Introduction of the Floquet-Magnus expansion in solid-state nuclear magnetic resonance spectroscopy

In this article, we present an alternative expansion scheme called Floquet-Magnus expansion (FME) used to solve a time-dependent linear differential equation which is a central problem in quantum physics in general and solid-state nuclear magnetic resonance (NMR) in particular. The commonly used methods to treat theoretical problems in solid-state NMR are the average Hamiltonian theory (AHT) and the Floquet theory (FT), which have been successful for designing sophisticated pulse sequences and understanding of different experiments. To the best of our knowledge, this is the first report of the FME scheme in the context of solid state NMR and we compare this approach with other series expansions. We present a modified FME scheme highlighting the importance of the (time-periodic) boundary conditions. This modified scheme greatly simplifies the calculation of higher order terms and shown to be equivalent to the Floquet theory (single or multimode time-dependence) but allows one to derive the effective Hamiltonian in the Hilbert space. Basic applications of the FME scheme are described and compared to previous treatments based on AHT, FT, and static perturbation theory. We discuss also the convergence aspects of the three schemes (AHT, FT, and FME) and present the relevant references.     

Low-field approach to double resonance in nuclear quadrupole resonance of spin-1 nuclei

Using double-resonance conditions, in which the Larmor frequency of a spin-1/2 nucleus is matched to one of the nuclear quadrupole resonance frequencies of a spin-1 nucleus, the authors demonstrate increased cross relaxation between the two nuclear spin species. They calculate the cross-relaxation rate using the motionally averaged heterogeneous dipole Hamiltonian as a perturbation to the combined quadrupole and Zeeman Hamiltonians. Using this cross-relaxation rate, in addition to hydrogen and nitrogen autorelaxation rates, expressions governing spin-1/2 and spin-1 spin-lattice relaxation are determined. With ammonium nitrate, containing nitrogen (spin-1) and hydrogen (spin-1/2), increased nitrogen signal and spin-lattice relaxation are demonstrated, using fields less than 120 G. The cross-relaxation rate is also measured and an overall signal/noise improvement by a factor of 2.3+/-0.1 is attained.     

High-resolution characterization of liquid-crystalline [60]fullerenes using solid-state nuclear magnetic resonance spectroscopy

Liquid-crystalline materials containing fullerenes are valuable in the development of supramolecular switches and in solar cell technology. In this study, we characterize the liquid-crystalline and dynamic properties of fullerene-containing thermotropic compounds using solid-state natural abundance (13)C NMR experiments under stationary and magic angle spinning sample conditions. Chemical shifts spectra were measured in isotropic, liquid-crystalline nematic and smectic A and crystalline phases using one-dimensional (13)C experiments, while two-dimensional separated local-field experiments were used to measure the (1)H- (13)C dipolar couplings in mesophases. Chemical shift and dipolar coupling parameters were used to characterize the structure and dynamics of the liquid-crystalline dyads. NMR data of fullerene-containing thermotropic liquid crystals are compared to that of basic mesogenic unit and mesomorphic promoter compounds. Our NMR results suggest that the fullerene-ferrocene dyads form highly dynamic liquid-crystalline phases in which molecules rotate fast around the symmetry axis on the characteristic NMR time scale of approximately 10 (-4) s.     

Theory of covariance nuclear magnetic resonance spectroscopy

Covariance nuclear magnetic resonance (NMR) spectroscopy provides an effective way for establishing nuclear spin connectivities in molecular systems. The method, which identifies correlated spin dynamics in terms of covariances between 1D spectra, benefits from a high spectral resolution along the indirect dimension without requiring apodization and Fourier transformation along this dimension. The theoretical treatment of covariance NMR spectroscopy is given for NOESY and TOCSY experiments. It is shown that for a large class of 2D NMR experiments the covariance spectrum and the 2D Fourier transform spectrum can be related to each other by means of Parseval's theorem. A general procedure is presented for the construction of a symmetric spectrum with improved resolution along the indirect frequency domain as compared to the 2D FT spectrum.     

Measurement of 15N-T1 relaxation rates in a perdeuterated protein by magic angle spinning solid-state nuclear magnetic resonance spectroscopy

In this paper, we present the measurement of (15)N-T(1) relaxation times in the solid state for a perdeuterated protein for which exchangeable protons are back substituted during recrystallization using a buffer which contains 10% H(2)O and 90% D(2)O. We find large variations of the (15)N relaxation time, even within the same beta sheet. By comparing (15)N-T(1) relaxation times measured for a protonated and a deuterated protein (using the above mentioned approach), we conclude that (1)H driven (15)N,(15)N spin diffusion has a significant impact on the absolute (15)N relaxation time in protonated proteins. This effect is important for a quantitative analysis of relaxation data in terms of molecular dynamics.     

