Multiple-quantum spin counting in magic-angle-spinning NMR via low-power symmetry-based dipolar recoupling

By using a symmetry-based R2(8)(1)R2(8)(-1) double-quantum (2Q) dipolar recoupling sequence, we demonstrate high-order multiple-quantum coherence (MQC) excitation at fast magic-angle spinning (MAS) frequencies up to 34 kHz. This scheme combines several attractive features, such as a relatively high dipolar scaling factor, good compensation to rf-errors, isotropic and anisotropic chemical shifts, as well as an ultra-low radio-frequency (rf) power requirement. The latter translates into nutation frequencies below 30 kHz for MAS rates up to 60 kHz, thereby permitting rf application for very long excitation periods without risk of damaging the NMR probehead or sample, while the compensation to chemical shifts improves as the MAS rate increases. (31)P MQC spin counting is demonstrated on powders of calcium hydroxyapatite (Ca5(PO4)3OH) and anhydrous sodium diphosphate (Na4P2O7), from which all even coherence orders up to 30 and 14 were detected, respectively, over the respective MAS ranges of 15-24 kHz and 20-34 kHz. The amplitude distributions among the (31)P MQC orders depend on the precise nutation frequency during recoupling, despite that the highest detected order was relatively insensitive to this parameter. An observed gradual transition from a Gaussian to exponential functionality of the MQC amplitude-profile is discussed in relation to the prevailing approach to derive spin-cluster sizes by fitting the MQC amplitude-distribution to a Gaussian decay, where minor systematic deviations between the model and experimental data are frequently reported.

Spherical tensor analysis of nuclear magnetic resonance signals

In a nuclear magnetic-resonance (NMR) experiment, the spin density operator may be regarded as a superposition of irreducible spherical tensor operators. Each of these spin operators evolves during the NMR experiment and may give rise to an NMR signal at a later time. The NMR signal at the end of a pulse sequence may, therefore, be regarded as a superposition of spherical components, each derived from a different spherical tensor operator. We describe an experimental method, called spherical tensor analysis (STA), which allows the complete resolution of the NMR signal into its individual spherical components. The method is demonstrated on a powder of a (13)C-labeled amino acid, exposed to a pulse sequence generating a double-quantum effective Hamiltonian. The propagation of spin order through the space of spherical tensor operators is revealed by the STA procedure, both in static and rotating solids. Possible applications of STA to the NMR of liquids, liquid crystals, and solids are discussed.

Triple-quantum dynamics in multiple-spin systems undergoing magic-angle spinning: application to 13C homonuclear correlation spectroscopy

We analyze the multiple-quantum dynamics governed by a new homonuclear recoupling strategy effecting an average dipolar Hamiltonian comprising three-spin triple-quantum operators (e.g., S(p)+S(q)+S(r)+) under magic-angle spinning conditions. Analytical expressions are presented for polarization transfer processes in systems of three and four coupled spins-1/2 subject to triple-quantum filtration (3QF), and high-order multiple-quantum excitation is investigated numerically in moderately large clusters, comprising up to seven spins. This recoupling approach gives highly efficient excitation of triple-quantum coherences: ideally, up to 67% of the initial polarization may be recovered by 3QF in three-spin systems in polycrystalline powders. Two homonuclear 2D correlation strategies are demonstrated experimentally on powders of uniformly 13C-labeled alanine and tyrosine: the first correlates the single-quantum spectrum in the first dimension with the corresponding 3QF spectrum along the other. The second protocol correlates triple-quantum coherences with their corresponding single-quantum coherences within triplets of coupled spins.

Multiple quantum spin counting techniques with quadrupolar nuclei

Phase incremented and continuous irradiation multiple spin correlation methods are applied to spin [Formula: see text] nuclei with small quadrupole couplings such as (7)Li in LiCl and are shown to successfully produce a coherently coupled dipolar spin network. Application to the analogous Na salt shows successful spin correlation evolving at a slower rate due to the weaker homonuclear dipolar coupling strength between Na nuclei. The results are analysed using a statistical approach. Spin counting is non-trivial as not only multiple quantum coherences between spins are generated but also within the quadrupolar spin levels. Na(2)C(2)O(4) is investigated as a material with non-negligible quadrupole coupling and it is in this limit that the spin correlation techniques are found to break down.

Determination of molecular geometry by high-order multiple-quantum evolution in solid-state NMR

The principles of molecular geometry determination by high-quantum heteronuclear local field spectroscopy in solid-state NMR are discussed. The extreme multiple-quantum coherences in a cluster of nuclear spins are allowed to evolve in the presence of heteronuclear through-space couplings to two spins of a different type. The multiple-quantum dephasing curve is independent of the homonuclear spin-spin couplings and may be described in terms of geometric parameters. The triple-quantum version of the experiment is demonstrated by determining the psi torsion angle in a [(15)N(2), (13)C(3)]-labeled sample of the peptide ala-ala-gly. Two regions of torsion angle space fit the experimental data, one in the neighborhood of -152 degrees and one in the neighborhood of +161 degrees. The latter determination is in excellent agreement with the X-ray estimate of +160.5 degrees.

Multiple-quantum nuclear magnetic resonance spectroscopy of coupled 1/2 spins in solids. Combination with cross-polarization and magic-angle spinning

Proton multiple-quantum coherence spectroscopy has been combined with magic-angle spinning (MAS) and cross-polarization (CP). This enables the detection of the proton (or any other abundant spin) multiple-quantum coherence spectrum via the high-resolution 13C (any other spin) nuclear magnetic resonance (NMR) spectrum. For this purpose multiple-quantum pulse sequences synchronised to sample rotation have been designed, and the average Hamiltonians of these sequences have been analysed. The analysis allows the design of optimal experimental conditions. As a demonstration of the technique, it has been applied to a mixture of adamantane and hexamethylethane. From earlier 13C spin diffusion experiments it was known that these two molecules form a mixed crystal. With our technique we detected two different phases with different molecular translational self-diffusion coefficients in this system.

Experimental detection of multiple-quantum coherence transfer in coupled spin solids by multi-dimensional NMR experiments

Three-dimensional multiple-quantum coherence experiments in coupled 1/2 spin solids have been designed to directly detect coherence transfers among all the accessible coherence orders during irradiation. The experiments have been performed on the coupled four-spin polycrystalline sample 1,2,3,4-tetrachloronaphthalene-bis(hexachlorocyclopentadiene) adduct. The experimental results reveal how the coherences transfer in this spin system, which support the theoretically deduced selection rules and can be used to assist more precise description of multiple-quantum coherence dynamics.