Multi-quantum quadrupole relaxation enhancement effects in 209Bi compounds.

1H spin-lattice nuclear magnetic resonance relaxation experiments have been performed for triphenylbismuth dichloride (C18H15BiCl2) and phenylbismuth dichloride (C6H5BiCl2) in powder. The frequency range of 20-128 MHz has been covered. Due to 1H-209Bi dipole-dipole interactions, a rich set of pronounced Quadrupole Relaxation Enhancement (QRE) peaks (quadrupole peaks) has been observed. The QRE patterns for both compounds have been explained in terms of single- and double-quantum transitions of the participating nuclei. The analysis has revealed a complex, quantum-mechanical mechanism of the QRE effects. The mechanism goes far beyond the simple explanation of the existence of three quadrupole peaks for 14N reported in literature. The analysis has been supported by nuclear quadrupole resonance results that independently provided the 209Bi quadrupole parameters (amplitude of the quadrupole coupling constant and asymmetry parameter).

209Bi quadrupole relaxation enhancement in solids as a step towards new contrast mechanisms in magnetic resonance imaging.

Motivated by the possibility of exploiting species containing high spin quantum number nuclei (referred to as quadrupole nuclei) as novel contrast agents for Magnetic Resonance Imaging, based on Quadrupole Relaxation Enhancement (QRE) effects, 1H spin-lattice relaxation has been investigated for tris(2-methoxyphenyl)bismuthane and tris(2,6-dimethoxyphenyl)bismuthane in powder. The relaxation experiment has been performed in the magnetic field range of 0.5 T to 3 T (the upper limit corresponds to the field used in many medical scanners). A very rich QRE pattern (several frequency specific 1H spin-lattice relaxation rate maxima) has been observed for both compounds. Complementary Nuclear Quadrupole Resonance experiments have been performed in order to determine the quadrupole parameters (quadrupole coupling constant and asymmetry parameters) for 209Bi. Knowing the parameters, the QRE pattern has been explained on the basis of a quantum-mechanical picture of the system including single and double-quantum coherences for the participating nuclei (1H and 209Bi). In this way the quantum-mechanical origin of the spin transitions leading to the QRE effects has been explained.

Structure and dynamics of [NH2(CH3)2]3Sb2Cl9 by means of 1H NMR relaxometry - quadrupolar relaxation enhancement effects.

1H spin-lattice relaxation experiments have been performed for [NH2(CH3)2]3Sb2Cl9 (tris(dimethylammonium)nonachlorodiantimonate(iii)) in the temperature range of 253-313 K and a broad range of frequencies - from 4 kHz to 40 MHz. From the analysis of quadrupolar relaxation enhancement effects (quadrupolar peaks) associated with 14N nuclei, two lattice sites characterized by different electric field gradient tensors have been revealed. The 14N quadrupolar couplings and asymmetry parameters at these sites differ by a factor of about two. Three motional processes have been identified and attributed to the overall dynamics of the NH2(CH3)2 cations (slow motion), dynamics of the NH2 groups (intermediate motion) and methyl group rotation (fast motion). It has been shown that the slow dynamics is only weakly temperature dependent, while the intermediate and fast motional processes are characterized by activation energies of 2.92 kJ mol-1 and 0.41 kJ mol-1, respectively. The correlation time of the slow dynamics is of the order of µs, while the intermediate dynamics is faster by 2-3 orders of magnitude (depending on temperature). All correlation times have turned out to be independent of the position of the cations in the lattice (they are the same for both lattice sites). The analysis presented in this work is an example of the potential of the quadrupolar relaxation enhancement effects as a method revealing information on the dynamics and structure of solids.

Dynamics of solid alanine by means of nuclear magnetic resonance relaxometry.

