Proton tunnelling in the hydrogen bonds of the benzoic acid dimer: (18)O substitution and isotope effects of the heavy atom framework

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.

Measurement of proton tunneling in short hydrogen bonds in single crystals of 3,5 pyridinedicarboxylic acid using nuclear magnetic resonance spectroscopy

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 tunneling does not occur in short hydrogen bonds since the ground state energy level lies above the potential barrier, yet these data show a temperature independent, proton tunneling rate below 77 K and a clear deviation from classical dynamics below 91 K. This study therefore suggests that proton tunneling occurs in all hydrogen bonds at low temperature and the crossover temperature to classical hopping must be determined when evaluating whether proton tunneling persists at higher temperature, for example in enzyme catalysis under physiological conditions.

Spin-symmetry conversion in methyl rotors induced by tunnel resonance at low temperature

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.

Quantum rotation and translation of hydrogen molecules encapsulated inside C₆₀: temperature dependence of inelastic neutron scattering spectra

The quantum dynamics of a hydrogen molecule encapsulated inside the cage of a C60 fullerene molecule is investigated using inelastic neutron scattering (INS). The emphasis is on the temperature dependence of the INS spectra which were recorded using time-of-flight spectrometers. The hydrogen endofullerene system is highly quantum mechanical, exhibiting both translational and rotational quantization. The profound influence of the Pauli exclusion principle is revealed through nuclear spin isomerism. INS is shown to be exceptionally able to drive transitions between ortho-hydrogen and para-hydrogen which are spin-forbidden to photon spectroscopies. Spectra in the temperature range 1.6≤T≤280 K are presented, and examples are given which demonstrate how the temperature dependence of the INS peak amplitudes can provide an effective tool for assigning the transitions. It is also shown in a preliminary investigation how the temperature dependence may conceivably be used to probe crystal field effects and inter-fullerene interactions.

Dynamic tunneling polarization as a quantum rotor analogue of dynamic nuclear polarization and the NMR solid effect

The populations of the tunneling states of CH(3) are manipulated by rf irradiation of weakly allowed sideband transitions within the manifold of tunneling-magnetic levels. Substantial positive and negative CH(3) tunneling polarizations are observed, providing a quantum rotor analogue of dynamic nuclear polarization and the solid effect in NMR. The field-cycling NMR technique used in the experiments employs level crossings between tunneling and Zeeman systems to report on the tunneling polarization. The tunneling lifetimes are measured and the field dependence investigated.

1H-19F spin-lattice relaxation spectroscopy: proton tunnelling in the hydrogen bond studied by field-cycling NMR

Proton tunnelling in the hydrogen bonds of two fluorine substituted benzoic acid dimers has been investigated using field-cycling NMR relaxometry. The close proximity of the (19)F nuclei to the hydrogen bond protons introduces heteronuclear (19)F-(1)H dipolar interactions into the spin-lattice relaxation processes. This renders the (1)H magnetisation-recovery biexponential and introduces multiple spectral density components into the relaxation matrix characterised by frequencies that are sums and differences of the (19)F and (1)H Larmor frequencies. Using field-cycling NMR pulse sequences that measure the spin-lattice relaxation and cross-relaxation rates we demonstrate how some of these multiple spectral density components can be separately resolved. This leads to an accurate determination of the correlation times that characterise the proton tunnelling motion. A broad spectrum of relaxation behaviour is illustrated and explored in the chosen samples and the investigation is used to explore the theory and practise of field-cycling NMR relaxometry in cases where heteronuclear interactions are significant.

Tunnelling magnetic resonances: dynamic nuclear polarisation and the diffusion of methyl group tunnelling energy

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 4.2K. 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.

A field-cycling NMR investigation of resonant spin-lattice relaxation features arising from tunnelling methyl groups

(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.

Quantum translator-rotator: inelastic neutron scattering of dihydrogen molecules trapped inside anisotropic fullerene cages

We report an inelastic neutron scattering investigation of the quantum dynamics of hydrogen molecules trapped inside anisotropic fullerene cages. Transitions among the manifold of quantized rotational and translational states are directly observed. The spectra recorded as a function of energy and momentum transfer are interpreted in terms of the rotational potential and the cage dimensions. The thermodynamics of orthohydrogen and parahydrogen are investigated through temperature dependence measurements.

Field-cycling NMR investigations of (13)C-(1)H cross-relaxation and cross-polarisation: the nuclear solid effect and dynamic nuclear polarisation

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.

Cryogenic NMR spectroscopy of endohedral hydrogen-fullerene complexes

We have observed 1H NMR spectra of hydrogen molecules trapped inside modified fullerene cages under cryogenic conditions. Experiments on static samples were performed at sample temperatures down to 4.3 K, while magic-angle-spinning (MAS) experiments were performed at temperatures down to 20 K at spinning frequencies of 15 kHz. Both types of NMR spectra show a large increase in the intramolecular 1H-1H dipolar coupling at temperatures below 50 K, revealing thermal selection of a small number of spatial rotational states. The static and MAS spectra were compared to estimate the degree of sample heating in high-speed cryogenic MAS-NMR experiments. The cryogenic MAS-NMR data show that the site resolution of magic-angle-spinning NMR may be combined with the high signal strength of cryogenic operation and that cryogenic phenomena may be studied with chemical site selectivity.

