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Radicals serve as source in dynamic nuclear polarization, but may also act as polarization sink. If the coupling between the electron spins and different nuclear reservoirs is stronger than any of the reservoirs' couplings to the lattice, radicals can mediate hetero-nuclear mixing. Here, we report radical-enhanced $^{13}$C relaxation in pyruvic acid doped with trityl. We find a linear dependence of the carbon $T_1$ on field between 5 mT and 2 T. We extend a model, employed previously for protons, to carbon, and predict efficient proton-carbon mixing via the radical Non-Zeeman reservoir, for fields from 20 mT to beyond 1 T. Discrepancies between the observed carbon relaxation and the model are attributed to enhanced direct hetero-nuclear mixing due to trityl-induced linebroadening, and a field-dependent carbon diffusion from the radical vicinity to the bulk. Measurements of hetero-nuclear polarization transfer up to 600 mT confirm the predicted mixing as well as both effects inferred from the relaxation analysis., 6 pages, 3 figures

The interactions between atoms and molecules may be described by a potential energy function of the nuclear coordinates. Nonbonded interactions between neutral atoms or molecules are dominated by repulsive forces at a short range and attractive dispersion forces at a medium range. Experimental data on the detailed interaction potentials for nonbonded interatomic and intermolecular forces are scarce. Here, we use terahertz spectroscopy and inelastic neutron scattering to determine the potential energy function for the nonbonded interaction between single He atoms and encapsulating C

The interactions between atoms and molecules may be described by a potential energy function of the nuclear coordinates. Non-bonded interactions are dominated by repulsive forces at short range and attractive dispersion forces at long range. Experimental data on the detailed interaction potentials for non-bonded interatomic and intermolecular forces is scarce. Here we use terahertz spectroscopy and inelastic neutron scattering to determine the potential energy function for the non-bonded interaction between single He atoms and encapsulating C60 fullerene cages, in the helium endofullerenes 3He and 4He, synthesised by molecular surgery techniques. The experimentally derived potential is compared to estimates from quantum chemistry calculations, and from sums of empirical two-body potentials., Comment: 25 pages, 14 figures, submitted to Journal of Chemical Physics

Accurate quantum simulations of the low-temperature inelastic neutron scattering (INS) spectra of HF@C

Accurate quantum simulations of the low-temperature inelastic neutron scattering (INS) spectra of HF@C60 are reported for two incident neutron wavelengths. They are distinguished by the rigorous inclusion of symmetry-breaking effects in the treatment and having the spectra computed with HF as the guest, rather than H2 or HD, as in the past work. The results demonstrate that the precedent-setting INS selection rule, originally derived for H2 and HD in near-spherical nanocavities, applies also to HF@C60, despite the large mass asymmetry of HF and the strongly mixed character of its translation−rotation eigenstates. This lends crucial support to the theoretical prediction made earlier that the INS selection rule is valid for any diatomic molecule in near-spherical nanoconfinement. The selection rule remains valid in the presence of symmetry breaking but is modified slightly in an interesting way. Comparison is made with the recently published experimental INS spectrum of HF@C60. The agreement is very good, apart from one peak for which our calculations suggest a reassignment. This reassignment is consistent with the measured INS spectrum presented in this work, which covers an extended energy range.

An overview is presented of the applications of fast field-cycling NMR to the study of quantum molecular tunnelling. Both incoherent and coherent tunnelling phenomena are examined. Examples presented include concerted double proton transfer in the hydrogen bonds of the benzoic acid dimer and coherent tunnelling of the quantum rotor CH3.

In this paper we report a methodology for calculating the inelastic neutron scattering spectrum of homonuclear diatomic molecules confined within nano-cavities of spherical symmetry. The method is based on the expansion of the confining potential into multipoles of the coupled rotational and translational angular variables. The Hamiltonian and the INS transition probabilities are evaluated analytically. The method affords a fast and computationally inexpensive way to simulate the inelastic neutron scattering spectrum of molecular hydrogen confined in fullerene cages. The potential energy surface is effectively parametrized in terms of few physical parameters comprising an harmonic term, anharmonic corrections and translation–rotation couplings. The parameters are refined by matching the simulations against the experiments and the excitation modes are identified for transfer energies up to 215 meV.