1H nuclear magnetic resonance relaxometry was applied to investigate the dynamics of l-alanine in the solid phase (powder). The experimental studies were carried out in a very broad frequency range, covering four orders of magnitude-from 4 kHz to 40 MHz (referring to the 1H resonance frequency) in order to probe motional processes of much different time scales by a single experiment. To get access to the dynamics of different proton groups of alanine, the 1H spin-lattice relaxation measurements were performed for non-deuterated and partially deuterated alanine. The experiments were carried out in the temperature range of 293 K-370 K (non-deuterated alanine) and 318 K-370 K (partially deuterated alanine). As a result of a thorough theoretical analysis of the extensive set of experimental results, three motional processes occurring on different time scales are identified and quantitatively described. The slowest process occurs on a time scale of µs and it is attributed to the collective dynamics of a 3D hydrogen bond network of alanine, while the intermediate, attributed to the dynamics of the NH3 group, corresponds to the range of tenths of ns. The fast process describes the rotation of the CH3 group.

(1)H NMR relaxometry and quadrupole relaxation enhancement as a sensitive probe of dynamical properties of solids--[C(NH2)3]3Bi2I9 as an example.

(1)H nuclear magnetic resonance relaxometry has been applied to reveal information on dynamics and structure of Gu3Bi2I9 ([Gu = C(NH2)3] denotes guanidinium cation). The data have been analyzed in terms of a theory of quadrupole relaxation enhancement, which has been extended here by including effects associated with quadrupole ((14)N) spin relaxation caused by a fast fluctuating component of the electric field gradient tensor. Two motional processes have been identified: a slow one occurring on a timescale of about 8 × 10(-6) s which has turned out to be (almost) temperature independent, and a fast process in the range of 10(-9) s. From the (1)H-(14)N relaxation contribution (that shows "quadrupole peaks") the quadrupole parameters, which are a fingerprint of the arrangement of the anionic network, have been determined. It has been demonstrated that the magnitude of the quadrupole coupling considerably changes with temperature and the changes are not caused by phase transitions. At the same time, it has been shown that there is no evidence of abrupt changes in the cationic dynamics and the anionic substructure upon the phase transitions.

Dynamics of [C3H5N2]6[Bi4Br18] by means of (1)H NMR relaxometry and quadrupole relaxation enhancement.

(1)H spin-lattice field cycling relaxation dispersion experiments in the intermediate phase II of the solid [C3H5N2]6[Bi4Br18] are presented. Two motional processes have been identified from the (1)H spin-lattice relaxation dispersion profiles and quantitatively described. It has been concluded that these processes are associated with anisotropic reorientations of the imidazolium ring, characterized by correlation times of the order of 10(-8) s-10(-9) s and of about 10(-5) s. Moreover, quadrupole relaxation enhancement (QRE) effects originating from slowly fluctuating (1)H-(14)N dipolar interactions have been observed. From the positions of the relaxation maxima, the quadrupole coupling parameters for the (14)N nuclei in [C3H5N2]6[Bi4Br18] have been determined. The (1)H-(14)N relaxation contribution associated with the slow dynamics has been described in terms of a theory of QRE [Kruk et al., Solid State Nucl. Magn. Reson. 40, 114 (2011)] based on the stochastic Liouville equation. The shape of the QRE maxima (often referred to as "quadrupole peaks") has been consistently reproduced for the correlation time describing the slow dynamics and the determined quadrupole coupling parameters.

Dynamics of ferroelectric bis(imidazolium) pentachloroantimonate(III) by means of nuclear magnetic resonance 1H relaxometry and dielectric spectroscopy.