Theory of stochastic dipolar recoupling in solid-state nuclear magnetic resonance

Dipolar recoupling techniques in solid-state nuclear magnetic resonance (NMR) consist of radio frequency (rf) pulse sequences applied in synchrony with magic-angle spinning (MAS) that create nonzero average magnetic dipole-dipole couplings under MAS. Stochastic dipolar recoupling (SDR) is a variant in which randomly chosen rf carrier frequency offsets are introduced to cause random phase modulations of individual pairwise couplings in the dipolar spin Hamiltonian. Several aspects of SDR are investigated through analytical theory and numerical simulations: (1) An analytical expression for the evolution of nuclear spin polarization under SDR in a two-spin system is derived and verified through simulations, which show a continuous evolution from coherent, oscillatory polarization exchange to incoherent, exponential approach to equilibrium as the range of random carrier offsets (controlled by a parameter f(max)) increases; (2) in a many-spin system, polarization transfers under SDR are shown to be described accurately by a rate matrix in the limit of large f(max), with pairwise transfer rates that are proportional to the inverse sixth power of pairwise internuclear distances; (3) quantum mechanical interferences among noncommuting pairwise dipole-dipole couplings, which are a complicating factor in solid-state NMR studies of molecular structures by traditional dipolar recoupling methods, are shown to be absent from SDR data in the limit of large f(max), provided that coupled nuclei have distinct NMR chemical shifts.     

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.     

Structural studies of NaPO3-MoO3 glasses by solid-state nuclear magnetic resonance and Raman spectroscopy

Vitreous samples were prepared in the (100 - x)% NaPO(3)-x% MoO(3) (0 相似文献   

Computer-aided spectral assignment in nuclear magnetic resonance spectroscopy

The proton-carbon correlation spectra, HMBC (heteronuclear multiple bond correlation) and HMQC (heteronuclear multiple quantum correlation), respectively, provide direct and remote connectivity information with high sensitivity. Their combination enables carbon-carbon proximity relationships to be deduced, which are formally identical to those produced by a fictitious INADEQUATE-2D experiment, where correlations would be established exclusively between atoms linked by one or two bonds. The CASA program uses these relationships, as well as DEPT spectra and elementary chemical-shift considerations to assign the ¹³C spectrum of a compound if its structure is known or assumed. If the structure conflicts with the experimental data, no assignment is produced. The CASA program serves as an aid to either spectral assignment or structural elucidation.     

Quantification of magnetic resonance spectroscopy signals with lineshape estimation

Quantification of magnetic resonance spectroscopy (MRS) signals is required for providing metabolite concentrations of the tissue under investigation. For estimating these concentrations several biochemical and acquisition conditions need to be taken into account. It is still a challenge to obtain reliable concentrations, as experimental conditions may have a detrimental effect on the spectral quality. The lineshape of MRS signals is affected, for instance, by inhomogeneities of the static magnetic field arising from imperfect shimming and tissue heterogeneities. To handle this type of distortions, we propose an extension of the self‐deconvolution method, where a common lineshape is estimated and a robust method with local regression is included to improve the smoothing of the estimated damping (or lineshape) function. This common lineshape is imposed in the metabolite quantification method and the spectral parameters (amplitude, frequency, damping and phase corrections) are obtained via nonlinear least squares. In this study, we considered distorted simulated, in vitro and in vivo rat brain signals which were lineshape corrected and quantitative results were compared in all three cases. Copyright © 2011 John Wiley & Sons, Ltd.     

SPAM-MQ-HETCOR: an improved method for heteronuclear correlation spectroscopy between quadrupolar and spin-1/2 nuclei in solid-state NMR

The recently introduced concept of soft pulse added mixing (SPAM) is used in two-dimensional heteronuclear correlation (HETCOR) NMR experiments between half-integer quadrupolar and spin-1/2 nuclei. The experiments employ multiple quantum magic angle spinning (MQMAS) to remove the second order quadrupolar broadening and cross polarization (CP) or refocused INEPT for magnetization transfer. By using previously unexploited coherence pathways, the efficiency of SPAM-MQ-HETCOR NMR is increased by a factor of almost two without additional optimization. The sensitivity gain is demonstrated on a test sample, AlPO(4)-14, using CP and INEPT to correlate (27)Al and (31)P nuclei. SPAM-3Q-HETCOR is then applied to generate (27)Al-(31)P spectra of the devitrified 41Na(2)O-20.5Al(2)O(3)-38.5P(2)O(5) glass and the silicoaluminophosphate ECR-40. Finally, the method allowed the acquisition of the first high resolution solid-state correlation spectra between (27)Al and (29)Si.     