Using magnetic field-cycling at cryogenic temperatures, low-field dipole–dipole driven NMR spectra have been recorded on 3-pentanone (CH 3 CH 2 C(O)CH 2 CH 3 ). The spectra are characterised by tunnelling sidebands arising from the quantum dynamics of the methyl (CH 3 ) rotors. From the sideband frequencies, the CH 3 tunnelling frequency is determined to be ν t = 3.05 ± 0.01 MHz. The tunnelling sidebands are characterised by A–E transitions in nuclear spin-symmetry, involving simultaneous changes in tunnelling and nuclear spin states. To gain further insight, a theoretical analysis of the spin Hamiltonian matrix has been used to calculate the sideband transition probabilities. These are subsequently used in a thermodynamic model to simulate the low-field NMR spectrum which is compared with experiment. The level-crossings encountered as part of the magnetic field-cycling NMR sequence are found to play an essential role in determining the tunnelling sideband intensities.

We detail the process of low-field thermal mixing (LFTM) between (1)H and (13)C nuclei in neat [1-(13)C] pyruvic acid at cryogenic temperatures (4-15 K). Using fast-field-cycling NMR, (1)H nuclei in the molecule were polarized at modest high field (2 T) and then equilibrated with (13)C nuclei by fast cycling (∼300-400 ms) to a low field (0-300 G) that activates thermal mixing. The (13)C NMR spectrum was recorded after fast cycling back to 2 T. The (13)C signal derives from (1)H polarization via LFTM, in which the polarized ('cold') proton bath contacts the unpolarised ('hot') (13)C bath at a field so low that Zeeman and dipolar interactions are similar-sized and fluctuations in the latter drive (1)H-(13)C equilibration. By varying mixing time (tmix) and field (Bmix), we determined field-dependent rates of polarization transfer (1/τ) and decay (1/T1m) during mixing. This defines conditions for effective mixing, as utilized in 'brute-force' hyperpolarization of low-γ nuclei like (13)C using Boltzmann polarization from nearby protons. For neat pyruvic acid, near-optimum mixing occurs for tmix∼ 100-300 ms and Bmix∼ 30-60 G. Three forms of frozen neat pyruvic acid were tested: two glassy samples, (one well-deoxygenated, the other O2-exposed) and one sample pre-treated by annealing (also well-deoxygenated). Both annealing and the presence of O2 are known to dramatically alter high-field longitudinal relaxation (T1) of (1)H and (13)C (up to 10(2)-10(3)-fold effects). Here, we found smaller, but still critical factors of ∼(2-5)× on both τ and T1m. Annealed, well-deoxygenated samples exhibit the longest time constants, e.g., τ∼ 30-70 ms and T1m∼ 1-20 s, each growing vs. Bmix. Mixing 'turns off' for Bmix∼100 G. That T1m≫τ is consistent with earlier success with polarization transfer from (1)H to (13)C by LFTM.

Inelastic neutron scattering, far-infrared spectroscopy, and cryogenic nuclear magnetic resonance are used to investigate the quantized rotation and ortho–para conversion of single water molecules trapped inside closed fullerene cages. The existence of metastable ortho -water molecules is demonstrated, and the interconversion of ortho -and para -water spin isomers is tracked in real time. Our investigation reveals that the ground state of encapsulated ortho water has a lifted degeneracy, associated with symmetry-breaking of the water environment.

The supramolecular complex, H2@C60, represents a model of a quantum rotor in a nearly spherical box. In providing a real example of a quantum particle entrapped in a small space, the system cuts to the heart of many important and fundamental quantum mechanical issues. This review compares the predictions of theory of the quantum behaviour of H2 incarcerated in C60 with the results of infrared spectroscopy, inelastic neutron scattering and nuclear magnetic resonance. For H2@C60, each of these methods supports the quantization of translational motion of H2 and the coupling of the translational motion with rotational motion and provides insights to the factors leading to breaking of the degeneracies of states expected for a purely spherical potential. Infrared spectroscopy and inelastic neutron scattering experiments at cryogenic temperatures provide direct evidence of a profound quantum mechanical feature of H2 predicted by Heisenberg based on the Pauli principle: the existence of two nuclear spin isomers, a nuclear spin singlet (para-H2) and a nuclear triplet (ortho-H2). Nuclear magnetic resonance is capable of probing the local lattice environment of H2@C60 through analysis of the H2 motional effects on the ortho-H2 spin dynamics (para-H2, the nuclear singlet state, is NMR silent). In this review we will show how the information obtained by three different forms of spectroscopy join together with quantum theory to create a complementary and consistent picture which strikingly shows the intrinsically quantum nature of H2@C60.