Some of haloantimonates(III) and halobismuthates(III) are ferroelectric. Bis(imidazolium) pentachloroantimonate(III), (C3N2H5)2SbCl5 (abbreviation: ICA) is the first example of such compounds with a one-dimensional anionic chain which exhibits ferroelectric properties. The relation between the ionic dynamics and network structure and the ferroelectric features is not clear. Here Nuclear Magnetic Resonance (NMR) (1)H spin-lattice relaxation experiments at 25 MHz are reported for ICA in the temperature range of 80 K-360 K, covering ferroelectric-paraelectric and structural phase transitions of the compound occurring at 180 and 342 K, respectively. The relaxation process is biexponential in the whole temperature range indicating two dynamically nonequivalent types of imidazolium cations. Temperature dependences of both relaxation contributions allow for identifying three motional processes. Two of them are cation-specific - i.e. they are attributed to the two types of imidazolium cations, respectively. The third process involves both types of cations, and it is characterized by much lower activation energy. Moreover, the relaxation data (combined with (1)H second moment measurements) show that the ferroelectric-paraelectric phase transition mechanism is governed, to a large extent, by the anionic network arrangement. The NMR studies are complemented by dielectric spectroscopy experiments performed in the vicinity of the Curie temperature, TC = 180 K, to get insight into the mechanism of the ferroelectric-paraelectric phase transition. The dielectric dispersion data show critical slowing down of the macroscopic relaxation time, τ, in ICA when approaching TC from the paraelectric side, indicating an order-disorder type of ferroelectrics.

Determining diffusion coefficients of ionic liquids by means of field cycling nuclear magnetic resonance relaxometry.

Field Cycling Nuclear Magnetic Resonance (FC NMR) relaxation studies are reported for three ionic liquids: 1-ethyl-3- methylimidazolium thiocyanate (EMIM-SCN, 220-258 K), 1-butyl-3-methylimidazolium tetrafluoroborate (BMIM-BF4, 243-318 K), and 1-butyl-3-methylimidazolium hexafluorophosphate (BMIM-PF6, 258-323 K). The dispersion of (1)H spin-lattice relaxation rate R1(ω) is measured in the frequency range of 10 kHz-20 MHz, and the studies are complemented by (19)F spin-lattice relaxation measurements on BMIM-PF6 in the corresponding frequency range. From the (1)H relaxation results self-diffusion coefficients for the cation in EMIM-SCN, BMIM-BF4, and BMIM-PF6 are determined. This is done by performing an analysis considering all relevant intra- and intermolecular relaxation contributions to the (1)H spin-lattice relaxation as well as by benefiting from the universal low-frequency dispersion law characteristic of Fickian diffusion which yields, at low frequencies, a linear dependence of R1 on square root of frequency. From the (19)F relaxation both anion and cation diffusion coefficients are determined for BMIM-PF6. The diffusion coefficients obtained from FC NMR relaxometry are in good agreement with results reported from pulsed- field-gradient NMR. This shows that NMR relaxometry can be considered as an alternative route of determining diffusion coefficients of both cations and anions in ionic liquids.

1H relaxation enhancement induced by nanoparticles in solutions: influence of magnetic properties and diffusion.

Magnetic nanoparticles that induce nuclear relaxation are the most promising materials to enhance the sensitivity in Magnetic Resonance Imaging. In order to provide a comprehensive understanding of the magnetic field dependence of the relaxation enhancement in solutions, Nuclear Magnetic Resonance (1)H spin-lattice relaxation for decalin and toluene solutions of various Fe2O3 nanoparticles was investigated. The relaxation experiments were performed in a frequency range of 10 kHz-20 MHz by applying Field Cycling method, and in the temperature range of 257-298 K, using nanoparticles differing in size and shape: spherical--5 nm diameter, cubic--6.5 nm diameter, and cubic--9 nm diameter. The relaxation dispersion data were interpreted in terms of a theory of nuclear relaxation induced by magnetic crystals in solution. The approach was tested with respect to its applicability depending on the magnetic characteristics of the nanocrystals and the time-scale of translational diffusion of the solvent. The role of Curie relaxation and the contributions to the overall (1)H spin-lattice relaxation associated with the electronic spin-lattice and spin-spin relaxation was thoroughly discussed. It was demonstrated that the approach leads to consistent results providing information on the magnetic (electronic) properties of the nanocrystals, i.e., effective electron spin and relaxation times. In addition, features of the (1)H spin-lattice relaxation resulting from the electronic properties of the crystals and the solvent diffusion were explained.

Primary and secondary relaxation process in plastically crystalline cyanocyclohexane studied by 2H nuclear magnetic resonance. II. Quantitative analysis.

