Homonuclear dipolar decoupling with very large scaling factors for high-resolution ultrafast magic angle spinning 1H solid-state NMR spectroscopy

Pure Isotropic Proton NMR Spectra in Solids using Deep Learning

The resolution of proton solid-state NMR spectra is usually limited by broadening arising from dipolar interactions between spins. Magic-angle spinning alleviates this broadening by inducing coherent averaging. However, even the highest spinning rates experimentally accessible today are not able to completely remove dipolar interactions. Here, we introduce a deep learning approach to determine pure isotropic proton spectra from a two-dimensional set of magic-angle spinning spectra acquired at different spinning rates. Applying the model to 8 organic solids yields high-resolution ¹ H solid-state NMR spectra with isotropic linewidths in the 50-400 Hz range.

Optimisation of 1H PMLG homonuclear decoupling at 60 kHz MAS to enable 15N-1H through-bond heteronuclear correlation solid-state NMR spectroscopy

The Lee–Goldburg condition for homonuclear decoupling in ¹H magic-angle spinning (MAS) solid-state NMR sets the angle θ, corresponding to arctan of the ratio of the rf nutation frequency, ν₁, to the rf offset, to be the magic angle, θ_m, equal to tan⁻¹(√2) = 54.7°. At 60 kHz MAS, we report enhanced decoupling compared to MAS alone in a ¹H spectrum of ¹⁵N-glycine with at θ = 30° for a ν₁ of ∼100 kHz at a ¹H Larmor frequency, ν₀, of 500 MHz and 1 GHz, corresponding to a high chemical shift scaling factor (λ_CS) of 0.82. At 1 GHz, we also demonstrate enhanced decoupling compared to 60 kHz MAS alone for a lower ν₁ of 51 kHz, i.e., a case where the nutation frequency is less than the MAS frequency, with θ = 18°, λ_CS = 0.92. The ratio of the rotor period to the decoupling cycle time, Ψ = τ_r/τ_c, is in the range 0.53 to 0.61. Windowed decoupling using the optimised parameters for a ν₁ of ∼100 kHz also gives good performance in a ¹H spin-echo experiment, enabling implementation in a ¹H-detected ¹⁵N–¹H cross polarisation (CP)-refocused INEPT heteronuclear correlation NMR experiment. Specifically, initial ¹⁵N transverse magnetisation as generated by ¹H–¹⁵N CP is transferred back to ¹H using a refocused INEPT pulse sequence employing windowed ¹H decoupling. Such an approach ensures the observation of through-bond N–H connectivities. For ¹⁵N-glycine, while the CP-refocused INEPT experiment has a lower sensitivity (∼50%) as compared to a double CP experiment (with a 200 μs ¹⁵N to ¹H CP contact time), there is selectivity for the directly bonded NH₃⁺ moiety, while intensity is observed for the CH₂¹H resonances in the double CP experiment. Two-dimensional ¹⁵N–¹H correlation MAS NMR spectra are presented for the dipeptide β-AspAla and the pharmaceutical cimetidine at 60 kHz MAS, both at natural isotopic abundance. For the dipeptide β-AspAla, different build-up dependence on the first spin-echo duration is observed for the NH and NH₃⁺ moieties demonstrating that the experiment could be used to distinguish resonances for different NH_x groups.

¹⁵N–¹H heteronuclear NMR correlation at natural abundance in the solid state via J couplings is enabled by optimisation of phase-modulated Lee–Goldburg (PMLG) ¹H homonuclear decoupling during the spin echoes, far from the ideal magic-angle condition.

On-the-Fly, Sample-Tailored Optimization of NMR Experiments

NMR experiments, indispensable to chemists in many areas of research, are often run with generic, unoptimized experimental parameters. This approach makes robust and automated acquisition on different samples and instruments extremely challenging. Here, we present NMR-POISE (Parameter Optimization by Iterative Spectral Evaluation), the first demonstration of on-the-fly, sample-tailored, and fully automated optimization of a wide range of NMR experiments. We illustrate how POISE maximizes spectral sensitivity and quality with a diverse set of 1D and 2D examples, ranging from HSQC and NOESY experiments to ultrafast and pure shift techniques. Our Python implementation of POISE has an interface integrated into Bruker's TopSpin software, one of the most widely used platforms for NMR acquisition and automation, allowing NMR optimizations to be run without direct user supervision. We predict that POISE will find widespread usage in academia and industry, where sample-specific and automated experiment optimization is mandatory.

