-functionalized ionic liquids, two types of hydrogen bonding coexist: the conventional H-bonds between cation and anion (c-a) and those between cation and cation (c-c), although the interaction between like-charged ions is supposed to be much weaker due to the repulsive Coulomb forces. Counting the cations involved in either (c-a) or (c-c) clusters is a challenge. For that purpose, we recently performed neutron diffraction (ND) measurements and molecular dynamics (MD) simulations at and above room temperature accompanied by NMR solid-state experiments in the glassy state of the ILs. In principle, these methods are suitable for determining the populations of (c-a) and (c-c) cluster species. For different reasons we could only address single temperatures and/or small temperature intervals above 300 K. The by far largest temperature range with reasonable efforts is accessible by simple infrared (IR) spectroscopy. However, counting (c-a) or (c-c) hydrogen bonds is a difficult task due to the different transition dipole moments resulting in varying intensities and broad vibrational bands. Here we present a method for deriving the number of cations involved in (c-a) ion pairs from IR spectra in the OH stretch region. This procedure provides access to the equilibria of (c-a) and (c-c) hydrogen bonds as a function of temperature allowing derivation of the transition enthalpy.

Cooperatively enhanced hydrogen bonds in ionic liquids: closing the loop with molecular mimics of hydroxy-functionalized cations.

We address the cooperative hydrogen bonding interactions in play between the ionic constituents of ionic liquids (ILs) with particular attention to those involving the attractive interactions between two cations in the system 1-(2-hydroxyethyl)pyridinium tetrafluoroborate [HEPy][BF4]. This is accomplished by comparing the temperature-dependent linear infrared spectra of [HEPy][BF4] with that of the molecular mimic of its cation, 2-phenylethanol (PhenEthOH). We then explored the structural motifs of these H-bonded configurations at the molecular level by analyzing the cryogenic ion vibrational predissociation spectroscopy of cold (∼35 K) gas phase cluster ions with quantum chemical methods. The analysis of the OH stretching bands reveals the formation of the various binding motifs ranging from the common +OHBF4- interaction in ion-pairs (c-a) to the unusual +OH+OH interaction (c-c) in linear and cyclic, homodromic H-bonding domains. Replacing ion-pairs by the molecular (neutral) analogue of the IL cation also results in the formation of positively charged cyclic motifs, with the bands of the gas phase cationic cyclic tetramer (HEPy+)(PhenEthOH)3 appearing quite close to those assigned previously to cyclic tetramers in the liquid. These conclusions are supported by density functional theory (DFT) calculations of the cationic and neutral clusters as well as the local structures in the liquid. Our combined experimental and theoretical approach for the gas and the liquid phases provides important insight into the competition between differently H-bonded and charged constituents in liquids.

Isolating the role of hydrogen bonding in hydroxyl-functionalized ionic liquids by means of vaporization enthalpies, infrared spectroscopy and molecular dynamics simulations.

The enthalpy of vaporization is mainly the amount of the energy needed for transferring quantities from the liquid into the gas phase. It simply describes the energy required to overcome the interaction energy between quantities if those evaporate as monomers as is the case for molecular liquids. The situation for ionic liquids (ILs) is more complex. We do not know the delicate composition of different types of interaction, neither for the liquid nor for the gas phase. Additionally, we have to consider that ILs evaporate as ion pairs which carry substantial interaction energy of all kind into the vapor phase. In this study, we measured the vaporization enthalpies of well-selected hydroxyl-functionalized and non-hydroxyfunctionalized ILs. In particular, we focussed on the case of hydroxyl-functionalized ILs providing possible hydrogen bonding between cation and anion in the liquid as well as in the gas phase. With infrared spectroscopy, we showed that all the hydroxyl groups are involved in hydrogen bonding in the liquid state of the ILs. However, molecular dynamics simulations showed that the evaporating ion pairs also include this hydrogen bond. A detailed analysis of the potential energies for all IL constituents showed that the hydrogen bond hinders favourable interaction between the polarizable ring of the cations and the anions leading to higher vaporization enthalpies for the hydroxyl-functionalized ILs.

Like-likes-Like: Cooperative Hydrogen Bonding Overcomes Coulomb Repulsion in Cationic Clusters with Net Charges up to Q=+6e.

