质子核磁共振谱的偶极魔角旋转边带强度的矩的展开

对于包含分子和分子基团绕至少一个轴高速运动的固体体系,本文推导出其质子核磁共振谱的偶极魔角旋转边带强度的理论计算表达式,建立了用其静态粉末谱的矩的展开的计算方法,计算出旋转边带强度按三十阶矩展开的系数,它可以处理包含高达十五阶边带的谱     

High-resolution solid-state NMR spectroscopy of protons with homonuclear dipolar decoupling schemes under magic-angle spinning

High-resolution NMR spectroscopy of ¹H spins in the solid state is normally rendered difficult due to the strong homonuclear ¹H–¹H dipolar couplings. Even under very high-speed magic-angle spinning (MAS) at ca. 60–70 kHz, these couplings are not completely removed. An appropriate radiofrequency pulse scheme is required to average out the homonuclear dipolar interactions in combination with MAS to get high-resolution ¹H NMR spectrum in solid state. Several schemes have been introduced in the recent past with a variety of applications also envisaged. Development of some of these schemes has been made possible with a clear understanding of the underlying spin physics based on bimodal Floquet theory. The utility of these high-resolution pulse schemes in combination with MAS has been demonstrated for spinning speeds of 10–65 kHz in a range of ¹H Larmor frequencies from 300 to 800 MHz.     

Pulsed Field Gradient Selection in Two-Dimensional Magic Angle Spinning NMR Spectroscopy of Dipolar Solids

The utility of gradient selection in MAS spectroscopy of dipolar solids is explored in two examples. In the first, rotor-synchronized gradients of appropriate strength and duration are applied to select¹H double-quantum coherences. The resulting DQ MAS spectrum of adamantane is compared with that acquired by the corresponding phase-cycling technique. As a second example, a¹H 2D exchange MAS experiment is performed on an elastomer sample. In this experiment, a gradient is applied to remove undesired coherences that would otherwise distort the spectrum for short mixing times. The diagonal-peak intensities in the resulting spectrum show a linear decrease with increasing mixing time indicating cross-relaxation by slow chain motions as the relevant process. Both types of experiments demonstrate the potential of gradient-selection techniques for MAS spectroscopy of dipolar solids.     

Bulk magnetization and 1H NMR spectra of magnetically heterogeneous model systems

Bulk magnetization and ¹H static and magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectra of two magnetically heterogeneous model systems based on laponite (LAP) layered silicate or polystyrene (PS) with low and high proton concentration, respectively, and ferrimagnetic Fe₂O₃ nano- or micro-particles have been studied. In LAP+Fe₂O₃, a major contribution to the NMR signal broadening is due to the dipolar coupling between the magnetic moments of protons and magnetic particles. In PS+Fe₂O₃, due to the higher proton concentration in polystyrene and stronger proton–proton dipolar coupling, an additional broadening is observed, i.e. ¹H MAS NMR spectra of magnetically heterogeneous systems are sensitive to both proton–magnetic particles and proton–proton dipolar couplings. An increase of the volume magnetization by ～1 emu/cm³ affects the ¹H NMR signal width in a way that is similar to an increase of the proton concentration by ～2×10²²/cm³. ¹H MAS NMR spectra, along with bulk magnetization measurements, allow the accurate determination of the hydrogen concentration in magnetically heterogeneous systems.     

Distribution effects on 1H double-quantum MAS NMR spectra

The effect of a distribution in the (1)H-(1)H dipolar coupling on (1)H double-quantum (DQ) magic angle spinning (MAS) nuclear magnetic resonance (NMR) spinning sideband patterns is considered. In disordered or amorphous materials a distribution in the magnitude of the (1)H-(1)H dipolar coupling is a realistic possibility. Simulations of the (1)H DQ MAS NMR spinning sideband spectra were performed with the two-spin approximation. These simulations reveal that a dipolar coupling distribution can greatly affect the DQ spectral shape and behavior of the DQ build-up. The spectral line shapes are quantified by measurement of the relative intensities of the DQ sidebands. These variations in the (1)H DQ NMR spectra are evaluated as a function of the width of the dipolar coupling distribution. As an example, the experimental DQ spinning sideband spectrum for a hydrated polyoxoniobate containing 15 H(2)O molecules per hexaniobate cluster, are better simulated with a distribution of dipolar couplings opposed to a single coupling constant.     