The double proton transfer reaction in the bridging hydrogen bonds of carboxylic acid dimers provides a model system for investigating the fundamental physics underpinning the role of quantum tunnelling in molecular dynamics. The behaviour of this system is used to discuss the possible role that tunnelling plays in the molecular dynamics that characterise more complex biological systems at high temperature. Copyright © 2010 John Wiley & Sons, Ltd.

The dynamic nuclear polarisation (DNP) of 1 H spins arising from methyl tunnelling magnetic resonances has been investigated in copper-doped zinc acetate dihydrate using field-cycling NMR spectroscopy at 4.2 K. The tunnel resonances appear in the field range 20–50 mT and trace out the envelope of the electron spin resonance spectrum of the Cu 2+ ion impurities. By investigating the DNP line shapes as a function of time, the cooling of the methyl tunnel reservoir has been probed. The role of spectral diffusion of tunnelling energy in determining the DNP line shapes has been investigated through experiments and numerical simulations based on a theoretical model that describes the time evolution of the 1 H polarisation and the tunnelling temperature. The model is discussed in detail in comparison with the experiments. All effects have been studied as a function of Cu 2+ ion concentration.

(1)H nuclear spin-lattice relaxation has been investigated in sodium acetate trihydrate and sorbic acid using field-cycling NMR in the solid state. The relaxation is dominated by the reorientation of the methyl groups. Resonant features arising from coherent tunnelling are observed in both the magnetic field dependence of the spin lattice relaxation rate, T(1)(-1)(B(z)) and in the inverse temperature dependence, T(1)(-1)(1/T). The two systems have different barrier heights and tunnelling frequencies, providing different perspectives on the tunnel resonance phenomena. The magnetic field dependence enables different spectral density components to be separately investigated and in the carboxylic acid, sorbic acid, concerted proton transfer in the hydrogen bonds is also identified at low field and low temperature. The methyl hindering barriers and the correlation times characterising the reorientational dynamics has been accurately determined in both materials.

A field-cycling NMR investigation of (1)H-(13)C polarisation transfer using cross-relaxation and the nuclear solid effect (NSE) is described. Dynamic nuclear polarisation (DNP) of the (13)C spins is observed when forbidden transitions are driven by r.f. irradiation at the sum and difference Larmor frequencies of the two nuclei. When the (1)H spins are pre-polarised, a significant transfer of polarisation to the (13)C nuclei is achieved in a time short compared with the spin-lattice relaxation time of (13)C. The cross-polarisation arising from the NSE is studied as a function of B-field and time. These results are compared with the solutions of the differential equations that govern the coupled system of (1)H-(13)C spins. The effects of cross-relaxation are incorporated into the model for the first time and good agreement between theory and experiment is obtained. The experiments have been conducted at 20K on a (13)C-enriched sample of benzoic acid.

The cavity inside fullerenes provides a unique environment for the study of isolated atoms and molecules. We report the encapsulation of hydrogen fluoride inside C60 using molecular surgery to give the endohedral fullerene HF@C60. The key synthetic step is the closure of the open fullerene cage with the escape of HF minimized. The encapsulated HF molecule moves freely inside the cage and exhibits quantization of its translational and rotational degrees of freedom, as revealed by inelastic neutron scattering and infrared spectroscopy. The rotational and vibrational constants of the encapsulated HF molecules were found to be redshifted relative to free HF. The NMR spectra display a large (1)H-(19)F J coupling typical of an isolated species. The dipole moment of HF@C60 was estimated from the temperature dependence of the dielectric constant at cryogenic temperatures and showed that the cage shields around 75% of the HF dipole.

A field-cycling NMR pulse sequence is described for studying cross-relaxation between unlike nuclear spins in the solid state. The technique has been applied to study proton tunneling in the hydrogen bonds of a carboxylic acid containing 19F and 1H spins. By studying the B-field dependence of the off-diagonal element of the relaxation matrix that characterizes the longitudinal polarizations, an accurate measure of the proton transfer rate is obtained.

Field-cycling NMR relaxometry has been employed to measure the spectral density for double proton transfer in the hydrogen bonds of benzoic acid. Data have been recorded in the intermediate temperature range characterising the crossover region between quantum and pseudo-classical regimes. The quantum-to-classical transition is shown to be smooth and at all temperatures the proton transfer is characterised by a single correlation time. A critical appraisal is given of competing theories.