Quantum chemical calculations have been employed to study kinetically stable cationic clusters, wherein the monovalent cations are trapped by hydrogen bonding despite strongly repulsive electrostatic forces. We calculated linear and cyclic clusters of the hydroxy-functionalized cation N-(3-hydroxypropyl) pyridinium, commonly used as cation in ionic liquids. The largest kinetically stable cluster was a cyclic hexamer that very much resembles the structural motifs of molecular clusters, as known for water and alcohols. Surprisingly, strong cooperative hydrogen bonds overcome electrostatic repulsion and result in cationic clusters with a high net charge up to Q=+6e. The structural, spectroscopic, and electronic signatures of the cationic and related molecular clusters of 3-phenyl-1-propanol could be correlated to NBO parameters, supporting the existence of "anti-electrostatic" hydrogen bonds (AEHB), as recently suggested by Weinhold. We also showed that dispersion forces enhance the cationic cluster formation and compensate the electrostatic repulsion of one additional positive charge.

The influence of like-charge attraction on the structure and dynamics of ionic liquids: NMR chemical shifts, quadrupole coupling constants, rotational correlation times and failure of Stokes-Einstein-Debye.

Ion pairing is one of the most fundamental atomic interactions in chemistry and biology. In contrast, pairing between like-charged ions remains an elusive concept. So far, this phenomenon was observed only for large-scaled structures, assemblies, stabilizing frameworks, or in aqueous solution wherein like-charge attraction is supported by mediating water molecules. Recently, we reported the formation of cationic clusters in pure ionic liquids (ILs) which all include hydroxyl groups (OH) for possible hydrogen bonding. In such structures like-charge repulsion is overcome by cooperative hydrogen bonds. The vibrational bands in the OH-stretch region of the infrared spectra can be clearly assigned to H-bonded ion pairs (c-a) or to H-bonded cationic clusters (c-c). The equilibrium between both types of ionic clusters can be controlled by using the same cation but differently strong interacting anions. In the present work, we study the influence of the cationic cluster formation on structural and dynamical NMR properties of ionic liquids, where we know that they form cationic clusters to different extent. First, we measure proton chemical shifts, δ1H, and determine deuteron quadrupole coupling constants, χD, from a calculated relation between both NMR properties. Reliable χD values for the liquid phase are a prerequisite for calculating reorientational correlation times, τOH, from measured deuteron relaxation times, T1. It is shown that the correlation times are significantly influenced by the amount of cationic clusters present in the IL. The Stokes-Einstein-Debye (SED) relation is valid for the ILs wherein H-bonded ion pairs (c-a) are the dominant species. With increasing cationic cluster (c-c) formation of e.g. cyclic tetramers, SED breaks down because of the structural heterogeneities.

Rotational and translational dynamics and their relation to hydrogen bond lifetimes in an ionic liquid by means of NMR relaxation time experiments and molecular dynamics simulation.

We report a concerted theoretical and experimental effort to determine the reorientational dynamics as well as hydrogen bond lifetimes for the doubly ionic hydrogen bond +OH⋯O- in the ionic liquid (2-hydroxyethyl)trimethylammonium bis(trifluoromethylsulfonyl)imide [Ch][NTf2] by using a combination of NMR relaxation time experiments, density functional theory (DFT) calculations, and molecular dynamics (MD) simulations. Due to fast proton exchange, the determination of rotational correlation times is challenging. For molecular liquids, 17O-enhanced proton relaxation time experiments have been used to determine the rotational correlation times for the OH vectors in water or alcohols. As an alternative to those expensive isotopic substitution experiments, we employed a recently introduced approach which is providing access to the rotational dynamics from a single NMR deuteron quadrupolar relaxation time experiment. Here, the deuteron quadrupole coupling constants (DQCCs) are obtained from a relation between the DQCC and the δ 1H proton chemical shifts determined from a set of DFT calculated clusters in combination with experimentally determined proton chemical shifts. The NMR-obtained rotational correlation times were compared to those obtained from MD simulations and then related to viscosities for testing the applicability of popular hydrodynamic models. In addition, hydrogen bond lifetimes were derived, using hydrogen bond population correlation functions computed from MD simulations. Here, two different time domains were observed: The short-time contributions to the hydrogen lifetimes and the reorientational correlation times have roughly the same size and are located in the picosecond range, whereas the long-time contributions decay with relaxation times in the nanosecond regime and are related to rather slow diffusion processes. The computed average hydrogen bond lifetime is dominated by the long-time process, highlighting the importance and longevity of hydrogen-bonded ion pairs in these ionic liquids.

Spectroscopic Evidence for an Attractive Cation-Cation Interaction in Hydroxy-Functionalized Ionic Liquids: A Hydrogen-Bonded Chain-like Trimer.