Direct coupling of capillary electrophoresis and nuclear magnetic resonance spectroscopy for the identification of a dinucleotide

Summary In this paper, a general peak capacity expression was evaluated using columns containing various packing materials under solvating gas chromatography (SGC) conditions. Differing from column efficiency, peak capacity can describe both separation capability and speed when introducing the dead time into the peak capacity expression. Various factors that influence peak capacity in SGC are described, including particle pore size, chemical surface modification, particle size, column length, temperature, and pressure.     

Bimodal Floquet description of heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance

A theoretical treatment of heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance is presented here based on bimodal Floquet theory. The conditions necessary for good heteronuclear decoupling are derived. An analysis of a few of the decoupling schemes implemented until date is presented with regard to satisfying such decoupling conditions and efficiency of decoupling. Resonance conditions for efficient heteronuclear dipolar decoupling are derived with and without the homonuclear (1)H-(1)H dipolar couplings and their influence on heteronuclear dipolar decoupling is pointed out. The analysis points to the superior efficiency of the newly introduced swept two-pulse phase-modulation (SW(f)-TPPM) sequence. It is shown that the experimental robustness of SW(f)-TPPM as compared to the original TPPM sequence results from an adiabatic sweeping of the modulation frequencies. Based on this finding alternative strategies are compared here. The theoretical findings are corroborated by both numerical simulations and representative experiments.     

13C nuclear magnetic resonance spectroscopy to determine olive oil grades

¹³C nuclear magnetic resonance spectroscopy was used in a first attempt to differentiate olive oil samples by grades. High resolution ¹³C NMR Distortionless Enhancement by Polarization Transfer (DEPT) spectra of 137 olive oil samples from the four grades, extra virgin olive oils, olive oils, olive pomace oils and lampante olive oils, were measured. The data relative to the resonance intensities (variables) of the unsaturated carbons of oleate (C-9 and C-10) and linoleate (L-9, L-10 and L-12) chains attached at the 1,3- and 2-positions of triacylglycerols were analyzed by linear discriminant analysis. The 1,3- and 2- carbons of the glycerol moiety of triacylglycerols along with the C-2, C-16 and C-18 resonance intensities of saturated, oleate and linoleate chains were also analyzed by linear discriminant analysis. The three discriminanting functions, which were calculated by using a stepwise variable selection algorithm, classified in the true group by cross-validation procedure, respectively, 76.9, 70.0, 94.4 and 100% of the extra virgin, olive oil, olive pomace oil and lampante olive oil grades.     

Interatomic distance measurement in solid-state NMR between a spin- 1/2 and a spin- 5/2 using a universal REAPDOR curve

A universal curve for the solid-state NMR REAPDOR experiment on an isolated spin-1/2-spin-5/2 pair is proposed that provides a simple means to measure their interatomic distance. REAPDOR data were obtained at three separate REAPDOR experiments using different values of the rotor spinning frequency. All points were fitted simultaneously to the universal formula without a need for full density matrix calculations. The 13C-17O distance of 2.45 A was measured between the C6 carbon and the 17O label in a tyrosine sample. The error of 8% in the dipolar coupling (Dfit = 278 Hz) is well within the 15% theoretical tolerance of this curve.     

Characterization of a three-component coupling reaction on proteins by isotopic labeling and nuclear magnetic resonance spectroscopy

A three-component Mannich-type electrophilic aromatic substitution reaction was previously developed to target the phenolic side chain of tyrosine residues on proteins. This reaction proceeds under mild conditions and provides a convenient alternative to lysine-targeting strategies. However, the use of reactive aldehydes, such as formaldehyde, warrants careful inspection of the reaction products to ensure that other modifications have not occurred. Through the use of isotopically enriched reagents, nuclear magnetic resonance (NMR)-based studies were used to obtain structural confirmation of the tyrosine-modification products. These experiments also revealed the formation of a reaction byproduct arising from the indole ring of tryptophan residues. Cysteine residues were shown to not participate in the reaction, except in the case of a reduced disulfide, which formed a dithioacetal. We anticipate that this analysis method will prove useful for the detailed study of a number of bioconjugation reactions.