Influencing the satellite transitions of half-integer quadrupolar nuclei for the enhancement of magic angle spinning spectra

Double frequency sweeps can induce spin transitions in a set of satellites of a half-integer quadrupolar nucleus by simultaneously passing through resonance for a satellite pair. It is shown that by transferring population from the outer spin levels to the inner |1/2 and |−1/2 levels an increased intensity for central transition spectra is obtained. Although Magic Angle Spinning in principle interferes with this process, and the adiabaticity of the passages is different for every crystallite in a powder, enhanced spectra with undistorted line shapes are obtained for I=3/2 (²³Na) and 5/2 (²⁷Al) spins experiencing quadrupolar interactions with ω_Q in the range 0.1–3 MHz. Even at spinning speeds up to 30 kHz significant enhancements are obtained. An analysis of the combined effects of double frequency sweeps (DFS) and MAS indeed shows strongly different effects for different crystallites in powder ranging from no gain at all to the theoretical maximum gain of 2I. As the effects are randomly distributed over all orientations on a sphere this is averaged over the whole line shape. Therefore, undistorted powder patterns are obtained enhanced by the average gain over the individual crystallites. Saturation of the satellite transitions, which can only be achieved if spin–spin relaxation is sufficiently strong, leads to identical results. Optimization of the sweeps should be toward an optimal effect on the population transfer to the central levels and chosen short with respect to spin–lattice relaxation times.     

Methyl and t-butyl reorientation in an organic molecular solid

We have determined the molecular and crystal structure of 4,5-dibromo-2,7-di-t-butyl-9,9-dimethylxanthene and measured the ¹H spin–lattice relaxation rate from 87 to 270 K at NMR frequencies of ω/2π=8.50, 22.5, and 53.0 MHz. All molecules in the crystal see the same intra and intermolecular environment and the repeating unit is half a molecule. We have extended models developed for ¹H spin–lattice relaxation resulting from the reorientation of a t-butyl group and its constituent methyl groups to include these rotors and the 9-methyl groups. The relaxation rate data is well-fitted assuming that the t-butyl groups and all three of their constituent methyl groups, as well as the 9-methyl groups all reorient with an NMR activation energy of 15.8±1.6 kJ mol⁻¹ corresponding to a barrier of 17.4±3.2 kJ mol⁻¹. Only intramethyl and intra-t-butyl intermethyl spin–spin interactions need be considered. A unique random-motion Debye (or BPP) spectral density will not fit the data for any reasonable choice of parameters. A distribution of activation energies is required.     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

H NMR study of N(CH3)4H(ClF2CCOO)2

The proton spin–lattice relaxation times and ¹H NMR second moments were measured over a wide range of temperature. The results were compared with those of the ¹⁹F NMR relaxation that we obtained earlier. For both nuclear species, the evolution of the longitudinal magnetizations with time is observed to be strongly bi-exponential and were in good quantitative agreement with the cross-relaxation theory.     

Relaxation times and line widths of isotopically-substituted nitroxides in aqueous solution at X-band

Optimization of nitroxides as probes for EPR imaging requires detailed understanding of spectral properties. Spin lattice relaxation times, spin packet line widths, nuclear hyperfine splitting, and overall lineshapes were characterized for six low molecular weight nitroxides in dilute deoxygenated aqueous solution at X-band. The nitroxides included 6-member, unsaturated 5-member, or saturated 5-member rings, most of which were isotopically labeled. The spectra are near the fast tumbling limit with T₁∼T₂ in the range of 0.50–1.1 μs at ambient temperature. Both spin–lattice relaxation T₁ and spin–spin relaxation T₂ are longer for ¹⁵N- than for ¹⁴N-nitroxides. The dominant contributions to T₁ are modulation of nitrogen hyperfine anisotropy and spin rotation. Dependence of T₁ on nitrogen nuclear spin state m_I was observed for both ¹⁴N and ¹⁵N. Unresolved hydrogen/deuterium hyperfine couplings dominate overall line widths. Lineshapes were simulated by including all nuclear hyperfine couplings and spin packet line widths that agreed with values obtained by electron spin echo. Line widths and relaxation times are predicted to be about the same at 250 MHz as at X-band.     

