Solid-state NMR spectroscopy

Abstract

Solid-state nuclear magnetic resonance (NMR) spectroscopy is an atomic-level method used to determine the chemical structure, three-dimensional structure, and dynamics of solids and semi-solids. This Primer summarizes the basic principles of NMR as applied to the wide range of solid systems. The fundamental nuclear spin interactions and the effects of magnetic fields and radiofrequency pulses on nuclear spins are the same as in liquid-state NMR. However, because of the anisotropy of the interactions in the solid state, the majority of high-resolution solid-state NMR spectra is measured under magic-angle spinning (MAS), which has profound effects on the types of radiofrequency pulse sequences required to extract structural and dynamical information. We describe the most common MAS NMR experiments and data analysis approaches for investigating biological macromolecules, organic materials, and inorganic solids. Continuing development of sensitivity-enhancement approaches, including ¹H-detected fast MAS experiments, dynamic nuclear polarization, and experiments tailored to ultrahigh magnetic fields, is described. We highlight recent applications of solid-state NMR to biological and materials chemistry. The Primer ends with a discussion of current limitations of NMR to study solids, and points to future avenues of development to further enhance the capabilities of this sophisticated spectroscopy for new applications.

FIG. 1.. Basics of solid-state NMR for structural analysis of biomolecules and materials.

a. Nuclear spin magnetic dipole moments (μ) precess around a static magnetic field (B₀) at a frequency that is identical to the transition frequency between the energy levels of the spins (ΔE=ħv₀) A radiofrequency (RF) coil wrapped around the sample at the top of an NMR probe that is inserted into the center of the magnet allows irradiation of the RF pulses as well as detection of the transition frequency of the nuclear magnetic moment. Angular velocity, ω=−γB. (b) The NMR frequencies of different nuclear isotopes depend on their gyromagnetic ratios (γ) and the magnetic field (B₀= 18.8 T, in this example). In addition, for spins of the same isotope, the frequency depends sensitively on the electronic environment of the individual nuclei. Schematic NMR spectra of a static powder containing three ¹³C nuclei relate to the chemical structure of attached functional groups. The broad powder pattern reflects chemical shift anisotropy (CSA), whose geometric average corresponds to the isotropic chemical shifts, which are detected when the sample undergoes magic-angle spinning (MAS). (c) MAS of the sample in the rotor yields high-resolution NMR spectra of solids by averaging the anisotropic part of the interaction to zero.

FIG. 2.. Some common solid-state NMR pulse sequences.

¹³C is used as an example of a heteronuclear (X) spin. (a) Cross polarization (CP). (b) 2D ¹H-¹³C heteronuclear chemical shift correlation (HETCOR) with ¹H homonuclear decoupling. (c) 2D ¹³C-¹³C correlation through dipolar spin diffusion. (d) 2D ¹³C-¹³C J-based refocused- incredible natural abundance double quantum transfer experiment (INADEQUATE). (e) The multiple-quantum MAS (MQMAS) experiment for quadrupolar nuclei. (f) X-Y rotational echo double resonance (REDOR) for heteronuclear distance measurement. (g) 2D ¹³C-¹H dipolar shift correlation (DIPSHIFT). (h) Centerband-only detection of exchange (CODEX) pulse sequence for studying slow motion. (i) 2D ¹H-detected hNH correlation under fast MAS. WALTZ is applied to yield heteronuclear scalar decoupling. In these pulse sequences, the heteronuclear decoupling scheme can be TPPM, SPINAL and other sequences, while the homonuclear decoupling scheme can be FSLG, DUMBO, and other sequences. The symbols t₁, t₂ and t₃ refer to time domain increments for 2D and 3D experiments, and 90° and 180° pulses are shown as filled and open narrow rectangles, respectively. DARR: dipolar-assisted rotational resonance. FSLG: frequency-switched Lee-Goldburg. TPPM: two-pulse phase modulation.

Fig. 3.. Representative solid-state NMR results and experiments.

