Deuteron Quadrupole Research Articles

Ion Mobility in Hydroxy-Functionalized Ionic Liquids Depends on Cationic Clustering: Tracking the Alkyl Chain Length Behavior with Deuteron NMR Relaxation.

Observing and quantifying the like-charge attraction in liquids and solutions is still challenging. However, we showed that elusive cation-cation hydrogen bonding may govern the structure and interaction in hydroxyl-functionalized ionic liquids. Therefore, cationic cluster formation depends on the shape, charge distribution, and functionality of the ions. We demonstrated by means of solid-state 2H NMR spectroscopy that cationic clusters change the structure and dynamics of ionic liquids. With increasing alkyl chain length, we observed two deuteron quadrupole coupling constants for the OD groups, differing by about 30 kHz. The lower value was assigned to the cation-cation interaction, indicating that the average (c-c) hydrogen bonds are stronger than the (c-a) hydrogen bonds between the cation and the anion despite the repulsive and attractive Coulomb interaction in the first and latter cases. Ion mobility could be studied by 2H NMR spectroscopy, although the deuterons in the hydrogen-bonded clusters underwent fast exchange. Our results also showed that simple relaxation models are not applicable anymore and that anisotropic motion must be considered.

Deuteron electromagnetic form factors and tensor polarization observables in the framework of the hard-wall AdS/QCD model

We study the electromagnetic form factors and tensor polarization observables of the deuteron in the framework of the hard-wall AdS/QCD model. We find a profile function for the bulk twist vector field, which describes the deuteron on the boundary and fix the infrared boundary cut-off of AdS space in accordance with the ground state mass of the deuteron. We obtain the deuteron charge monopole, quadrupole, and magnetic dipole form factors and tensor polarization observables from the bulk Lagrangians for the deuteron and photon field interactions. We plot the momentum transfer dependence of the form factors and tensor polarization observables and compare our numerical results with those in the soft-wall model and experimental data.

The Influence of Deuterium Isotope Effects on Structural Rearrangements, Ensemble Equilibria, and Hydrogen Bonding in Protic Ionic Liquids.

We report strong isotope effects for the protic ionic liquid triethylammonium methanesulfonate [TEA][OMs] by means of deuterium solid-state NMR spectroscopy covering broad temperature ranges from 65 K to 313 K. Both isotopically labelled PILs differ in non-deuterated and fully deuterated ethyl groups of the triethyl ammonium cations. The N-D bond of both cations is used as sensitive probe for hydrogen bonding and structural ordering. The 2 H NMR line shape analysis provides the deuteron quadrupole coupling constants and the characteristics of a broad heterogeneous phase with simultaneously present static and mobile states indicating plastic crystal behavior. The temperatures where both states are equally populated differ by about 80 K for the two PILs, showing that deuteration of the ethyl groups in the trialkylammonium cations tremendously shifts the equilibrium towards the static state. In addition, it leads to a significant less cooperative transition, associated with a significantly reduced standard molar transition entropy.

High-Temperature Quantum Tunneling and Hydrogen Bonding Rearrangements Characterize the Solid-Solid Phase Transitions in a Phosphonium-Based Protic Ionic Liquid.

We report the complex phase behavior of the glass forming protic ionic liquid (PIL) d3‐octylphosphonium bis(trifluoromethylsulfonyl)imide [C8H17PD3][NTf2] by means of solid‐state NMR spectroscopy. Combined line shape and spin relaxation studies of the deuterons in the PD3 group of the octylphosphonium cation allow to map and correlate the phase behavior for a broad temperature range from 71 K to 343 K. In the solid PIL at 71 K, we observed a static state, characterized by the first deuteron quadrupole coupling constant reported for PD3 deuterons. A transition enthalpy of about 12 kJ mol−1 from the static to the mobile state with increasing temperature suggests the breaking of a weak, charge‐enhanced hydrogen bond between cation and anion. The highly mobile phase above 100 K exhibits an almost disappearing activation barrier, strongly indicating quantum tunneling. Thus, we provide first evidence of tunneling driven mobility of the hydrogen bonded P−D moieties in the glassy state of PILs, already at surprisingly high temperatures up to 200 K. Above 250 K, the mobile phase turns from anisotropic to isotropic motion, and indicates strong internal rotation of the PD3 group. The analyzed line shapes and spin relaxation times allow us to link the structural and dynamical behavior at molecular level with the phase behavior beyond the DSC traces.