A single crystal NMR investigation has been made of proton transfer in benzoic acid at low temperature when phonon-assisted tunnelling dominates this dynamics. Precise knowledge of the hydrogen coordinates was employed to minimise the assumptions that are made in reducing NMR data to provide information on the rate of proton transfer and the properties of the potential energy surface. The geometry associated with the molecular rearrangement was investigated through orientation dependent measurements of the proton spin–lattice relaxation time, while the temperature dependence of the proton dipolar spectrum was used to evaluate the energy difference between the two benzoic acid tautomers. Below 100 K, this energy asymmetry is constant.

The concerted two proton transfer in the hydrogen bonds of para -halogen substituted derivatives of benzoic acid has been investigated using conventional NMR relaxometry combined with field-cycling measurements of the magnetic field dependence of the proton spin–lattice relaxation rate. Thus, the inverse correlation time describing the proton transfer process has been determined over a wide range of temperature. The energy difference between the two proton configurations was determined in all four compounds to be significantly larger than in the prototype model system of benzoic acid dimers. This energy difference exceeds the cut-off frequency of the acoustic phonon spectrum of the crystal as well as the frequency of two lowest modes promoting proton tunnelling. The low temperature limit of the tunnelling rate was found to be one order of magnitude higher than in benzoic acid. For the four compounds studied, this rate and its increase at higher temperature exhibit a different behaviour to benzoic acid which is attributed to the details of the level structure and energy gaps between states corresponding predominantly to one or the other proton configuration. A new adaptation of the phonon-assisted theory is proposed which applies to these cases of high energy asymmetry. To assist in the interpretation of the data, a powder neutron diffraction structure determination of 4-bromobenzoic acid is reported together with DFT calculations on the hydrogen bond structures of all members of the 4-halogen substituted derivatives.

The tunneling and librational dynamics of the methyl groups of acetyl-acetone were investigated by inelastic and quasielastic neutron scattering at ambient and high pressure (4 kbar) for a variety of isotopic compounds. Samples, prepared by quenching the liquid, are shown to consist of a mixture of keto and enol forms of the molecule. This fact explains difficulties in the data analysis of previous studies. In the present work the contributions of the two forms could be separated, by preparing pure enol samples as well as keto-enriched samples. Two inequivalent methyl groups are identified for the enol form with barrier heights of the hindering potential in the range of 220–800 K. These potential barriers are fairly sensitive to deuteration of the nonmethyl protons and to disorder in the crystal. In contrast, for the keto form the potential is insensitive to these factors. These differences reflect the influence of the hydrogen-bonded proton on the methyl group dynamics in the enol molecule.

Some applications of magnetic field-cycling NMR in the study of molecular tunnelling are reviewed with selected examples. Experiments on the rotational tunnelling of methyl groups describe the techniques that are available for studying coherent tunnelling. The case of incoherent phonon-assisted tunnelling is described in the context of proton transfer in the hydrogen bond. The importance of developing broadband techniques in NMR is emphasised.

We report an inelastic neutron scattering (INS) study of H2 molecule encapsulated inside the fullerene C60 which confirms the recently predicted selection rule, the first to be established for the INS spectroscopy of aperiodic, discrete molecular compounds. Several transitions from the ground state of para-H2 to certain excited translation-rotation states, forbidden according to the selection rule, are systematically absent from the INS spectra, thus validating the selection rule with a high degree of confidence. Its confirmation sets a precedent, as it runs counter to the widely held view that the INS spectroscopy of molecular compounds is not subject to any selection rules.

Inelastic neutron scattering (INS) has been employed to investigate the quantum dynamics of water molecules permanently entrapped inside the cages of C60 fullerene molecules. This study of the supramolecular complex, H2O@C60, provides the unique opportunity to study isolated water molecules in a highly symmetric environment. Free from strong interactions, the water molecule has a high degree of rotational freedom enabling its nuclear spin isomers, ortho-H2O and para-H2O to be separately identified and studied. The INS technique mediates transitions between the ortho and para spin isomers and using three INS spectrometers, the rotational levels of H2O have been investigated, correlating well with the known levels in gaseous water. The slow process of nuclear spin conversion between ortho-H2O and para-H2O is revealed in the time dependence of the INS peak intensities over periods of many hours. Of particular interest to this study is the observed splitting of the ground state of ortho-H2O, raising the three-fold degeneracy into two states with degeneracy 2 and 1 respectively. This is attributed to a symmetry-breaking interaction of the water environment.

