Single- and multiple-quantum cross-polarization in NMR of quadrupolar nuclei in static samples

Cross-polarization from a spin I=1/2 nucleus (e.g., ¹H) to a spin S = 3/2 nucleus (e.g., ²³Na) or a spin S = 5/2 nucleus (e.g., ²⁷A1 or ⁿO) in static powder samples is investigated. The results of conventional (single-quantum), three-quantum, and five-quantum cross-polarization experiments are presented and discussed. Based on a generalization of an existing theory of cross-polarization to quadrupolar nuclei, computer simulations are used to model the intensity and lineshape variations observed in cross-polarized NMR spectra as a function of the radio-frequency field strengths of the two simultaneous spin-locking pulses. These intensity and lineshape variations can also be understood in terms of the spin S = 3/2 or 5/2 nutation rates determined from experimental quadrupolar nutation spectra. The results of this study are intended as a preliminary step towards understanding single- and multiple-quantum cross-polarization to quadrupolar nuclei under MAS conditions and the application of these techniques to the MQMAS NMR experiment.     

Multiple-Quantum J-Resolved NMR Spectroscopy (MQ-JRES): Measurement of Multiple-Quantum Relaxation Rates and Relative Signs of Spin Coupling Constants

The technique of multiple-quantum J-resolved NMR spectroscopy (MQ-JRES) is introduced and applied to the spin system SI₃–M (such as in the example given here, the ¹³CH₃–¹²CH in alanine). The SI₃ spin system was excited to its highest quantum state (8S_yI_xI_yI_y), which consists of four coherences: quadruple quantum of (3I + S), double quantum of (3I − S), double quantum of (I + S), and zero quantum of (I − S). In the MQ spectrum generated from the projection onto the F₁ dimension, the resonances of the different multiple-quantum coherences are resolved by their coupling constants to the remote spin (M). The absorptive lineshapes in both F₁ and F₂ dimensions enable accurate measurements of transverse relaxation rates, and both amplitude and relative signs of the long-range coupling constants are to be derived from either frequency or time domain data. The selective detection of MQ-JRES spectra of the individual MQ coherences using either phase cycling or pulsed field gradients is presented.     

Theoretical and experimental assessment of single- and multiple-quantum cross-polarization in solid state NMR

Continuous wave cross-polarization (CP) NMR experiments with magic angle spinning (MAS) are reviewed for the case of isolated spin pairs I-S, with spin quantum numbers I = ½ and S ½ (1/2, 3/2, …). For two spin-1/2 nuclei, the Hartmann-Hahn matching conditions are examined at various sample rotation rates ν_R, especially with regard to off-resonance behaviour. In addition to signal enhancement, the CPMAS experiment can be used for the selective determination of inter-nuclear distances between spin-1/2 nuclei. Theoretical examination of the CP transfers to single-quantum (1Q-CPMAS) and multiple-quantum (MQ-CPMAS) levels of quadrupolar nuclei is presented. Simple analytical formulae describing the Hartmann-Hahn matching under various experimental conditions are verified using computer simulations of the spin density matrix under MAS, and the experimental data. The strategies for the most efficient acquisition of 1Q-CPMAS and MQ-CPMAS spectra are extensively discussed.     

High-resolution NMR of quadrupolar nuclei using mixed multiple-quantum coherences

A multiple-quantum magic angle spinning (MQMAS) NMR experiment of quadrupolar nuclei is demonstrated, which uses two different multiple quantum coherences in t(1) to refocus the quadrupolar broadening. This experiment has the potential of achieving improved resolution over current techniques.     

Spinning Sidebands in Slow-Magic-Angle-Spinning NMR Spectra Arising from TightlyJ-Coupled Spin Pairs

Complex spinning sidebands are observed in magic-angle-spinning (MAS) NMR spectra arising from isolated tightlyJ-coupled spin pairs under slow spinning conditions. Such spinning sidebands are sensitive to the magnitude and relative orientation of the chemical-shift tensors, the dipolar-coupling tensor, and the sign of the indirect spin–spin (J) coupling. We show that it is possible to extract information concerning such NMR parameters from an analysis of the observed spinning sidebands. As an example, numerical simulations are carried out to reproduce observed³¹P MAS NMR spectra of a phosphole tetramer (1) ando-bis(diphenylphosphino)benzene (2), so that invaluable information concerning the orientations of the phosphorus chemical-shift tensors and the sign ofJ(³¹P,³¹P) can be deduced. Simulations are carried out by numerically evaluating the spin-density matrix of the spin system.     