Solid-state NMR of endohedral hydrogen–fullerene complexes

We present an overview of solid-state NMR studies of endohedral H(2)-fullerene complexes, including (1)H and (13)C NMR spectra, (1)H and (13)C spin relaxation studies, and the results of (1)H dipole-dipole recoupling experiments. The available data involves three different endohedral H(2)-fullerene complexes, studied over a wide range of temperatures and applied magnetic fields. The symmetry of the cage influences strongly the motionally-averaged nuclear spin interactions of the endohedral H(2) species, as well as its spin relaxation behaviour. In addition, the non-bonding interactions between fullerene cages are influenced by the presence of endohedral hydrogen molecules. The review also presents several pieces of experimental data which are not yet understood, one example being the structured (1)H NMR lineshapes of endohedral H(2) molecules trapped in highly symmetric cages at cryogenic temperatures. This review demonstrates the richness of NMR phenomena displayed by H(2)-fullerene complexes, especially in the cryogenic regime.

Isotope effects associated with tunneling and double proton transfer in the hydrogen bonds of benzoic acid

The isotope effects associated with double proton transfer in the hydrogen bonds of benzoic acid (BA) dimers have been measured using field-cycling (1)H NMR relaxometry and quasielastic neutron scattering. By studying mixed isotope (hydrogen and deuterium) samples, the dynamics of three isotopologues, BA-HH, BA-HD, and BA-DD, have been investigated. Low temperature measurements provide accurate measurements of the incoherent tunneling rate, k(0). This parameter scales accurately with the mass number, m, according to the formula k(0)=(E/m)e(-Fm) providing conclusive evidence that the proton transfer process is a strongly correlated motion of two hydrons. Furthermore, we conclude that the tunneling pathway is the same for the three isotopologue species. Measurements at higher temperatures illuminate the through barrier processes that are mediated via intermediate or excited vibrational states. In parallel with the investigation of proton transfer dynamics, the theoretical and experimental aspects of studying spin-lattice relaxation in single crystals of mixed isotope samples are investigated in depth. Heteronuclear dipolar interactions between (1)H and (2)H isotopes contribute significantly to the overall proton spin-lattice relaxation and it is shown that these must be modeled correctly to obtain accurate values for the proton transfer rates. Since the sample used in the NMR measurements was a single crystal, full account of the orientation dependence of the spin-lattice relaxation with respect to the applied B field was incorporated into the data analysis.

Proton tunneling in a hydrogen bond measured by cross-relaxation field-cycling NMR

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.

A 13C field-cycling NMR relaxometry investigation of proton tunnelling in the hydrogen bond: dynamic isotope effects, the influence of heteronuclear interactions and coupled relaxation

Concerted double proton transfer in the hydrogen bonds of a carboxylic acid dimer has been studied using 13C field-cycling NMR relaxometry. Heteronuclear 13C-1H dipolar interactions dominate the 13C spin-lattice relaxation which is significantly influenced by the polarisation state of the 1H Zeeman reservoir. The methodology of field-cycling experiments for such heteronuclear spin-coupled systems is studied experimentally and theoretically, including an investigation of various saturation-recovery and polarisation-recovery pulse sequence schemes. A theoretical model of the spin-lattice relaxation of this coupled system is presented which is corroborated by experiment. Spectral density components with frequencies omega(C), omega(C) + omega(H), and omega(C) - omega(H) are mapped out experimentally from the magnetic field dependence of the 13C and 1H spin-lattice relaxation and the proton transfer rate at low temperature is determined from their widths. Any dynamic isotope effect on the proton tunnelling in the hydrogen bond arising from 13C enrichment in the skeletal framework of the dimer is found to be smaller than experimental uncertainties (approximately 5%).

Evidence for coherent proton tunneling in a hydrogen bond network

We observed coherent proton tunneling in the cyclic network of four hydrogen bonds in calix[4]arene. The tunneling frequency of 35 megahertz was revealed by a peak in the magnetic field dependence of the proton spin-lattice relaxation rate measured with field-cycling nuclear magnetic resonance in the solid state at temperatures below 80 kelvin. The amplitude of the coherent tunneling peak grows with temperature according to a Boltzmann law with energy D/kB = (125 +/- 10) kelvin (where kB is Boltzmann's constant). The tunneling peak can be interpreted in the context of level crossings in the region where the tunneling frequency matches the proton Larmor frequency. The tunneling spectrum reveals fine structure that we attribute to coupling between the hydrogen bonds in the network. The characteristics of the tunneling peak are interpreted in the context of the potential energy surface experienced by the hydrogen atoms in the network.

Bi-exponential nuclear spin-lattice relaxation in solid hexafluoroacetylacetone

The reorientation of CF3 rotors in solid hexafluoroacetylacetone has been studied using pulsed NMR techniques. The temperature dependence of both fluorine (19F) and hydrogen (1H) nuclear spin-lattice relaxation has been measured using saturation-recovery pulse sequences. Following saturation of one of the spin reservoirs, the evolution with time of the longitudinal magnetisations associated with both nuclei are observed to be strongly bi-exponential. A theory is presented for the spin-lattice relaxation which is mediated by the heteronuclear dipole-dipole interaction between 19F and 1H nuclei. The experimental results are in good quantitative agreement with this relaxation theory. The spectral density functions have been evaluated using the known molecular structure and they are consistent with the experimental data. From this analysis we conclude that the relaxation is dominated by an intramolecular 19F-1H dipolar interaction. The spectral density function J(0)(omega H-omega F) makes an important contribution to the relaxation theory with the result that the motional spectrum is conveniently sampled at the difference frequency between 1H and 19F Larmor precessions. Two physically distinguishable CF3 rotors have been identified in this investigation, their dynamics are characterised by activation energies of 7.5 +/- 0.4 and 13.3 +/- 0.8 kJ mol-1, respectively.