Investigation of the nuclear liquid-gas phase transition in the static AMD

Nuclear liquid-gas phase transitions are investigated in the framework of static antisymmetrized molecular dynamics (static AMD) model under either a constant volume or a constant pressure. A deuteron quadrupole momentum fluctuation thermometer is applied to extract the temperature of fragmenting systems of 36Ar and 100Sn. A plateau structure of caloric curves is observed under a constant volume for those system with a density ρ ⩽ 0.03 fm−3. A clear backbending in the caloric curves, which indicates a first order phase transition, is observed under a constant pressure with all pressures studied. The similar behavior of caloric curves of 36Ar and 100Sn systems indicates that there is no strong system size effect under a constant volume or a constant pressure. Both the mass distributions and the light particle multiplicities show a strong α clusterization at low excitation energies in the static AMD simulations. The liquid-gas phase transition measures of the multiplicity derivative (dM/dT) and the normalized variance of Z max (NVZ) are applied. The experimental caloric curves are also compared with those of 100Sn of the static AMD simulations under both the constant volume and the constant pressure conditions. Discussions are presented with the available experimental results and those from the static AMD simulations. Large errors in the experimental temperature measurements and those in the reconstruction technique for the primary fragmenting source hinder to draw a conclusion whether the phase transition occurs under either a constant volume or a constant pressure. This study suggests that different measures for the liquid-gas phase transitions should be examined besides the caloric curves in order to draw a conclusion.

High-accuracy calculation of the deuteron charge and quadrupole form factors in chiral effective field theory

We present a comprehensive analysis of the deuteron charge and quadrupole form factors based on the latest two-nucleon potentials and charge density operators derived in chiral effective field theory. The single- and two-nucleon contributions to the charge density are expressed in terms of the proton and neutron form factors, for which the most up-to-date empirical parametrizations are employed. By adjusting the fifth-order short-range terms in the two-nucleon charge density operator to reproduce the world data on the momentum-transfer dependence of the deuteron charge and quadrupole form factors, we predict the values of the structure radius and the quadrupole moment of the deuteron: $r_{\rm str}=1.9729\substack{+0.0015\\ -0.0012}\ \text{fm},\ Q_d=0.2854\substack{+0.0038\\ -0.0017}\ \text{fm}^2. $ A comprehensive and systematic analysis of various sources of uncertainty in our predictions is performed. Following the strategy advocated in our recent publication Phys. Rev. Lett. 124, 082501 (2020), we employ the extracted structure radius together with the accurate atomic data for the deuteron-proton mean-square charge radii difference to update the determination of the neutron charge radius, for which we find: $r_n^2=-0.105\substack{+0.005\\ -0.006} \, \text{fm}^2$. Given the observed rapid convergence of the deuteron form factors in the momentum-transfer range of $Q \simeq 1-2.5$ fm$^{-1}$, we argue that this intermediate-energy domain is particularly sensitive to the details of the nucleon form factors and can be used to test different parametrizations.

Clusters of Hydroxyl-Functionalized Cations Stabilized by Cooperative Hydrogen Bonds: The Role of Polarizability and Alkyl Chain Length.

We explore quantum chemical calculations for studying clusters of hydroxyl-functionalized cations kinetically stabilized by hydrogen bonding despite strongly repulsive electrostatic forces. In a comprehensive study, we calculate clusters of ammonium, piperidinium, pyrrolidinium, imidazolium, pyridinium, and imidazolium cations, which are prominent constituents of ionic liquids. All cations are decorated with hydroxy-alkyl chains allowing H-bond formation between ions of like charge. The cluster topologies comprise linear and cyclic clusters up to the size of hexamers. The ring structures exhibit cooperative hydrogen bonds opposing the repulsive Coulomb forces and leading to kinetic stability of the clusters. We discuss the importance of hydrogen bonding and dispersion forces for the stability of the differently sized clusters. We find the largest clusters when hydrogen bonding is maximized in cyclic topologies and dispersion interaction is properly taken into account. The kinetic stability of the clusters with short-chained cations is studied for the different types of cations ranging from hard to polarizable or exhibiting additional functional groups such as the acidic C(2)-H position in the imidazolium-based cation. Increasing the alkyl chain length, the cation effect diminishes and the kinetic stability is exclusively governed by the alkyl chain tether increasing the distance between the positively charged rings of the cations. With adding the counterion tetrafluoroborate (BF4−) to the cationic clusters, the binding energies immediately switch from strongly positive to strongly negative. In the neutral clusters, the OH functional groups of the cations can interact either with other cations or with the anions. The hexamer cluster with the cyclic H-bond motive and “released” anions is almost as stable as the hexamer built by H-bonded ion pairs exclusively, which is in accord with recent IR spectra of similar ionic liquids detecting both types of hydrogen bonding. For the cationic and neutral clusters, we discuss geometric and spectroscopic properties as sensitive probes of opposite- and like-charge interaction. Finally, we show that NMR proton chemical shifts and deuteron quadrupole coupling constants can be related to each other, allowing to predict properties which are not easily accessible by experiment.