Multiple-quantum cross-polarization and two-dimensional MQMAS NMR of quadrupolar nuclei

Cross-polarization from (1)H to the multiple-quantum coherences of a quadrupolar nucleus is used in combination with the two-dimensional multiple-quantum magic angle spinning (MQMAS) NMR experiment in order to extract high-resolution CPMAS NMR spectra. The technique is demonstrated on (23)Na (S = 3/2), (17)O, (27)Al (both S = 5/2), and (45)Sc (S = 7/2) nuclei, showing the applicability of multiple-quantum cross-polarization to systems with differing spin quantum number, gyromagnetic ratio, and relative nuclide abundance. The utility of this two-dimensional MAS NMR experiment for spectral editing and site-specific measurement of cross-polarization intensities is demonstrated. The possibility of direct cross-polarization to higher order multiple-quantum coherences is also considered and three-, five-, and seven-quantum cross-polarized (45)Sc MAS NMR spectra are presented.     

A Comparison between REDOR and θ-REDOR for Measuring C–D Dipolar Interactions in Solids

¹³C-observe REDOR and θ-REDOR experiments for recovering the ¹³C–²D dipolar interaction during MAS NMR are compared. It is found that limited ²D RF power may severely compromise the performance of the REDOR experiment whereas the θ-REDOR experiment can be designed to work well. Results are presented for an isolated ¹³C–²D spin pair with a large deuterium quadrupolar coupling constant and for a ¹³C coupled to three methyl deuterons undergoing fast methyl group rotation.     

Iterative Lineshape Fitting of MAS NMR Spectra: A Tool to Investigate HomonuclearJCoupling in Isolated Spin Pairs

Possibilities and limitations of iterative lineshape fitting procedures of MAS NMR spectra of isolated homonuclear spin pairs, aiming at determination of magnitudes and orientations of the various interaction tensors, are explored. Requirements regarding experimental MAS NMR spectra as well as simulation and fitting procedures are discussed. Our examples chosen are the isolated³¹P spin pairs in solid Na₄P₂O₇· 10H₂O, (1), and Cd(NO₃)₂· 2PPh₃, (2). In both cases the two³¹P chemical shielding tensors in the molecular unit are related byC₂symmetry, and determination of the orientations of these two tensors in the molecular frame is possible. In addition, aspects of homonuclearJcoupling will be addressed. For 1, both magnitude and sign of²J_iso(³¹P,³¹P) (J_iso= −19.5 ± 2.5 Hz) are obtained; for 2, (J_iso= +139 ± 3 Hz) anisotropy ofJwith an orientation of theJ-coupling tensor collinear, or nearly collinear, with the dipolar coupling tensor can be excluded, while absence or presence of anisotropy ofJwith any other relative orientation of theJ-coupling tensor cannot be determined.     

Rotor-encoded heteronuclear MQ MAS NMR spectroscopy of half-integer quadrupolar and spin I=1/2 nuclei

A new two-dimensional heteronuclear multiple-quantum magic-angle spinning (MQ MAS) experiment is presented which combines high resolution for the half-integer quadrupolar nucleus with information about the dipolar coupling between the quadrupolar nucleus and a spin I=1/2 nucleus. Homonuclear MQ coherence is initially created for the half-integer quadrupolar nucleus by a single pulse as in a standard MQ MAS experiment. REDOR recoupling of the heteronuclear dipolar coupling then allows the creation of a heteronuclear multiple-quantum coherence comprising multiple- and single-quantum coherence of the quadrupolar and spin I=1/2 nucleus, respectively, which evolves during t1. Provided that the t1 increment is not rotor synchronized, rotor-encoded spinning-sideband patterns are observed in the indirect dimension. Simulated spectra for an isolated IS spin pair show that these patterns depend on the recoupling time, the magnitude of the dipolar coupling, the quadrupolar parameters, as well as the relative orientation of the quadrupolar and dipolar principal axes systems. Spectra are presented for Na2HPO4, with the heteronuclear 23Na-1HMQ MAS experiments beginning with the excitation of 23Na (spin I=3/2) three-quantum coherence. Coherence counting experiments demonstrate that four- and two-quantum coherences evolve during t1. The heteronuclear spinning-sideband patterns observed for the three-spin H-Na-H system associated with the Na(2) site are analyzed. For an IS2 system, simulated spectra show that, considering the free parameters, the spinning-sideband patterns are particularly sensitive to only, first, the angle between the two IS internuclear vectors and, second, the two heteronuclear dipolar couplings. It is demonstrated that the proton localization around the Na(2) site according to the literature crystal structure of Na2HPO4 is erroneous. Instead, the experimental data is consistent with two alternative different structural arrangements, whereby either there is a deviation of 10 degrees from linearity for the case of two identical Na-H distances, or there is a linear arrangement, but the two Na-H distances are different. Furthermore, the question of the origin of spinning-sidebands in the (homonuclear) MQ MAS experiment is revisited. It is shown that the asymmetric experimental MQ sideband pattern observed for the low-C(Q) Na(2) site in Na(2)HPO4 can only be explained by considering the 23Na chemical shift anisotropy.     