Globally optimal superconducting magnets part I: minimum stored energy (MSE) current density map

Accurate determination of ¹H NMR signal intensities is useful for quantitative analysis of the hydrogen content and also to determine the relative peak intensity ratios in different application scenarios. To this end we have investigated the reliability and sources of intensity errors in ¹H solid-state MAS NMR. If sufficient resolution can be achieved by very high spinning speeds and high magnetic fields, quantification is straight forward. However, for poorly resolved spectra we show that small phase errors add a considerable amount of uncertainty. An analytical expression for the phase induced intensity-errors allowed us to suggest a robust and reliable recipe which is based on a combination of the spin-echo experiment, an extrapolation technique and a deconvolution algorithm which includes fitting of the signal phase. It significantly reduces errors caused by phase distortions, homonuclear dipolar dephasing, the receiver dead time delay and baseline rolling. The method was validated experimentally on samples with strong homonuclear dipolar interactions.     

A15N-1H dipolar CSA solid-state NMR study of polymorphous polyglycine (-CO-CD2-15NH-)n

The solid-state¹H MAS (magic-angle spinning),²H static,¹⁵N CP (cross polarization)-MAS and¹⁵N-¹H dipolar CSA (chemical shielding anisotropy) NMR (nuclear magnetic resonance) spectra of two different modifications of C_α-deuterated^l5N-polyglycine, namely PG I and PG II (-CO-CD₂-^l5NH-)_n are measured. The data from these spectra are compared to previous NMR, infrared, Raman and inelastic neutron scattering work. The deuteration of C_α eliminates the largest intramolecular¹H-¹H dipolar coupling. The effect of the remaining (N)H-(N)H interaction (～5 kHz) is not negligible compared to the¹⁵N-¹H coupling (about 10 kHz). Its effect on the dipolar CSA spectra, described as a two-spin system, is analyzed analytically and numerically and it is shown that those parts of the powder spectrum, which correspond to orientations with a strong dipolar¹⁵N-¹H interaction, can be described as an effective two-spin system, permitting the measurement of the strength of the¹⁵N-¹H dipolar interaction and the orientation of the dipolar vector with respect to the¹⁵N CSA frame. While in the PG II system the¹⁵N CSA tensor is collinear with the amide plane, in the PG I system the CSA tensor is tilted ca. 16° with respect to the (δ₁₁δ₂₂) CSA plane.     

Quantification of homonuclear dipolar coupling networks from magic-angle spinning 1H NMR

Numerical simulations of magic-angle spinning (MAS) spectra of dipolar-coupled nuclear spins have been used to assess different approaches to the quantification of dipolar couplings from ¹H solid-state NMR. Exploiting the translational symmetry of periodic spin systems allows extended networks with ‘realistic’ numbers of spins to be considered. The experimentally accessible parameter is shown to be the root-sum-square of the dipolar couplings to a given spin. The effectiveness of either fitting the resulting spinning sideband spectra to small spin system models, or using analyses based on moment expansions, has been examined. Fitting of the spinning sideband pattern is found to be considerably more robust with respect to experimental noise than frequency domain moment analysis. The influence of the MAS rate and system geometry on robustness of the quantification is analysed and discussed.     

High-resolution 1H and 13C NMR of solid 2-Aminobenzoic acid

Three crystalline modifications of 2-aminobenzoic acid (anthranilic acid) have been studied by ¹³C CP/MAS and ¹H CRAMPS NMR. The peaks are assigned and discussed in relation to (a) the neutral or zwitterionic nature of the molecules, (b) the crystal structures, known for two of the polymorphs, (c) residual (N,C) dipolar splittings, (d) hydrogen bonding and (e) dynamic exchange. The value of applying both types of spectroscopy to such studies is stressed.     