NMR study of YP and YPO4 as 2-qubits quantum computers

The ³¹P-NMR experiments in YP and YPO₄ as 2-qubits quantum computers were performed at room temperature under magnetic fields of 6.3 and 11.75 T with a coherent type pulsed FT-NMR spectrometer. The full width at half of the maximum intensity of NMR spectrum for ³¹P is compared with the second moment caused by the dipolar field. The obtained spin–lattice relaxation times T₁ of 1.2 and 320 s for the P nuclei in YP and YPO₄, respectively, suggest both compounds have the advantage of increasing the numbers of quantum computing operations.     

Multivariate Image Analysis of Magnetic Resonance Images with the Direct Exponential Curve Resolution Algorithm (DECRA): Part 2: Application to Human Brain Images

Owing to the heterogeneity of living tissues, it is challenging to quantify tissue properties using magnetic resonance imaging. Within a single voxel, contributions to the signal may result from several types of¹H nuclei with varied chemical (e.g., −CH₂−, −OH) and physical environments (e.g., tissue density, compartmentalization). Therefore, mixtures of¹H environments are prevalent. Furthermore, each unique type of¹H environment may possess a unique and characteristic spin–lattice relaxation time (T₁) and spin–spin relaxation time (T₂). A method for resolving these unique exponentials is introduced in a separate paper (Part 1. Algorithm and Model System) and uses the direct exponential curve resolution algorithm (DECRA). We present results from an analysis of images of the human head comprising brain tissues.     

A nuclear magnetic resonance study of the phase transitions and electric quadrupole Raman processes of M5H3(SO4)4·H2O (M=Na, K, Rb, and Cs) single crystals

The spin–lattice relaxation times and spin–spin relaxation times for ¹H and M in M₅H₃(SO₄)₄·H₂O (M=Na, K, Rb, and Cs) single crystals grown using the slow-evaporation method were measured as functions of temperature. Two kinds of protons were identified in the M₅H₃(SO₄)₄·H₂O structure: acid protons and water protons. Our experimental results show that the acid and water protons in Cs₅H₃(SO₄)₄·H₂O are involved in phase transitions of this crystal, whereas neither type of proton is involved in the phase transitions of the other three crystal type (M₅H₃(SO₄)₄·H₂O; M=Na, K, and Rb). Moreover, the relaxation times for the M (=Na, K, and Rb) nuclei in these crystals were found to decrease with increasing temperature and can be described with (k=2). The T₁ results for M (=Na, K, and Rb) in M₅H₃(SO₄)₄·H₂O crystals can be explained in terms of a relaxation mechanism in which the lattice vibrations are coupled to the nuclear electric quadrupole moments.     

Brute-force NMR-ON on 90NbCu, 101mRhCu and110mAgAg

Brute-force nuclear magnetic resonance on oriented nuclei (BF-NMRON) experiments have been performed for ⁹⁰NbCu, ^101m RhCu and ^110m AgAg at about 10mK. Narrow resonance spectra were detected. Using the known values of the g-factors, the Knight shift has been deduced: K(⁹⁰NbCu) = 0.62(24) %, K(^101m RhCu) = 0.87(27)%. The effective spin–lattice relaxation times were also measured.     

Contributions of Spin–Lattice Relaxation to the Echo Decay of Planar Cu in High-Temperature Superconductors

Measurement ofT_2G, the Gaussian component of the spin-echo envelope of planar Cu nuclei in high-temperature superconductors, gives important information about the real part of the Cu electron spin susceptibility. In the traditional picture of the planar Cu echo decay, the internuclear coupling is assumed to remain static with respect to spin–lattice relaxation and mutual exchange fluctuations. In some circumstances, however, this assumption breaks down. We calculate the internuclear corrections arising from spin–lattice relaxation to the conventional theory ofT_2Gand show thatT_2Gcan be easily corrected for these effects. We argue that mutual exchanges due to the perpendicular indirect couplings are suppressed in these materials. For YBa₂Cu₄O₈, we find a correction on the order of 10% inT_2Gand using the corrected values we find that the isotope ratio⁶³T_2G/⁶⁵T_2Gagrees with theory.     