Cross-correlation effects in NMR spectra of a spin 1/2 scalar coupled to a spin S≥1

In the frame of the density matrix formalism the lineshapes and dynamic frequency shifts in the multiplet structure of a spinI = 1/2 scalar coupled to a quadrupolar nucleus with a spinS ≥ 1 undergoing dipolar (D), quadrupolar (Q) and chemical shift anisotropy (CSA) relaxation are studied. Analytic expressions for the cross-correlation spectral densities J^Q-CSA, J_D-Q, J^D-CSA and also for the real and imaginary Redfield elements of the relaxation matrix were obtained in the general case of noncoincident and nonaxial Q, D, and CSA tensors. On the assumption that CSA and Q interactions are comparable in magnitude the contributions of cross-correlation terms CSA-Q, CSA-D, Q-D in the linewidth and dynamic shifts of the multiplet pattern of a spinI = 1/2 were analyzed in a wide interval of correlation times (10⁻¹²-10⁻⁷ s) for a spin system¹³C-¹¹B and³¹P-⁵⁹Co as an example.     

A Definitive Example of Aluminum-27 Chemical Shielding Anisotropy

Solid-state²⁷Al NMR spectra have been obtained for a crystalline 1:1 complex of AlCl₃and OPCl₃. Aluminum chloride phosphoryl chloride, AlCl₃· OPCl₃(1), is unusual in that the Al–O–P bond angle is close to 180°. From analysis of the²⁷Al MAS NMR spectra, it was determined that the²⁷Al nuclear quadrupole coupling constant is 6.0(1) MHz, the asymmetry in the electric field gradient (efg) tensor is 0.15(2), and the isotropic chemical shift, δ_iso(²⁷Al), is 88(1) ppm. Solid-state²⁷Al NMR of a stationary sample reveals a line shape affected by a combination of anisotropic chemical shielding and second-order quadrupolar interactions. Analysis of this spectrum yields a chemical shift anisotropy of 60(1) ppm and orientations of the chemical shift and electric field gradient tensors in the molecular frame. Experimental results are compared with those calculated usingab initioHartree–Fock and density functional theory.     

The magnetic structure on the ground state of the equilateral triangular spin tube

The ground state of the frustrated equilateral triangular spin tube CsCrF₄ is still hidden behind a veil though NMR spectrum broaden into 2 T at low temperature. In order to investigate the spin structure in an ordered state by ¹⁹F-NMR, we have determined the anisotropic hyperfine coupling tensors for each three fluorine sites in the paramagnetic state. The measurement field was raised up to 10 T to achieve highest resolution. The preliminary analysis using the obtained hyperfine tensors has shown that the archetypal 120°-type structure in ab-plane does not accord with the NMR spectra of ordered state.     

Al Multiple-Quantum MAS NMR of Mechanically Treated Bayerite (α-Al(OH)3) and Silica Mixtures

Two-dimensional ²⁷Al multiple-quantum magic angle spinning (MQMAS) NMR experiments are used to study mixtures of bayerite (α-Al(OH)₃) with either silicic acid (SiO₂.nH₂O) or silica gel (SiO₂) that have been ground together for varying lengths of time. This mechanical treatment produces changes in the ²⁷Al MAS and MQMAS NMR spectra that correspond to the formation of new Al species. Mean values of the quadrupolar interaction (P_Q) and isotropic chemical shift (δ_CS) are extracted from the two-dimensional ²⁷Al NMR spectra for each of these species. The presence of significant distributions of both ²⁷Al quadrupolar and chemical shift parameters is demonstrated and the effect of grinding duration on the magnitudes of these distributions is discussed.     