We analyze the results of our previously reported 2H nuclear magnetic resonance (NMR) experiments in the plastically crystalline (PC) phase of cyanocyclohexane (Part I of this work) to study the fast secondary relaxation (or ß-process) in detail. Both, the occurrence of an additional minimum in the spin-lattice relaxation T1 and the pronounced effects arising in the solid-echo spectrum above the glass transition temperature T(g) = 134 K, allow for a direct determination of the restricting geometry of the ß-process in terms of the "wobbling-in-a-cone" model. Whereas at temperatures below T(g) the reorientation is confined to rather small solid angles (below 10°), the spatial restriction decreases strongly with temperature above T(g), i.e., the distribution of cone angles shifts continuously towards higher values. The ß-process in the PC phase of cyanocyclohexane proceeds via the same mechanism as found in structural glass formers. This is substantiated by demonstrating the very similar behavior (for T < T(g)) of spin-lattice relaxation, stimulated echo decays, and spectral parameters when plotted as a function of (taken from dielectric spectroscopy). We do, however, not observe a clear-cut relation between the relaxation strength of the ß-process observed by NMR (calculated within the wobbling-in-a-cone model) and dielectric spectroscopy.

Zero-field splitting in nickel(II) complexes: a comparison of DFT and multi-configurational wavefunction calculations.

The zero-field splitting (ZFS) is an important quantity in the electron spin Hamiltonian for S = 1 or higher. We report calculations of the ZFS in some six- and five-coordinated nickel(II) complexes (S = 1), using different levels of theory within the framework of the ORCA program package [F. Neese, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2, 73 (2012)]. We compare the high-end ab initio calculations (complete active space self-consistent field and n-electron valence state perturbation theory), making use of both the second-order perturbation theory and the quasi-degenerate perturbation approach, with density functional theory (DFT) methods using different functionals. The pattern of results obtained at the ab initio levels is quite consistent and in reasonable agreement with experimental data. The DFT methods used to calculate the ZFS give very strongly functional-dependent results and do not seem to function well for our systems.

Translational diffusion in paramagnetic liquids by 1H NMR relaxometry: nitroxide radicals in solution.

For nitroxide radicals in solution one can identify three frequency regimes in which (1)H spin-lattice relaxation rate of solvent molecules depend linearly on square root of the (1)H resonance frequency. Combining a recently developed theory of nuclear (proton) spin-lattice relaxation in solutions of nitroxide radicals [D. Kruk et al., J. Chem. Phys. 137, 044512 (2012)] with properties of the spectral density function associated with translational dynamics, relationships between the corresponding linear changes of the relaxation rate (for (14)N spin probes) and relative translational diffusion coefficient of the solvent and solute molecules have been derived (in analogy to (15)N spin probes [E. Belorizky et al., J. Phys. Chem. A 102, 3674 (1998)]). This method allows a simple and straightforward determination of diffusion coefficients in spin-labeled systems, by means of (1)H nuclear magnetic resonance (NMR) relaxometry. The approach has thoroughly been tested by applying to a large set of experimental data-(1)H spin-lattice relaxation dispersion results for solutions of different viscosity (decalin, glycerol, propylene glycol) of (14)N and (15)N spin probes. The experiments have been performed versus temperature (to cover a broad range of translational diffusion coefficients) using field cycling spectrometer which covers three decades in (1)H resonance frequency, 10 kHz-20 MHz. The limitations of NMR relaxometry caused by the time scale of the translational dynamics as well as electron spin relaxation have been discussed. It has been shown that for spin-labeled systems NMR relaxometry gives access to considerably faster diffusion processes than for diamagnetic systems.

1H relaxation dispersion in solutions of nitroxide radicals: influence of electron spin relaxation.