Biomolecular solid state NMR with magic-angle spinning at 25K

A magic-angle spinning (MAS) probe has been constructed which allows the sample to be cooled with helium, while the MAS bearing and drive gases are nitrogen. The sample can be cooled to 25 K using roughly 3 L/h of liquid helium, while the 4-mm diameter rotor spins at 6.7 kHz with good stability (±5 Hz) for many hours. Proton decoupling fields up to at least 130 kHz can be applied. This helium-cooled MAS probe enables a variety of one-dimensional and two-dimensional NMR experiments on biomolecular solids and other materials at low temperatures, with signal-to-noise proportional to 1/T. We show examples of low-temperature ¹³C NMR data for two biomolecular samples, namely the peptide Aβ_14–23 in the form of amyloid fibrils and the protein HP35 in frozen glycerol/water solution. Issues related to temperature calibration, spin–lattice relaxation at low temperatures, paramagnetic doping of frozen solutions, and ¹³C MAS NMR linewidths are discussed.     

Attenuation of Nuclear Orientation of 127In in Gd and the InGd Korringa Spin–Lattice Relaxation Time Constant

The nuclear spin–lattice relaxation of ¹²⁷In implanted into pure gadolinium metal has been measured using the method of integral attenuation of on-line nuclear orientation. The Korringa constant is determined to be C_K (¹²⁷InGd, B_pol = 0.5 T) = 0.133(18) sK. The result is compared with relaxation of In nuclei inFe.     

Expanding the Frequency Range of the Solid-State T1 ρ Experiment for Heteronuclear Dipolar Relaxation

Solid-state spin–lattice relaxation in the rotating frame permits the investigation of dynamic processes with correlation times in the range of microseconds. The relaxation process in organic solids is driven by the fluctuation of the local magnetic field due to the dipole–dipole interaction of the probe nuclei (¹³C,¹⁵N) with ¹H in close proximity. However, its effect is often hidden by a competing relaxation process due to the contact between the rotating frame ¹³C/¹⁵N Zeeman and ¹H dipolar reservoirs. In most cases the latter process becomes superior for the commonly applied low and moderate spin-lock fields and practically does not provide information about the molecular dynamics. To suppress this undesired process and to expand the dynamic range of T_{1 ρ} experiments, we present two approaches. The first one uses a resonance offset of the frequency of the spin-lock irradiation, which leads to a significant enhancement of the effective spin-lock frequency without the application of destructive high transmitter powers. We derive the theory and demonstrate the applicability of the method on various model compounds. The second approach utilizes heteronuclear ¹H decoupling during the ¹³C/¹⁵N spin-lock irradiation which disrupts the contact between the ¹³C/¹⁵N Zeeman and ¹H dipolar reservoirs. We demonstrate the method and discuss the results qualitatively.     

Study of nuclear quadrupole interactions and quadrupole Raman processes of Ga and Ga in a β-Ga2O3:Cr single crystal

Nuclear magnetic resonance (NMR) data and the spin–lattice relaxation times, T₁, of ⁶⁹Ga and ⁷¹Ga nuclei in a β-Ga₂O₃:Cr³⁺ single crystal were obtained using FT NMR spectrometry. Four sets of NMR spectra for ⁶⁹Ga (I = 3/2) and ⁷¹Ga (I = 3/2) were obtained in the crystallographic planes. The ⁶⁹Ga and ⁷¹Ga nuclei each had two chemically inequivalent Ga_I and Ga_II centers. Each of the ⁶⁹Ga and ⁷¹Ga isotopes yielded two different central NMR resonance lines originating from Ga_I and Ga_II sites. The nuclear quadrupole coupling constants and asymmetry parameters of ⁶⁹Ga_I, ⁶⁹Ga_II, ⁷¹Ga_I, and ⁷¹Ga_II centers in a β-Ga₂O₃:Cr³⁺ crystal were obtained. Analysis of the EFG tensor principal axes (PAs) for Ga nuclei and the ZFS tensor PAs for the Cr³⁺ ion confirmed that the Cr³⁺ paramagnetic impurity ion substitutes for the Ga³⁺ ion in the oxygen octahedron. In addition, the temperature dependencies of the ⁶⁹Ga and ⁷¹Ga relaxation rates were consistent with Raman processes, as T₁⁻¹ ∝ T². Even though the Cr³⁺ impurities are paramagnetic, the relaxations were dominated by electric quadrupole interactions of the nuclear spins in the temperature range investigated.     