Product Operator Theory for Spin‐5/2 Nuclei: Application to 2D J‐Resolved NMR Spectroscopy

Product operator theory is a simple quantum mechanical method that has often been used to analytically describe multi‐pulse NMR experiments for weakly coupled spin systems. Considering the existence of 2D‐J resolved NMR spectra of aqueous solutions containing S = 5/2 nuclear spins, the product operator formalism has been extended to the weakly coupled IS (I = 1/2, S = 5/2) spin system. The evolution of I_x, I_y, I_xS_z and I_yS_z product operators under spin–spin coupling Hamiltonian are given here. The analytical results obtained are applied to the well‐known gated decoupler pulse sequence for heteronuclear 2D‐J resolved NMR spectroscopy.     

EPR of Er3+, Nd3+, and Ce3+ ions in YAlO3 single crystals

EPR spectra of the Er³⁺, Nd³⁺, and Ce³⁺ ions substituting for the Y³⁺ ion in the YAlO₃ yttrium orthoaluminate lattice are studied. The EPR spectra of these rare-earth ions are described by a spin Hamiltonian of rhombic symmetry with an effective spin S=1/2. The principal values of the g tensors were determined from an analysis of the angular dependences of the EPR spectra. The orientation of the local magnetic axes of paramagnetic centers relative to the YAlO₃ crystallographic directions are shown to depend on the actual rare-earth species. The EPR spectra exhibit a hyperfine structure due to the ¹⁶⁷Er, ¹⁴³Nd, and ¹⁴⁵Nd odd isotopes, which permitted unambiguous identification of these spectra. The hyperfine coupling constants for the odd erbium and neodymium isotopes are determined.     

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.     

Differential Line Broadening in the Presence of Quadrupolar–CSA Interference

The formalism for calculating the lineshape of a spin 1/2J-coupled to a high-spin nucleus undergoing quadrupolar and chemical shift anisotropy (CSA) relaxations is derived in the case where the tensors of both interactions are noncoincident and nonaxial. The expressions show that the CSA–quadrupolar interference term which is responsible for the asymmetry of lines involves a term depending on tensorial parameters. The effect of this term on the lineshapes is discussed with respect to three cases, namely coincident–axially symmetric, noncoincident–axially symmetric, and general noncoincident quadrupolar and CSA tensors. These cases are considered in the analysis of the lineshape of the¹H-decoupled spectra of the³¹P nucleusJ-coupled to the⁵⁹Co nucleus encountered in the tetrahedral cluster HFeCo₃(CO)₁₁PPh₂H.     

Li NMR in lithium borate glasses

In anticipation of using fluctuations in the nuclear dipolar and quadrupolar interaction as a probe of lithium ion motion in lithium borate glasses, the static values of these interactions were measured using a variety of echo techniques. The static quadrupolar echo spectrum of ⁷Li and a calculation of the dipolar interaction in crystalline Li₂B₄O₇ (same chemical composition as the glass under study) were used to estimate the strength of the two interactions. These indicate that the dipolar and quadrupolar interactions for ⁶Li will be of similar size and the dipolar interaction will be dominated by the unlike spin interaction between the ⁶Li and the ¹⁰B, ¹¹B spins. An appropriate theoretical model is proposed and explicit expressions for the echo amplitude are calculated in terms of the dipolar and quadrupolar second moments. This single spin model takes into account the quadrupolar interaction but treats the dipolar interaction as an effective magnetic field. Experimental results are presented which show the essential validity of the model and measurements lead to reasonable values for the dipolar and quadrupolar second moments. The relative merits of the various echo techniques are discussed.     

HYSCORE analysis of nitrogen hyperfine interactions

A semiquantitative treatment of hyperfine sublevel correlation spectra of aS=1/2,I=1 spin system is presented. The derived closed analytical expressions allow the determination of components of the dipolar and quadrupolar coupling tensors. The method is applicable if nonsecular terms can be neglected and if canonical orientations of the hyperfine interactions can be selected via a dominantg matrix or hyperfine anisotropy.