High-temperature and high-pressure NMR investigations of low viscous fluids confined in mesoporous systems

Abstract In this contribution, the relaxation and diffusional behaviors of low viscous fluids, water and methanol confined into mesoporous silica and controlled size pore glass were investigated. The engineered porous systems are relevant to geologically important subsurface energy materials. The engineered porous proxies were characterized by Brunauer–Emmett–Teller (BET) surface analyzer, nuclear magnetic resonance (NMR) spectroscopy, and electron microscopy (EM) to determine surface area, pore-wall protonation and morphology of these materials, respectively. The confined behavior of the low viscous fluids was studied by varying pore diameter, fluid-to-solid ratio, temperature, and pressure, and then compared to bulk liquid state. Both relaxation and diffusion behaviors for the confined fluids showed increasing deviation from pure bulk fluids as the fluid-to-solid ratio was decreased, and surface-to-volume ratio (S/V) was varied. Variable pressure deuteron NMR relaxation of confined D2O and confined methanol, deuterated at the hydroxyl or methyl positions, were performed to exploit the sensitivity of the deuteron quadrupole moment to molecular rotation. The methanol results demonstrated greater pressure dependence than those for water only in bulk. The deviations from bulk liquid behavior arise from different reasons such as confinement and the interactions between confined fluid and the nano-pore wall. The results of the present report give insight into the behavior of low viscosity fluid in nano-confined geometries under different state conditions.

Hyperfine structure in the HD molecule

We investigate interactions between the proton spin, the deuteron spin, and the orbital angular momentum in the electronic ground state of the HD molecule. These interactions lead to hyperfine splittings of molecular energy levels. Our numerical results for the first rotational level agree well with the currently most accurate measurement performed by Ramsey {\em et al.} in the 1950s. Knowledge of the hyperfine structure of other levels is necessary for the accurate determination of rovibrational transition energies in spectroscopic measurements. We present theoretical predictions and share the numerical code used to perform numerical calculations. This work sets the ground for high precision spectroscopic tests of hyperfine interactions in molecular systems. In particular we determine the value of the deuteron quadrupole moment $Q = 0.2856(2)$ fm$^2$ and give outlook for improving its accuracy by three orders of magnitude.

Freezing the Motion in Hydroxy-Functionalized Ionic Liquids-Temperature Dependent NMR Deuteron Quadrupole Coupling Constants for Two Types of Hydrogen Bonds Far below the Glass Transition.

We measured the deuteron quadrupole coupling constants (DQCCs) for hydroxy-functionalized ionic liquids (ILs) with varying alkyl chain length over the temperature range between 60 and 200 K by means of solid-state NMR spectroscopy. For all temperatures, the 2H spectra show two DQCCs representing different types of hydrogen bonds. Higher values, ranging from 220 to 250 kHz, indicate weaker hydrogen bonds between cation and anion (c-a), and lower values varying from 165 to 210 kHz result from stronger hydrogen bonds between the OD groups of cations (c-c), in agreement with recent observations in infrared, neutron diffraction, and NMR studies. We observed different temperature dependencies for (c-a) and (c-c) hydrogen bonding. From the static pattern of the 2H spectra at the lowest temperatures, we derived the true DQCCs being up to 20 kHz larger than recently reported values measured at the glass transition temperature. We were able to freeze the librational motions of the hydrogen bonds in the ILs. The temperature dependence of the (c-a) and (c-c) cluster populations in the glassy state is opposite to that observed in the liquid state, partly anticipating the behavior of ILs tending to crystallize.

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

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.

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

AbstractWe 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.

Simultaneous determination of deuteron quadrupole coupling constants and rotational correlation times: the model case of hydrogen bonded ionic liquids.

We show that deuteron quadrupole coupling constants (DQCCs), and reorientational correlation times of molecular bonds N-D that are involved in hydrogen bonding, can be determined from NMR T1 relaxation time experiments simultaneously. For this purpose, we used trialkylammonium-based protic ionic liquids (PILs) as model compounds. They exhibit high viscosities and wide liquid ranges that allow measurements far beyond the extreme narrowing region (ω0τc ≪ 1). The T1 minima already occur at temperatures significantly above room temperature. We obtain reasonable DQCCs for the liquid phase if anisotropic motion is considered. The DQCCs are very small due to attractive Coulomb interaction between the cation and anion, which is further enhanced by hydrogen bonding. The DQCCs strongly depend on the interaction strength of the anion but are independent of the alkyl chain length of the trialkyl ammonium cations pointing to the exclusive cation-anion interaction along the hydrogen bond.

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.