Paramagnetic Proton Nuclear Spin Relaxation Theory of Low-Symmetry Complexes for Electron Spin Quantum NumberS=

A generalization of the modified Solomon–Bloembergen–Morgan (MSBM) equations has been derived in order to describe paramagnetic relaxation enhancement (PRE) of paramagnetic complexes characterized by both a transient (Δ^ZFS_t) and a static (Δ^ZFS_s) zero-field splitting (ZFS) interaction. The new theory includes the effects of static ZFS, hyperfine coupling, and angular dependence and is presented for the case of electron spin quantum numberS= , for example, Mn(II) and Fe(III) complexes. The model gives the difference from MSBM theory in terms of a correction term δ which is given in closed analytical form. The theory may be important in analyzing the PRE of proton spin–lattice relaxation dispersion measurements (NMRD profiles) of low-symmetry aqua–metal complexes which are likely to be formed upon transition metal ions associated with charged molecular surfaces of biomacromolecules. The theory has been implemented with a computer program which calculates solvent water protonT₁NMRD profiles using both MSBM and the new theory.     

The influence of the O–O isotope substitution on spin dynamics of (La0.25Pr0.75)0.7Ca0.3MnO3: La NMR data

The ¹³⁹La NMR spectra and spin–spin relaxation times have been measured for the ¹⁶O and ¹⁸O isotope-substituted manganite (La_0.25Pr_0.75)_0.7Ca_0.3MnO₃ in the external magnetic field of 5 T. The NMR signal wipe-out has been observed in the ¹⁸O-enriched sample in the charge-ordered state. This phenomenon is connected with a sharp increase in the spin–spin relaxation rate. The great isotope-effect observed provides a clear evidence of an essential role of oxygen motion in controlling the long-range magnetic order in manganites.     

Directional behavior of nuclear quadrupole resonance in YBa2Cu3O6

Powder samples of YBa₂Cu₃O₆ were magnetically aligned and the anisotropies in the systems were studied by means of Cu(1) nuclear quadrupole resonance (NQR) in the absence of external magnetic fields. Our room temperature measurements of the NQR lineshapes and the spin–lattice and spin–spin relaxation times as a function of the aligning magnetic field indicate that full microscopic alignment can be achieved by using a magnetic field of about 4.7 T, for which doublet line patterns arising from a hyperfine splitting were observed.     

Sodium Ions in Ordered Environments in Biological Systems: Analysis of Na NMR Spectra

Experimentsthat selectively excite I = nuclei exhibiting residual quadrupolar splittings are used to acquire ²³Na NMR spectra from a range of biologically relevant samples containing sodium in ordered environments. Three complementary approaches to the analysis of such spectra are described: (i) measurement of relaxation rates, (ii) extraction of homogeneous linewidths from two-dimensional Jeener–Broekaert spectra, and (iii) simultaneous fitting of detailed theoretical functions to a series of one-dimensional Jeener–Broekaert spectra. Analysis of relaxation rates provides evidence for compartmentation in bovine nasal cartilage. Each approach is used to demonstrate the presence of anisotropy in transverse relaxation in porcine tendon. For certain samples containing collagen, a good theoretical fit to the spectra was obtained using a model that allows for anisotropic relaxation by including the effects of slow lateral and radial diffusion.     

Relaxation-induced dipolar exchange with recoupling-An MAS NMR method for determining heteronuclear distances without irradiating the second spin

A new magic-angle spinning NMR method for distance determination between unlike spins, where one of the two spins in question is not irradiated at all, is introduced. Relaxation-induced dipolar exchange with recoupling (RIDER) experiments can be performed with conventional double-resonance equipment and utilize the familiar π-pulse trains to recouple the heteronuclear dipolar interaction under magic-angle spinning conditions. Longitudinal relaxation of the passive spin during a delay between two recoupling periods results in a dephasing of the heteronuclear coherence and consequently a dephasing of the magnetization detected after the second recoupling period. The information about the dipolar coupling is obtained by recording normalized dephasing curves in a fashion similar to the REDOR experiment. At intermediate mixing times, the dephasing curves also depend on the relaxation properties of the passive spin, i.e., on single- and double-quantum longitudinal relaxation times for the case of I = 1 nuclei, and these relaxation times can be estimated with this new method. To a good approximation, the experiment does not depend on possible quadrupolar interactions of the passive spin, which makes RIDER an attractive method when distances to quadrupolar nuclei are to be determined. The new method is demonstrated experimentally with ¹⁴N and ²H as heteronuclei and observation of ¹³C in natural abundance.