We address the formation of hydrogen bonded domains among the cationic constituents of the ionic liquid (IL) 1-(3-hydroxypropyl)pyridinium tetrafluoroborate [HPPy][BF4 ] by means of cryogenic ion vibrational predissociation spectroscopy of cold (ca. 35 K) gas-phase cluster ions and quantum chemistry. Specifically, analysis of the OH stretching bands reveals a chain-like OH⋅⋅⋅OH⋅⋅⋅OH⋅⋅⋅BF4 - binding motif involving the three cations in the cationic quinary cluster ion (HPPy+ )3 (BF4 - )2 . Calculations show that this cooperative H-bond attraction compensates for the repulsive Coulomb forces and results in stable complexes that successfully compete with those in which the OH groups are predominantly attached to the counter anions. Our combined experimental and theoretical approach provides insight into the cooperative effects that lead to the formation of hydrogen bonded domains involving the cationic constituents of ILs.

Controlling the kinetic and thermodynamic stability of cationic clusters by the addition of molecules or counterions.

Whereas ion pairing is one of the most fundamental atomic interactions in chemistry and biology, pairing between like-charged ions remains an elusive concept. This phenomenon was only reported for large-scaled structures, assemblies or stabilizing frameworks. Recently, we could report the formation of cationic clusters in pure ionic liquids. In such structures like-charge repulsion is attenuated by cooperative hydrogen bonds. In the present work, we investigate the possible formation of cationic clusters in the gas phase beyond those found in the neutral ionic liquids wherein the positive charges are fully balanced by anions. Based on the ionic liquid (2-hydroxyethyl)trimethylammonium bis(trifluoromethylsulfonyl)imide we calculated differently charged cationic clusters including varying numbers of cation-like molecules (3-3-dimethyl-1-butanol) or ionic liquid anions (NTf2). We give the number of molecules or anions which are needed to transfer the cationic clusters from the meta-stable into the thermodynamically stable regime. We analyze the charge, the size and the structural motif of these clusters. A particular focus we put on the cooperativity of hydrogen bonding and the role of dispersion forces for the cluster stability. We also show that interaction energies and charge transfer within the cationic clusters can be related to spectroscopic parameters such as NMR chemical shifts and IR vibrational frequencies. Finally, we suggest clusters which should be observable in demanding gas phase experiments.

When Like Charged Ions Attract in Ionic Liquids: Controlling the Formation of Cationic Clusters by the Interaction Strength of the Counterions.

The properties of ionic liquids are described by a subtle balance between Coulomb interaction, hydrogen bonding, and dispersion forces. We show that lowering the attractive Coulomb interaction by choosing weakly coordinating anions leads to the formation of cationic clusters. These clusters of like-charged ions are stabilized by cooperative hydrogen bonding and controlled by the interaction potential of the anion. IR and NMR spectroscopy combined with computational methods are used to detect and characterize these unusual, counter-intuitively formed clusters. They can be only observed for weakly coordinating anions. When cationic clusters are formed, cyclic tetramers are particularly stable. Therein, cooperative hydrogen-bond attraction can compete with like-charge repulsion. We present a simple but effective spectroscopic scale for the possibility of like-charge attraction in ionic liquids, based on IR and NMR signatures.

Kinetics of Hydrogen Bonding between Ions with Opposite and Like Charges in Hydroxyl-Functionalized Ionic Liquids.

Hydrogen-bonded structures and their lifetimes in ionic liquids (ILs) are governed by the subtle balance between Coulomb interactions, hydrogen bonding, and dispersion forces. Despite the dominant Coulomb interaction, local and directional hydrogen bonds (HBs) can play an important role in the behavior of ILs. Compared to water, the archetype of hydrogen-bonded liquids, ILs have larger constituents and higher viscosities but are typically lacking a three-dimensional HB network. Hydroxyl-functionalized ionic liquids are even more special: regular HBs between cations and anions (ca) are accompanied by HBs between pairs of cations (cc). Recently, infrared (IR) measurements have suggested that the (cc) HBs are even stronger than their (ca) counterparts and their strength can be controlled via the hydroxyalkyl chain length. In this paper, we show by means of molecular dynamics (MD) simulations that the presence of HBs has a profound effect on the molecular mobility of the ions. We investigate the kinetic mechanism of hydrogen bonding in ILs and show that the lifetimes and hence the stability of (cc) HBs increase with the chain length, making them more stable than the respective (ca) HBs. The observed HB equilibrium can explain the peculiar chain length dependence of the relative molecular mobilities of the ions by a direct comparison between hydroxyl-functionalized ILs with their nonfunctionalized counterparts.