Inside Cover: Characterization of Doubly Ionic Hydrogen Bonds in Protic Ionic Liquids by NMR Deuteron Quadrupole Coupling Constants: Differences to H‐bonds in Amides, Peptides, and Proteins (Angew. Chem. Int. Ed. 45/2017)

Inside Cover: Characterization of Doubly Ionic Hydrogen Bonds in Protic Ionic Liquids by NMR Deuteron Quadrupole Coupling Constants: Differences to H‐bonds in Amides, Peptides, and Proteins (Angew. Chem. Int. Ed. 45/2017)

Characterization of Doubly Ionic Hydrogen Bonds in Protic Ionic Liquids by NMR Deuteron Quadrupole Coupling Constants: Differences to H-bonds in Amides, Peptides, and Proteins.

We present the first deuteron quadrupole coupling constants (DQCCs) for selected protic ionic liquids (PILs) measured by solid-state NMR spectroscopy. The experimental data are supported by dispersion-corrected density functional theory (DFT-D3) calculations and molecular dynamics (MD) simulations. The DQCCs of the N-D bond in the triethylammonium cations are the lowest reported for deuterons in PILs, indicating strong hydrogen bonds between ions. The NMR coupling parameters are compared to those in amides, peptides, and proteins. The DQCCs show characteristic behavior with increasing interaction strength of the counterion and variation of the H-bond motifs. We report the similar presence of the quadrupolar splitting pattern and the narrow liquid line in the NMR spectra over large temperature ranges, indicating the heterogeneous nature of PILs.

Electromagnetic Structure of Two- and Three-Nucleon Systems: An Effective Field Theory Description

I discuss the use of chiral effective field theory (χEFT) to describe electromagnetic reactions in the two- and three-nucleon systems. I review the results of χEFT power counting for charge and current operators up to [Formula: see text] relative to leading order, before showing that renormalization-group arguments imply that short-distance electromagnetic operators play a larger role than suggested by this standard counting. A detailed examination of χEFT's predictions for the electromagnetic form factors of deuterium and the trinucleons, and for the threshold captures np→dγ and nd→tγ, enables a critical appraisal of the theory's performance in these contexts. Recent χEFT calculations using the [Formula: see text] chiral perturbation theory (χPT) potential yielded both form factors that agree with experimental data for Q2<0.25 GeV2 and an excellent description of the challenging threshold captures. Short-distance M1 operators are essential to this success, and the addition of a short-distance part of the nucleon–nucleon charge operator produces precise predictions of the deuteron charge and quadrupole form factors in this kinematic domain.

Deuteron quadrupole coupling constants and reorientational correlation times in protic ionic liquids.

We describe a method for the accurate determination of deuteron quadrupole coupling constants χD for N-D bonds in triethylammonium-based protic ionic liquids (PILs). This approach was first introduced by Wendt and Farrar for O-D bonds in molecular liquids, and is based on the linear relationship between the deuteron quadrupole coupling constants χD, and the proton chemical shifts δ(1)H, as obtained from DFT calculated properties in differently sized clusters of the compounds. Thus the measurement of δ(1)H provides an accurate estimate for χD, which can then be used for deriving reorientational correlation-times τND, by means of NMR deuteron quadrupole relaxation time measurements. The method is applied to pure PILs including differently strong interacting anions. The obtained χD values vary between 152 and 204 kHz, depending on the cation-anion interaction strength, intensified by H-bonding. We find that considering dispersion corrections in the DFT-calculations leads to only slightly decreasing χD values. The determined reorientational correlation times indicate that the extreme narrowing condition is fulfilled for these PILs. The τc values along with the measured viscosities provide an estimate for the volume/size of the clusters present in solution. In addition, the correlation times τc, and the H-bonded aggregates were also characterized by molecular dynamics (MD) simulations.

Deuteron form factors in a phenomenological approach**Supported by NSFC (11475192, 10975146, 11035006, 10775148)

The electromagnetic form factors of the deuteron, particularly its quadrupole form factor, are studied with the help of a phenomenological Lagrangian approach where the vertex of the deuteron–proton–neutron with D-state contribution is explicitly taken into account. The results show the importance of this contribution to the deuteron quadrupole form factor in the approach.

Covariant spectator theory ofnpscattering: Deuteron quadrupole moment

The deuteron quadrupole moment is calculated using two CST model wave functions obtained from the 2007 high precision fits to $np$ scattering data. Included in the calculation are a new class of isoscalar $np$ interaction currents automatically generated by the nuclear force model used in these fits. The prediction for model WJC-1, with larger relativistic P-state components, is 2.5% smaller that the experimental result, in common with the inability of models prior to 2014 to predict this important quantity. However, model WJC-2, with very small P-state components, gives agreement to better than 1%, similar to the results obtained recently from $\chi$EFT predictions to order N$^3$LO.