Inelastic neutron scattering (INS) has been employed to investigate the quantum dynamics of water molecules permanently entrapped inside the cages of C60 fullerene molecules. This study of the supramolecular complex, H2O@C60, provides the unique opportunity to study isolated water molecules in a highly symmetric environment. Free from strong interactions, the water molecule has a high degree of rotational freedom enabling its nuclear spin isomers, ortho-H2O and para-H2O to be separately identified and studied. The INS technique mediates transitions between the ortho and para spin isomers and using three INS spectrometers, the rotational levels of H2O have been investigated, correlating well with the known levels in gaseous water. The slow process of nuclear spin conversion between ortho-H2O and para-H2O is revealed in the time dependence of the INS peak intensities over periods of many hours. Of particular interest to this study is the observed splitting of the ground state of ortho-H2O, raising the three-fold degeneracy into two states with degeneracy 2 and 1 respectively. This is attributed to a symmetry-breaking interaction of the water environment.

We report an inelastic neutron scattering (INS) study of a H2 molecule encapsulated inside the fullerene C60 which confirms the recently predicted selection rule, the first to be established for the INS spectroscopy of aperiodic, discrete molecular compounds. Several transitions from the ground state of para-H2 to certain excited translation-rotation states, forbidden according to the selection rule, are systematically absent from the INS spectra, thus validating the selection rule with a high degree of confidence. Its confirmation sets a precedent, as it runs counter to the widely held view that the INS spectroscopy of molecular compounds is not subject to any selection rules.

In this letter, we present NMR spin-lattice and relaxometry data for proton transfer in one of the shortest known N-H∙∙∙O hydrogen bonds in a single crystal of 3,5 pyridinedicarboxylic acid (35PDCA). It is widely believed that proton transfer by quantum tunnelling does not occur in short hydrogen bonds since the ground state energy level lies above the potential barrier yet this data shows a temperature independent, proton tunnelling rate below 77 K and a clear deviation from classical dynamics below 91 K. This study therefore suggests that proton tunnelling occurs in all hydrogen bonds at low temperature and the cross-over temperature to classical hopping must be determined when evaluating whether proton tunnelling persists at higher temperature, for example in enzyme catalysis under physiological conditions.

The water-endofullerene H2O@C60 provides a unique chemical system in which freely rotating water molecules are confined inside homogeneous and symmetrical carbon cages. The spin conversion between the ortho and para species of the endohedral H2O was studied in the solid phase by low-temperature nuclear magnetic resonance. The experimental data are consistent with a second-order kinetics, indicating a bimolecular spin conversion process. Numerical simulations suggest the simultaneous presence of a spin diffusion process allowing neighbouring ortho and para molecules to exchange their angular momenta. Cross-polarization experiments found no evidence that the spin conversion of the endohedral H2O molecules is catalysed by (13)C nuclei present in the cages.

Vibrational spectra of several isotopomers of benzoic acid (BA) crystals have been recorded by inelastic neutron scattering and are compared with spectra calculated for different potential energy surfaces (PES). These PES were obtained within the harmonic approximation from quantum chemical density functional theory (DFT) calculations made for the monomer, the isolated dimer, and the crystal using different codes and different levels of basis functions. Without refinement of the force constants, agreement between calculated and observed spectra is already sufficient for an unambiguous assignment of all vibrational modes. The best agreement was obtained with periodic DFT calculations. The most prominent discrepancy between calculated and observed frequencies was found for the out-of-plane O–H bending modes. For these modes (as well as for the in-plane bending and the O–H stretching modes) the anharmonicity of the potential was calculated, and the anharmonic correction was shown to account for about one-thi...

Double-proton transfer in the hydrogen bonds of the benzoic acid dimer is described by an asymmetric double-well potential. At low temperature, the hydrogen bond dynamics are dominated by phonon-assisted tunnelling and the correlation time for proton transfer is independent of temperature. We report proton transfer measurements on samples that incorporate a small concentration of thioindigo dye molecules as a substitutional impurity. The potential energy surface, particularly the energy asymmetry of the double-well potential, of dimers within a sphere of influence of the guest molecule is perturbed. These dimers exhibit a distribution of energy asymmetries and correlation times. The system is analogous to disordered systems such as glasses and provides insight into low-frequency excitations that are invoked to explain the molecular dynamics in those systems. Field-cycling NMR relaxometry was used to make a direct measurement of the spectral density of the sample at low temperatures and to identify the contribution made by the proton transfer dynamics of the hydrogen bonds in the vicinity of the guest molecules. The mean proton transfer rate and asymmetry of these dimers have been measured and are compared with the values characteristic of dimers that are remote from impurity centres. The proficiency of field-cycling NMR relaxometry, and the advantages over conventional narrow band spin–lattice relaxation measurements, is discussed.