Real figure of two-dimensional spin-echo NMR spectra for a homonuclear two-spin system in rotating solids

Two-dimensional (2D) spin-echo NMR experiments have been carried out on polycrystalline [2,3-¹³C₂]-alanine under magic-angle sample spinning (MAS) conditions, so that two unusual resonance lines emerged along the F₁ axis (Kuwahara, D., Nakai, T., Ashida, J., and Miyajima, S., 1999, Chem. Phys. Lett., 305, 35). To examine the spectral structure observed in the F₁ direction more closely the 2D NMR experiment was undertaken using a sufficiently small t_l increment, yielding many more resonance lines on a spectrum sliced along the F₁ axis. The line distribution had a very unique and interesting structure. To elucidate the line positions theoretically, the signal for the 2D spin-echo experiment performed with any t₁ increment was calculated analytically for a homonuclear two-spin-1/2 system undergoing MAS. Virtually six resonance lines (exactly 12 resonance lines) occurred on a spectrum sliced along the F₁ axis. In addition, it was demonstrated that the intensities of some resonance lines were largely dependent on the dipolar interaction.     

1H–13C hetero-nuclear dipole–dipole couplings of methyl groups in stationary and magic angle spinning solid-state NMR experiments of peptides and proteins

¹³C NMR of isotopically labeled methyl groups has the potential to combine spectroscopic simplicity with ease of labeling for protein NMR studies. However, in most high resolution separated local field experiments, such as polarization inversion spin exchange at the magic angle (PISEMA), that are used to measure ¹H–¹³C hetero-nuclear dipolar couplings, the four-spin system of the methyl group presents complications. In this study, the properties of the ¹H–¹³C hetero-nuclear dipolar interactions of ¹³C-labeled methyl groups are revealed through solid-state NMR experiments on a range of samples, including single crystals, stationary powders, and magic angle spinning of powders, of ¹³C₃ labeled alanine alone and incorporated into a protein. The spectral simplifications resulting from proton detected local field (PDLF) experiments are shown to enhance resolution and simplify the interpretation of results on single crystals, magnetically aligned samples, and powders. The complementarity of stationary sample and magic angle spinning (MAS) measurements of dipolar couplings is demonstrated by applying polarization inversion spin exchange at the magic angle and magic angle spinning (PISEMAMAS) to unoriented samples.     

Spatial Structure of the Decapeptide Val-Ile-Lys-Lys-Ser-Thr-Ala-Leu-Leu-Gly in Water and in a Complex with Sodium Dodecyl Sulfate Micelles

We have studied the spatial structure of the decapeptide Val-Ile-Lys-Lys-Ser-Thr-Ala-Leu-Leu-Gly in aqueous solution and in a complex with sodium dodecyl sulfate (SDS) micelles by ¹H nuclear magnetic resonance (NMR) spectroscopy and two-dimensional (2-D) NMR spectroscopy (total correlation spectroscopy and nuclear Overhauser effect spectroscopy (NOESY)). The approach used to determine the decapeptide spatial structure was based on analysis of the ¹H?C¹³C residual dipolar couplings in the molecules partially aligned in lyotropic liquid crystalline media. Analysis of the interproton distances obtained from the 2-D NOESY NMR spectrum was used to reveal the spatial structure of the decapeptide in a complex with SDS micelles. Complex formation was confirmed by analysis of ¹H chemical shifts in the NMR spectrum of the decapeptide and analysis of the signs and values of NOEs in a solution with SDS micelles.     

A Multiple-Quantum 1H NMR Study of Partially Oriented Biphenylene

¹H multiple-quantum NMR spectra were used to aid in the solution of the complex one-quantum spectrum of the eight-spin system of biphenylene, which was partially oriented in a liquid crystal. Analysis of the six- and seven-quantum spectra was sufficient to provide a useful starting point to assign lines in the one-quantum spectrum, which would have been difficult to do otherwise. The dipolar coupling constants were then used to determine the proton geometry of the molecule.     