The work presents a theory of nuclear ((1)H) spin-lattice relaxation dispersion for solutions of (15)N and (14)N radicals, including electron spin relaxation effects. The theory is a generalization of the approach presented by Kruk et al. [J. Chem. Phys. 137, 044512 (2012)]. The electron spin relaxation is attributed to the anisotropic part of the electron spin-nitrogen spin hyperfine interaction modulated by rotational dynamics of the paramagnetic molecule, and described by means of Redfield relaxation theory. The (1)H relaxation is caused by electron spin-proton spin dipole-dipole interactions which are modulated by relative translational motion of the solvent and solute molecules. The spectral density characterizing the translational dynamics is described by the force-free-hard-sphere model. The electronic relaxation influences the (1)H relaxation by contributing to the fluctuations of the inter-molecular dipolar interactions. The developed theory is tested against (1)H spin-lattice relaxation dispersion data for glycerol solutions of 4-oxo-TEMPO-d16-(15)N and 4-oxo-TEMPO-d16-(14)N covering the frequency range of 10 kHz-20 MHz. The studies are carried out as a function of temperature starting at 328 K and going down to 290 K. The theory gives a consistent overall interpretation of the experimental data for both (14)N and (15)N systems and explains the features of (1)H relaxation dispersion resulting from the electron spin relaxation.

ESR lineshape and 1H spin-lattice relaxation dispersion in propylene glycol solutions of nitroxide radicals--joint analysis.

Electron Spin Resonance (ESR) spectroscopy and Nuclear Magnetic Relaxation Dispersion (NMRD) experiments are reported for propylene glycol solutions of the nitroxide radical: 4-oxo-TEMPO-d16 containing (15)N and (14)N isotopes. The NMRD experiments refer to (1)H spin-lattice relaxation measurements in a broad frequency range (10 kHz-20 MHz). A joint analysis of the ESR and NMRD data is performed. The ESR lineshapes give access to the nitrogen hyperfine tensor components and the rotational correlation time of the paramagnetic molecule. The NMRD data are interpreted in terms of the theory of paramagnetic relaxation enhancement in solutions of nitroxide radicals, recently presented by Kruk et al. [J. Chem. Phys. 138, 124506 (2013)]. The theory includes the effect of the electron spin relaxation on the (1)H relaxation of the solvent. The (1)H relaxation is caused by dipole-dipole interactions between the electron spin of the radical and the proton spins of the solvent molecules. These interactions are modulated by three dynamic processes: relative translational dynamics of the involved molecules, molecular rotation, and electron spin relaxation. The sensitivity to rotation originates from the non-central positions of the interacting spin in the molecules. The electronic relaxation is assumed to stem from the electron spin-nitrogen spin hyperfine coupling, modulated by rotation of the radical molecule. For the interpretation of the NMRD data, we use the nitrogen hyperfine coupling tensor obtained from ESR and fit the other relevant parameters. The consistency of the unified analysis of ESR and NMRD, evaluated by the agreement between the rotational correlation times obtained from ESR and NMRD, respectively, and the agreement of the translation diffusion coefficients with literature values obtained for pure propylene glycol, is demonstrated to be satisfactory.

Evolution of the dynamic susceptibility in molecular glass formers: results from light scattering, dielectric spectroscopy, and NMR.

Although broadly studied, molecular glass formers are not well investigated above their melting point. Correlation times down to 10(-12) s are easily accessible when studying low-T(g) systems by depolarized light scattering, employing a tandem-Fabry-Perot interferometer and a double monochromator. When combining these techniques with state-of-the-art photon correlation spectroscopy (PCS), broad band susceptibility spectra become accessible which can compete with those of dielectric spectroscopy (DS). Comparing the results with those from DS, optical Kerr effect, and NMR, we describe the evolution of the susceptibilities starting from the boiling point T(b) down to T(g), i.e., from simple liquid to glassy dynamics. Special attention is given to the emergence of the excess wing contribution which is also probed by PCS and which signals a crossover of the spectral evolution. The process is attributed to a small-angle precursor process of the α-relaxation, and the apparent probe dependent stretching of the α-process is explained by a probe dependent contribution of the excess wing. Upon cooling, its emergence is linked to a strong decrease of the strength of the fast dynamics which is taken as reorientational analog of the anomaly of the Debye-Waller factor. Many glass formers show in addition a slow ß-process which manifests itself rather universally in NMR, in DS, however, with different amplitudes, but not at all in PCS experiments. Finally, a three-parameter function is discussed interpolating τ(α)(T) from T(b) to T(g) by connecting high- and low-temperature dynamics.