Understanding the Nature of Nuclear Magnetic Resonance Relaxation by Means of Fast-Field-Cycling Relaxometry and Molecular Dynamics Simulations-The Validity of Relaxation Models.

Fast-field-cycling relaxometry is a nuclear magnetic resonance method growing in popularity; yet, theoretical interpretation is limited to analytical models of uncertain accuracy. We present the first study calculating fast-field-cycling dipolar coupling directly from a molecular dynamics simulation trajectory. In principle, the frequency-resolved dispersion contains both rotational and translational diffusion information, among others. The present joint experimental/molecular dynamics study demonstrates that nuclear magnetic resonance properties calculated from the latter reproduce measured dispersion curves and temperature trends faithfully. Furthermore, molecular dynamics simulations can verify interpretation model assumptions by providing actual diffusion coefficients and correlation times.

Chain Length Dependence of Hydrogen Bond Linkages between Cationic Constituents in Hydroxy-Functionalized Ionic Liquids: Tracking Bulk Behavior to the Molecular Level with Cold Cluster Ion Spectroscopy.

Hydroxy functionalization of cations in ionic liquids (ILs) can lead to formation of contacts between their OH groups [so-called (c-c) interactions]. One class of these linkages involves cooperatively enhanced hydrogen bonds to anionic partners that are sufficiently strong to overcome the repulsion between two positively charged centers. Herein, we clarify how the propensity for the formation of (c-c) contacts depends on the alkyl chain length between two cationic rings and their OH groups by analyzing the temperature-dependent IR spectra of bulk ILs as well as the vibrational predissociation spectra of ∼35 K complexes comprised of two cations and one anion. This study compares the behavior of two cationic derivatives with ethyl and propyl chains complexed with two different anions: bis(trifluoromethylsulfonyl)imide and tetrafluoroborate. Only the bulk ILs with the longer chain propyl derivative [HPMPip+ = 1-(3-hydroxypropyl)-1-methylpiperidinium] display (c-c) interactions. Molecular-level aspects of this docking arrangement are revealed by analyzing the OH stretching fundamentals displayed by the ternary complexes.

Cationic clustering influences the phase behaviour of ionic liquids.

"Unlike charges attract, but like charges repel". This conventional wisdom has been recently challenged for ionic liquids. It could be shown that like-charged ions attract each other despite the powerful opposing electrostatic forces. In principle, cooperative hydrogen bonding between ions of like-charge can overcome the repulsive Coulomb interaction while pushing the limits of chemical bonding. The key challenge of this solvation phenomenon is to establish design principles for the efficient formation of clusters of like-charged ions in ionic liquids. This is realised here for a set of well-suited ionic liquids including the same hydrophobic anion but different cations all equipped with hydroxyethyl groups for possible H-bonding. The formation of H-bonded cationic clusters can be controlled by the delocalization of the positive charge on the cations. Strongly localized charge results in cation-anion interaction, delocalized charge leads to the formation of cationic clusters. For the first time we can show, that the cationic clusters influence the properties of ILs. ILs comprising these clusters can be supercooled and form glasses. Crystalline structures are obtained only, if the ILs are dominantly characterized by the attraction between opposite-charged ions resulting in conventional ion pairs. That may open a new path for controlling glass formation and crystallization. The glass temperatures and the phase transitions of the ILs are observed by differential scanning calorimetry (DSC) and infrared (IR) spectroscopy.

Structural Motifs in Cold Ternary Ion Complexes of Hydroxyl-Functionalized Ionic Liquids: Isolating the Role of Cation-Cation Interactions.

We address the competition between intermolecular forces underlying the recent observation that ionic liquids (ILs) with a hydroxyl-functionalized cation can form domains with attractive interactions between the nominally repulsive positively charged constituents. Here we show that this behavior is present even in the isolated ternary (HEMIm+)2NTf2- complex (HEMIm+ = 1-(2-hydroxyethyl)-3-methylimidazolium) cooled to about 35 K in a photodissociation mass spectrometer. Of the three isomers isolated by double resonance techniques, one is identified to exhibit direct contact between the cations. This linkage involves a cooperative H-bond wherein the OH group on one cation binds to the OH group on the other, which then attaches to the basic N atom of the anion. Formation of this motif comes at the expense of the usually dominant interaction of the acidic C(2)H group on the Im ring with molecular anions, as evidenced by isomer-dependent shifts in the C(2)H vibrational fundamentals.