A low-E magic angle spinning probe for biological solid state NMR at 750 MHz

Crossed-coil NMR probes are a useful tool for reducing sample heating for biological solid state NMR. In a crossed-coil probe, the higher frequency ¹H field, which is the primary source of sample heating in conventional probes, is produced by a separate low-inductance resonator. Because a smaller driving voltage is required, the electric field across the sample and the resultant heating is reduced. In this work we describe the development of a magic angle spinning (MAS) solid state NMR probe utilizing a dual resonator. This dual resonator approach, referred to as “low-E,” was originally developed to reduce heating in samples of mechanically aligned membranes. The study of inherently dilute systems, such as proteins in lipid bilayers, via MAS techniques requires large sample volumes at high field to obtain spectra with adequate signal-to-noise ratio under physiologically relevant conditions. With the low-E approach, we are able to obtain homogeneous and sufficiently strong radiofrequency fields for both ¹H and ¹³C frequencies in a 4 mm probe with a ¹H frequency of 750 MHz. The performance of the probe using windowless dipolar recoupling sequences is demonstrated on model compounds as well as membrane-embedded peptides.     

Magic-angle-spinning NMR on solid biological systems. Analysis Of the origin of the spectral linewidths

Magic-angle-spinning (MAS) high-power ¹H-decoupled ¹³C and ³¹P NMR has been applied to solid biological materials to obtain information about the mechanisms that determine the spectral linewidths. The line broadening in MAS ³¹P NMR spectra of solid tobacco mosaic virus (TMV) has been investigated by selective saturation and T₂ measurements. About 90 Hz stems from homogeneous effects, whereas the inhomogeneous contribution is approximately 100 Hz. The inhomogeneous line broadening is assigned to macroscopic inhomogeneities in the sample and not to variations in the nucleotide bases along the RNA strand in TMV. It is concluded that sample preparation is of vital importance for obtaining well-resolved spectra. Under optimal preparation techniques the isotropic values of the chemical shift of the different ³¹P sites have been determined to obtain information about the secondary structure of the viral RNA. The chemical shift anisotropy has been determined from the relative intensities of the spinning side bands in the spectra. The chemical shift information is used to make a tentative assignment of the resonance in terms of the three structurally distinguishable phosphate groups in TMV. The origin of the linewidths in MAS NMR has been examined further by ¹³C NMR of approximately 10% ¹³C-enriched coat protein of cowpea chlorotic mottle virus, using selective excitation and saturation techniques, as well as measurements of the relaxation times T_1γ and T₂. The CO resonance in the spectrum is composed of an inhomogeneous and homogeneous part with a total linewidth of 700 Hz. The homogeneous linewidth, contributing with 200 Hz, is found to arise from slow molecular motions in the solid on a millisecond timescale.     

Magic Angle-Oriented Sample Spinning (MAOSS): A New Approach toward Biomembrane Studies

The application of magic angle sample spinning (MAS) NMR to uniformly aligned biomembrane samples is demonstrated as a new general approach toward structural studies of membrane proteins, peptides, and lipids. The spectral linewidth from a multilamellar lipid dispersion is dominated, in the case of protons, by the dipolar coupling. For low-γ or dilute spins, however, the chemical shift anisotropy dominates the spectral linewidth, which is reduced by the two-dimensional order in a uniformly aligned lipid membrane. The remaining line broadening, which is due to orientational defects (“mosaic spread”) can be easily removed at low spinning speeds. This orientational order in the sample also allows the anisotropic intermolecular motions of membrane components (such as rotational diffusion, τ_c= 10⁻¹⁰s) for averaging dipolar interactions to be utilized, e.g., by placing the membrane normal parallel to the rotor axis. The dramatic resolution improvement for protons which are achieved in a lipid sample at only 220 Hz spinning speed in a 9.4 T field is slightly better than any data published to date using ultra-high fields (up to 17.6 T) and high-speed spinning (14 kHz). Additionally, the analysis of spinning sidebands provides valuable orientational information. We present the first¹H,³¹P, and¹³C MAS spectra of uniformly aligned dimyristoylphosphatidylcholine (DMPC) bilayers. Also,¹H resolution enhancement for the aromatic region of the M13 coat protein reconstituted into DMPC bilayers is presented. This new method combines the high resolution usually achieved by MAS with the advantages of orientational constraints obtained by working with macroscopically oriented samples. We describe the general potential and possible perspectives of this technique.     