Intermolecular relaxation in glycerol as revealed by field cycling 1H NMR relaxometry dilution experiments.

(1)H spin-lattice relaxation rates R(1) = 1/T(1) have been measured for partly deuterated glycerol-h(5) diluted in fully deuterated glycerol-h(0) for progressively lower concentrations of glycerol-h(5). By means of the field cycling (FC) technique relaxation dispersion data, R(1)(ω), have been collected for several temperatures in the frequency range of 10 kHz-20 MHz. In order to disclose the spectral shape of the intra- and intermolecular relaxation, extrapolation of the relaxation data to the zero concentration limit has been performed. The paper confirms that the low frequency excess contribution to the total relaxation rate R(1)(ω) previously reported for several liquids is of intermolecular origin and reflects translational motion, whereas the high-frequency part is attributed to molecular rotation. Thus, intra- and intermolecular relaxation contributions are spectrally separated. The intermolecular relaxation itself contains also a contribution from rotational motion, which is due to non-central positions of the interacting nuclei in the molecule. This eccentricity effect is quantitatively reproduced by treating the intermolecular spectral density as a sum of translational-like (described by the free diffusion model) and rotational-like contributions (described by a Cole-Davidson function). Applying frequency-temperature superposition master curves as well as individual relaxation dispersion data, R(1)(ω), are analyzed. It is demonstrated that, in spite of the rotational influence, the translational diffusion coefficients, D(T), can be extracted from the (1)H relaxation dispersion which gives (1)H NMR relaxometry the potential to become a routine technique determining the diffusion coefficient in liquids.

1H relaxation dispersion in solutions of nitroxide radicals: effects of hyperfine interactions with 14N and 15N nuclei.

(1)H relaxation dispersion of decalin and glycerol solutions of nitroxide radicals, 4-oxo-TEMPO-d(16)-(15)N and 4-oxo-TEMPO-d(16)-(14)N was measured in the frequency range of 10 kHz-20 MHz (for (1)H) using STELAR Field Cycling spectrometer. The purpose of the studies is to reveal how the spin dynamics of the free electron of the nitroxide radical affects the proton spin relaxation of the solvent molecules, depending on dynamical properties of the solvent. Combining the results for both solvents, the range of translational diffusion coefficients, 10(-9)-10(-11) m(2)/s, was covered (these values refer to the relative diffusion of the solvent and solute molecules). The data were analyzed in terms of relaxation formulas including the isotropic part of the electron spin - nitrogen spin hyperfine coupling (for the case of (14)N and (15)N) and therefore valid for an arbitrary magnetic field. The influence of the hyperfine coupling on (1)H relaxation of solvent molecules depending on frequency and time-scale of the translational dynamics was discussed in detail. Special attention was given to the effect of isotope substitution ((14)N/(15)N). In parallel, the influence of rotational dynamics on the inter-molecular (radical - solvent) electron spin - proton spin dipole-dipole coupling (which is the relaxation mechanism of solvent protons) was investigated. The rotational dynamics is of importance as the interacting spins are not placed in the molecular centers. It was demonstrated that the role of the isotropic hyperfine coupling increases for slower dynamics, but it is of importance already in the fast motion range (10(-9)m(2)/s). The isotope effects is small, however clearly visible; the (1)H relaxation rate for the case of (15)N is larger (in the range of lower frequencies) than for (14)N. It was shown that when the diffusion coefficient decreases below 5 × 10(-11) m(2)/s electron spin relaxation becomes of importance and its role becomes progressively more significant when the dynamics slows done. As far as the influence of the rotational dynamics is concerned, it was show that this process is of importance not only in the range of higher frequencies (like for diamagnetic solutions) but also at low and intermediate frequencies.