The dynamics of proton transfer along the hydrogen bonds of dimers of benzoic acid has been characterized in single crystals and powders at temperatures between 10 K and 110 K by quasi-elastic neutron scattering (QENS) and by proton spin-lattice relaxation using field-cycling NMR spectroscopy. These measurements define the geometry of the proton transfer, the energy difference between the two tautomers of benzoic acid corresponding to the two proton positions, as well as the proton correlation time. The proton jump vector agrees well with expectations from recent crystallographic data. The energy difference between tautomers of A/kB=86.5±1.5 K is in contradiction with the lower value of A/kB=50 K derived from older 13C NMR and infrared absorption measurements. NMR and QENS measurements provide mutually consistent values of the proton correlation time, τc, and an accurate characterization of the dynamics at temperatures where the onset of thermally activated processes is observed. Tunneling in an excited v...

A low-field NMR and inelastic neutron scattering investigation of tunnelling methyl dynamics in methyl acetate has been performed. Tunnel frequencies of 1.3 μeV and 0.31 neV have been measured for the two chemically distinct methyl groups in the molecule. From the known crystal structure at 145 K, the observed quantum methyl dynamics can be reproduced from a time-independent, molecular mechanics calculation based on ab initio techniques and empirical atom–atom potentials. Although no spectral evidence of coupled methyl dynamics exists, the delocalisation and reorientation of the methyl groups at low temperature must be included in the calculation in view of the strong coupling potentials. This is achieved with a quantum mechanical mean-field approach.

Two-proton exchange along the two hydrogen bonds mediates the tautomerization in benzoic acid (BA) dimers. Optical spectroscopy and quasi-elastic neutron scattering (QENS) have been employed to characterize the proton dynamics in doped and pure BA crystals. The proton motion in BA is govemed by a multidimensional potential energy surface (PES), and recent theoretical methods, based on a perturbative instanton approach, to describe tunneling in such PES are presented. This PES is also modulated by the interaction with the solid state environment as manifest by the energy difference between the otherwise equivalent tautomers. The value of this energy difference in pure crystals is an important parameter in the data analysis of NMR and QENS. Both methods give mutually consistent values that differ significantly from earlier determinations via infrared and 13 C NMR as well as a recent evaluation using neutron diffraction data. The energy difference between tautomers is altered for dimers in the vicinity of impurity molecules. This is the basis for the optical spectroscopic methods, which enable a direct and accurate determination of the level structure and tautomerization dynamics of these coupled dimers in the limit of very low temperatures, where coherent tunneling is also observed in some cases. Measurements with new impurity molecules make it possible to monitor simultaneously at least 10 different tautomer configurations and prove that the influence of the probe molecules on the proton dynamics is small. The transition to thermally activated barrier crossing at higher temperatures is accessed via the width of the QENS line that is determined by the inverse of the proton correlation time. The quantitative data analysis of the scattered intensity as a function of temperature and scattering angle yields the energy difference, A, betwcen the two wells (A/k B =90±20 K), the length (0.686 A), and direction of the proton jump vector. These measurements complement NMR investigations presented in the preceding paper.

Double proton transfer in the hydrogen bonds of carboxylic acid dimers has been investigated via measurements of the dispersion of the proton spin-lattice relaxation time, T 1 , using magnetic field-cycling NMR. A plot of the spin-lattice relaxation rate, T as a function of magnetic field, provides a direct measurement of the motional spectrum and hence of the proton transfer rate. In the materials studied, these NMR experiments are optimised for the low temperature region where the dynamics are dominated by incoherent quantum tunnelling. Measurements of the proton transfer rate at higher temperatures have been made using quasi-elastic neutron scattering (QENS) and these facilitate the characterisation of the transition between quantum and classical dynamics in the intermediate temperature region. The role of tunnelling in the excited vibrational states of the double minimum potential (DMP) which characterises the system is revealed in these measurements and has been analysed according to the behaviour of a particle in a DMP which is coupled to a bath of phonons. The complementarity between the NMR and QENS techniques is emphasised and discussed, and the dynamic range accessible to the field-cycling NMR technique is explored through studying a range of related materials.