Indirectly detected heteronuclear correlation solid-state NMR spectroscopy of naturally abundant 15N nuclei

Two-dimensional indirectly detected through-space and through-bond ¹H{¹⁵N} solid-state NMR experiments utilizing fast magic angle spinning (MAS) and homonuclear multipulse ¹H decoupling are evaluated. Remarkable efficiency of polarization transfer can be achieved at a MAS rate of 40 kHz by both cross-polarization and INEPT, which makes these methods applicable for routine characterizations of natural abundance solids. The first measurement of 2D ¹H{¹⁵N} HETCOR spectrum of natural abundance surface species is also reported.     

Why does PMLG proton decoupling work at 65 kHz MAS?

Schemes such as phase-modulated Lee–Goldburg (PMLG) for homonuclear dipolar decoupling have been shown to yield high-resolution ¹H spectra at high magic-angle spinning (MAS) frequencies of 50–70 kHz. This is at variance to the commonly held notion that these methods require MAS frequencies not comparable to the cycle frequencies of the pulse schemes. Here, a theoretical argument, based on bimodal Floquet theory, is presented to explain this aspect together with conditions where PMLG type of schemes may be successful at high MAS frequencies.     

Aromatic spectral editing techniques for magic-angle-spinning solid-state NMR spectroscopy of uniformly 13C-labeled proteins

The four aromatic amino acids in proteins, namely histidine, phenylalanine, tyrosine, and tryptophan, have strongly overlapping ¹³C chemical shift ranges between 100 and 160 ppm, and have so far been largely neglected in solid-state NMR determination of protein structures. Yet aromatic residues play important roles in biology through π–π and cation–π interactions. To better resolve and assign aromatic residues' ¹³C signals in magic-angle-spinning (MAS) solid-state NMR spectra, we introduce two spectral editing techniques. The first method uses gated ¹H decoupling in a proton-driven spin-diffusion (PDSD) experiment to remove all protonated ¹³C signals and retain only non-protonated carbon signals in the aromatic region of the ¹³C spectra. The second technique uses chemical shift filters and ¹H–¹³C dipolar dephasing to selectively detect the Cα, Cβ and CO cross peaks of aromatic residues while suppressing the signals of all aliphatic residues. We demonstrate these two techniques on amino acids, a model peptide, and the microcrystalline protein GB1, and show that they significantly simplify the 2D NMR spectra and both reveal and permit the ready assignment of the aromatic residues' signals.     

Study on ethyl groups with two different orientations in [N(C2H5)4]2CuBr4

The crystal structure and phase transition temperature of [N(C₂H₅)₄]₂CuBr₄ are studied using X-ray diffraction and differential scanning calorimetry (DSC); measurements revealed a tetragonal structure and the two phase transition temperatures T_C of 204 K and 255.5 K. The structural geometry near T_C is discussed in terms of the chemical shifts for ¹H magic angle spinning (MAS) nuclear magnetic resonance (NMR) and ¹³C cross-polarization (CP)/MAS NMR. The two inequivalent ethyl groups are distinguishable by the ¹³C NMR spectrum. The molecular motions are discussed in terms of the spin–lattice relaxation times T_1ρ in the rotating frame for ¹H MAS NMR and ¹³C CP/MAS NMR. The T_1ρ results reveal that the ethyl groups undergo tumbling motion, and furthermore that the ethyl groups are highly mobile.