(a) Resonance assignment experiments. The chemical shifts of ¹³C, ¹⁵N, and ¹H are correlated to obtain sequence-specific assignment of all chemical shifts. (b) Intra-residue hCANH and inter-residue hCA(CO)NH correlation spectra of Aβ fibrils . (c) ¹H-¹⁹F REDOR to measure internuclear distances to 1.5 nm. The spectra shown is for the model protein GB1, where amide protons that are close to the ¹⁹F spins manifest intensities in the difference spectrum ΔS . The REDOR dephasing for the cross peaks is fit to give the ¹H-¹⁹F distances. (d) Centerband-only detection of exchange (CODEX) to study slow motion as shown with an experiment used to determine the rates of helical jumps in isotactic-poly(4-methyl-1-pentene) as shown with helix axis model (right) . (e)¹⁷O magic angle spinning (MAS, left) and multiple-quantum MAS (MQMAS, right) spectra of MgSiO₃, showing resolution of six distinct O species. Lineshapes simulated using density functional theory (DFT) calculated values are also shown (red), enabling assignment of all signals .

Fig. 4.. Applications of solid-state NMR to biological chemistry.

(a, b) Examples of membrane protein studies. (a) Atomic-resolution structures of the influenza B M2 proton channel in its closed and open states . The structures, determined using interhelical distance experiments such as ¹³C-¹⁹F REDOR and orientation experiments, reveal a distinct activation mechanism of the channel compared to influenza A M2 protein. (b) Structural changes of a Asp-His-Trp triad in the pentameric light-driven proton pump, green proteorhodopsin (GPR) . DNP NMR experiments revealed tautomeric and rotameric structural changes of His75 to mediate proton transfer. (c, d) Examples of amyloid fibril studies. (c) The binding site of sulindac sulfide to the Alzheimer’s disease Aβ peptide is determined by 2D experiments and chemical shift perturbation . Structure on left generated using PDB: 2LMN. (d) Atomic-resolution structure of the glucagon amyloid fibril. The peptide assembles as an antiparallel cross-β fibril that contains two coexisting molecular conformations. These two conformations manifest as two sets of chemical shifts for each atom in the spectra . (e) The polysaccharide-rich cell walls of plants, bacterial and fungi can be studied using 2D and 3D NMR to understand how macromolecular packing and dynamics explain the properties of these biomaterials. The 2D ¹³C refocused-INADEQUATE correlation spectra resolve the chemical shifts of dynamic matrix polysaccharides in Arabidopsis cell walls.

Fig. 5.. Applications of solid-state NMR to materials chemistry.

(a) Prediction of the hydrous defects in wadsleyite, an inner Earth mineral found at depths of 400–600 km. Structure searching is used to predict possible structures for which NMR parameters are calculated using density functional theory (DFT), boxes in spectrum represent where structures (colours coordinate) were predicted.. (b) Determination of the mesoscale structure of multivariate molecular organic frameworks (MOFs) containing linkers with different functional groups . ¹³C-¹⁵N REDOR combined with molecular dynamics (MD) simulations allow the distinction of alternating cluster forms from random, small and large cluster forms. (c) ¹³C CPMAS spectra of high-temperature reaction products of ethylene-¹³C2 on zeolite HZSM-5 catalysts beds . The spectra elucidated the mechanism of methanol to hydrocarbon catalysis, establishing that methanol and dimethyl ether react on cyclic organic species contained in the cages or channels of the inorganic host. (d) Prediction of ⁸⁹Y NMR spectra of pyrochlores using ensemble-based modeling. NMR parameters of all possible cation arrangements are predicted using DFT and their Boltzmann-weighted contributions to the spectrum are then determined to obtain detailed information on the local geometry . (e) Pressure induced evolution of the distributions of the Si–O distances and Si–O–Si inter-tetrahedra bond angles in vitreous silica quenched from high pressure. 2D dynamic-angle-spinning ¹⁷O NMR spectra show that with increasing pressure, the mean Si–O–Si bond angle decreases while the mean Si–O distance increases . (f) Structure of inorganic–organic hybrid perovskites . 5-ammonium valeric acid iodide was used to stabilize the structure of α-FAPbI3. MAS NMR in combination with DFT was used to determine the atomic-level structure.

Fig. 6.. Outlook for MAS solid-state NMR.

(a) Sensitivities of methyl ¹H resonances of a typical selectively methyl protonated protein (V44γ1 from α-spectrin SH3) as a function of magnetic field strength expressed as ¹H Larmor frequencies . These sensitivities were measured at different MAS rates. (b) Quadrupolar NMR lineshapes of an ¹⁷O enriched metal-organic framework measured using a 35 T series-connected hybrid magnet illustrate the potential of high magnetic fields . Blue and red solid lines indicate experimental and simulated lineshapes, respectively. Areas on spectrum highlighted in green and yellow correspond to different ¹⁷O nuclei.