Field-cycling NMR in the solid state at low temperature (4.2 K) has been employed to measure the tunneling spectra of methyl (CH3) rotors in phenylacetone and toluene. The phenomenon of tunnel resonance reveals anomalies in (1)H magnetization from which the following tunnel frequencies have been determined: phenylacetone, νt = 6.58 ± 0.08 MHz; toluene, νt(1) = 6.45 ± 0.06 GHz and νt(2) = 7.07 ± 0.06 GHz. The tunnel frequencies in the two samples differ by three orders of magnitude, meaning different experimental approaches are required. In phenylacetone the magnetization anomalies are observed when the tunnel frequency matches one or two times the (1)H Larmor frequency. In toluene, doping with free radicals enables magnetization anomalies to be observed when the tunnel frequency is equal to the electron spin Larmor frequency. Cross-polarization processes between the tunneling and Zeeman systems are proposed and form the basis of a thermodynamic model to simulate the tunnel resonance spectra. These invoke space-spin interactions to drive the changes in nuclear spin-symmetry. The tunnel resonance lineshapes are explained, showing good quantitative agreement between experiment and simulations.

Field-cycling (1)H NMR relaxometry has been used to measure the rate of concerted double proton transfer in the hydrogen bonds of (16)O and (18)O isotopologues of benzoic acid dimers. The experiments have been conducted in the solid state at low temperature 13.3 ≤ T ≤ 80 K where the dynamics are dominated by incoherent proton tunnelling. The low temperature tunnelling rate in the (16)O isotopologue is observed to be approximately 15% faster than in the (18)O isotopologue. The difference is attributed to an isotope effect of the heavy atom framework of the benzoic acid dimer resulting from displacements of the oxygen atoms that accompany the proton transfer. Sources of systematic uncertainty have been minimized in the design of the experimental protocols and the experiments are critically appraised in formally assigning the measured differences to an effect of mass on the tunnelling dynamics.

The incoherent tunnelling rate for proton transfer in the hydrogen bonds of benzoic acid dimers has been measured by field cycling NMR from the dispersion of the proton spin-lattice relaxation time which maps out the spectral density function directly. The intermediate region between quantum and classical dynamics has been studied by measuring the inverse correlation time for proton transfer as a function of temperature and the contribution made by tunnelling in the excited states of the double minimum potential has been determined.

This Theo Murphy Meeting Issue contains papers presented at a Discussion Meeting held at the Kavli Centre of the Royal Society in March 2012. The meeting brought together a wide variety of scientists working on different aspects of small-molecule endofullerenes—those intriguing chemical systems in which small molecules such as H 2 or H 2 O are encapsulated in tiny carbon cages.

Nuclear magnetic resonance (NMR) techniques are extensively used in many areas of basic and clinical research, as well as in diagnostic medicine. However, NMR signals are intrinsically weak, and this imposes substantial constraints on the amounts and concentrations of materials that can be detected. The signals are weak because of the low energies characteristic of NMR and the resulting very low (typically 0.0001-0.01%) polarization of the nuclear spins. Here, we show that exposure to very low temperatures and high magnetic fields, in conjunction with nanoparticle-mediated relaxation enhancement, can be used to generate extremely high nuclear polarization levels on a realistic timescale; with copper nanoparticles at 15 mK and 14 T, (13)C polarization grew towards its equilibrium level of 23% with an estimated half-time of about 60 hours. This contrasts with a (13)C half-time of at least one year in the presence of aluminium nanoparticles. Cupric oxide nanoparticles were also effective relaxation agents. Our findings lead us to suspect that the relaxation may be mediated, at least in part, by the remarkable magnetic properties that some nanoparticle preparations can display. This methodology offers prospects for achieving polarization levels of 10-50% or more for many nuclear species, with a wide range of potential applications in structural biology and medicine.

Many approaches are now available for achieving high levels of nuclear spin polarization. One of these methods is based on the notion that as the temperature is reduced, the equilibrium nuclear polarization will increase, according to the Boltzmann distribution. The main problem with this approach is the length of time it may take to approach thermal equilibrium at low temperatures, since nuclear relaxation times (characterized by the spin-lattice relaxation time T1) can become very long. Here, we show, by means of relaxation time measurements of frozen solutions, that selected lanthanide ions, in the form of their chelates with DTPA, can act as effective relaxation agents at low temperatures. Differential effects are seen with the different lanthanides that were tested, holmium and dysprosium showing highest relaxivity, while gadolinium is ineffective at temperatures of 20 K and below. These observations are consistent with the known electron-spin relaxation time characteristics of these lanthanides. The maximum relaxivity occurs at around 10 K for Ho-DTPA and 20 K for Dy-DTPA. Moreover, these two agents show only modest relaxivity at room temperature, and can thus be regarded as relaxation switches. We conclude that these agents can speed up solid state NMR experiments by reducing the T1 values of the relevant nuclei, and hence increasing the rate at which data can be acquired. They could also be of value in the context of a simple low-cost method of achieving several-hundred-fold improvements in polarization for experiments in which samples are pre-polarized at low temperatures, then rewarmed and dissolved immediately prior to analysis.