1H NMR relaxation in glycerol solutions of nitroxide radicals: effects of translational and rotational dynamics.

(1)H spin-lattice relaxation rates in glycerol solutions of selected nitroxide radicals at temperatures between 200 K and 400 K were measured at 15 MHz and 25 MHz. The frequency and temperature conditions were chosen in such a way that the relaxation rates go through their maximum values and are affected by neither the electron spin relaxation nor the electron-nitrogen nucleus hyperfine coupling, so that the focus could be put on the mechanisms of motion. By comparison with (1)H spin-lattice relaxation results for pure glycerol, it has been demonstrated that the inter-molecular electron spin-proton spin dipole-dipole interactions are affected not only by relative translational motion of the solvent and solute molecules, but also by their rotational dynamics as the interacting spins are displaced from the molecular centers; the eccentricity effects are usually not taken into account. The (1)H relaxation data have been decomposed into translational and rotational contributions and their relative importance as a function of frequency and temperature discussed in detail. It has been demonstrated that neglecting the rotational effects on the inter-molecular interactions leads to non-realistic conclusions regarding the translational dynamics of the paramagnetic molecules.

Sensitivity of 2H NMR spectroscopy to motional models: proteins and highly viscous liquids as examples.

In order to study to what extent mechanisms of molecular motion can be unambiguously revealed by (2)H NMR spectroscopy, (2)H spectra for proteins (chicken villin protein headpiece HP36, selectively methyl-deuterated at leucine-69, C(δ) D(3)) and binary systems of high viscosity (benzene-d(6) in tricresyl phosphate) have been carefully analyzed as illustrative examples (the spectra are taken from the literature). In the first case, a model of restricted diffusion mediated by jumps between rotameric orientations has been tested against jump- and free diffusion models which describe rotational motion combined with jump dynamics. It has been found that the set of (2)H spectra of methyl-deuterated at leucine-69 chicken villin protein headpiece HP36 can be consistently explained by different motional models as well as by a gaussian distribution of correlation times assuming isotropic rotation (simple brownian diffusion model). The last finding shows that when the possible distribution of correlation times is not very broad one might not be able to distinguish between heterogeneous and homogenous (but more complex) dynamics by analyzing (2)H lineshapes. For benzene-d(6) in tricresyl phosphate, the dynamics is heterogeneous and it has been demonstrated that a gaussian distribution of correlation times reproduces well the experimental lineshapes, while for a Cole-Davidson distribution the agreement is somewhat worse. For inquires into the sensitivity of quadrupolar NMR spectral analysis (by "quadrupolar NMR spectroscopy we understand NMR spectroscopy of nuclei possessing quadrupole moment), the recently presented theoretical approach [Kruk et al., J. Chem. Phys. 135, 224511 (2011)] has been used as it allows simulating quadrupolar spectra for arbitrary motional conditions by employing the stochastic Liouville equation.

Nuclear quadrupole resonance lineshape analysis for different motional models: stochastic Liouville approach.

A general theory of lineshapes in nuclear quadrupole resonance (NQR), based on the stochastic Liouville equation, is presented. The description is valid for arbitrary motional conditions (particularly beyond the valid range of perturbation approaches) and interaction strengths. It can be applied to the computation of NQR spectra for any spin quantum number and for any applied magnetic field. The treatment presented here is an adaptation of the "Swedish slow motion theory," [T. Nilsson and J. Kowalewski, J. Magn. Reson. 146, 345 (2000)] originally formulated for paramagnetic systems, to NQR spectral analysis. The description is formulated for simple (Brownian) diffusion, free diffusion, and jump diffusion models. The two latter models account for molecular cooperativity effects in dense systems (such as liquids of high viscosity or molecular glasses). The sensitivity of NQR slow motion spectra to the mechanism of the motional processes modulating the nuclear quadrupole interaction is discussed.