Double proton transfer in the hydrogen bonds of the benzoic acid dimer has been studied using proton NMR measurements on a single crystal. Both the NMR absorption spectrum and the spin-lattice relaxation time, T 1 , are dominated by the dipolar interaction between the two protons in the dimer and measurements have been made in the temperature range from 300 down to 10 K. The spectrum exhibits motional narrowing and T 1 is sensitive to the dynamics over the whole range. Quantitative analysis of the data has enabled measurements of the inter-proton distance, the asymmetry energy of the double minimum potential and the correlation time. Incoherent quantum tunnelling characterises the dynamics at low temperature ( T

We report a correlation between the rate of incoherent tunneling associated with proton transfer in hydrogen bonds and the structure of aromatic carboxylic acid dimers. The compressibility of the hydrogen bond in benzoic acid, specifically the oxygen–oxygen distance r(O⋅⋅O), has been measured as a function of hydrostatic pressure up to 3.2 kbar using neutron powder diffraction. All data were recorded at a temperature of 5 K. Using previously published pressure dependence NMR measurements, we have investigated the relationship between the dynamics in the quantum regime and r(O⋅⋅O) in the hydrogen bonds of benzoic acid. The incoherent tunneling rate increases exponentially with decreasing r(O⋅⋅O). This behavior is attributed to the increase in the tunneling matrix element as the potential wells and the localized eigenfunctions of the double minimum potential which characterize the system are brought into closer proximity. There is a quantitative agreement between this study, in which the hydrogen bonds are ...

In NMR the polarisation of the Zeeman system may be routinely probed and manipulated by applying resonant rf pulses. As with spin-½ nuclei, at low temperature the quantum tunnelling states of a methyl rotor are characterised by two energy levels and it is interesting to consider how these tunnelling states might be probed and manipulated in an analogous way to nuclear spins in NMR. In this paper experimental procedures based on magnetic field-cycling NMR are described where, by irradiating methyl tunnelling sidebands, the polarisations of the methyl tunnelling systems are measured and manipulated in a prescribed fashion. At the heart of the technique is a phenomenon that is closely analogous to dynamic nuclear polarisation and the solid effect where forbidden transitions mediate polarisation transfer between ¹H Zeeman and methyl tunnelling systems. Depending on the irradiated sideband, both positive and negative polarisations of the tunnelling system are achieved, the latter corresponding to population inversion and negative tunnelling temperatures. The transition mechanics are investigated through a series of experiments and a theoretical model is presented that provides good quantitative agreement.

The quantum and classical dynamics of hydrogen atoms in the hydrogen bonds of tetrafluoroterephthalic acid have been studied using nuclear magnetic resonance (NMR), and inelastic neutron scattering (INS). The temperature dependence of the correlation time for the motion has been investigated using measurements of the spin-lattice relaxation of both hydrogen and fluorine nuclei in the temperature range 20 K ⩽ T ⩽ 300 K, and quasi-elastic neutron scattering measurements above 250 K. It is shown that the spin-lattice relaxation is governed by modulations of both homonuclear (1H-1H) and heteronuclear (1H-19F) dipolar interactions and the magnetization recovery is multi-exponential. Expressions for the elements of the spin-lattice relaxation matrix are derived and, together with a simple theory for the hydrogen bond dynamics, a good fit and satisfactory account of the experimental NMR and INS data are obtained. The low temperature dynamics are governed by incoherent tunnelling, and a comparison is made with th...

Experiments are described in which the rotation of methyl groups in solids at helium temperatures is driven using external magnetic fields. The orientation of the nuclear magnetic dipoles is caused to oscillate in synchronism with coherent tunnelling rotation, switching time-dependent internal-magnetic-field gradients due to the dipole-dipole interaction to produce a small steady torque. The resulting change in the frequency of tunnelling, of the order of 150 kHz, is detected by field cycling NMR.

NMR techniques have been developed to study methyl group reorientation and hydrogen bond dynamics as a function of hydrostatic pressure. This paper briefly reviews some earlier work and presents new results of the pressure dependence of the reorientation of two distinct methyl groups in methyl ethyl ketone.