Structural Refinement of Carbimazole by NMR Crystallography

The characterization of the three-dimensional structure of solids is of major importance, especially in the pharmaceutical field. In the present work, NMR crystallography methods are applied with the aim to refine the crystal structure of carbimazole, an active pharmaceutical ingredient used for the treatment of hyperthyroidism and Grave’s disease. Starting from previously reported X-ray diffraction data, two refined structures were obtained by geometry optimization methods. Experimental ¹H and ¹³C isotropic chemical shift measured by the suitable ¹H and ¹³C high-resolution solid state NMR techniques were compared with DFT-GIPAW calculated values, allowing the quality of the obtained structure to be experimentally checked. The refined structure was further validated through the analysis of ¹H-¹H and ¹H-¹³C 2D NMR correlation experiments. The final structure differs from that previously obtained from X-ray diffraction data mostly for the position of hydrogen atoms.

Fast remote correlation experiments for 1H homonuclear decoupling in solids

In ¹H MAS spectra, the residual homogeneous broadening under MAS is due to a combination of higher-order shifts and splittings. We have recently shown how the two-dimensional anti-z-COSY experiment can be used for the removal of the splittings. However, this requires spectra with high resolution in the indirect dimension (t₁), leading to experiment times of hours. Here, we show how anti-z-COSY can be adapted to be combined with the two-dimensional one pulse (TOP) transformation which leads to significantly reduced experimental time while retaining the line narrowing effect. The experiment is demonstrated on a powdered sample of L-histidine monohydrochloride monohydrate, where the new TAZ-COSY sequence at 100 kHz MAS, yields between a factor 1.6 and 2.3 increase in resolution compared with the equivalent one-pulse experiment, in just 20 min. The same methodology is also adapted for the acquisition of liquid state ¹H homodecoupled data, and an example is given for testosterone.

Homonuclear Decoupling in 1 H NMR of Solids by Remote Correlation

The typical linewidths of ¹H NMR spectra of powdered organic solids at 111 kHz magic‐angle spinning (MAS) are of the order of a few hundred Hz. While this is remarkable in comparison to the tens of kHz observed in spectra of static samples, it is still the key limit to the use of ¹H in solid‐state NMR, especially for complex systems. Here, we demonstrate a novel strategy to further improve the spectral resolution. We show that the anti‐z‐COSY experiment can be used to reduce the residual line broadening of ¹H NMR spectra of powdered organic solids. Results obtained with the anti‐z‐COSY sequence at 100 kHz MAS on thymol, β‐AspAla, and strychnine show an improvement in resolution of up to a factor of two compared to conventional spectra acquired at the same spinning rate.

High-resolution 1H NMR of powdered solids by homonuclear dipolar decoupling

The development of homonuclear dipolar decoupling sequences to obtain high-resolution ¹H NMR spectra from solids has recently celebrated its 50th birthday. Over the years, a series of different decoupling schemes have been developed, starting with the pioneering Lee-Goldburg and WAHUHA sequences up to the most recent generation of experimentally optimized phase-modulated schemes such as eDUMBO-1₂₂ and LG4. These schemes can all yield over an order of magnitude reduction in ¹H NMR linewidths in solids. Here we provide an overview and a broad experimental comparison of the performance of the main sequences, which has so far been absent in the literature, especially between the newest and the oldest decoupling schemes. We compare experimental results obtained using eight different decoupling schemes (LG, WHH-4, MREV-8, BR-24, FSLG/PMLG, DUMBO-1, eDUMBO-1₂₂ and LG4) on three different microcrystalline powdered samples (alanine, glycine and β-AspAla) and at three different MAS rates (3.0, 12.5 and 22.0 kHz). Finally, since these sequences can be technically demanding, we describe the experimental protocol we have used to optimize these schemes with the aim to provide simple guidelines for the optimization of CRAMPS experiments for all NMR users.

Line narrowing in 1H NMR of powdered organic solids with TOP-CT-MAS experiments at ultra-fast MAS

The residual broadening observed in ¹H spectra of rigid organic solids at natural abundance under 111 kHz magic angle spinning (MAS) is typically a few hundred Hertz. Here we show that refocusable and non-refocusable interactions contribute roughly equally to this residual at high-fields (21.14 T), and suggest that the removal of the non-refocusable part will produce significant increase in spectral resolution. To this end, we demonstrate an experiment for the indirect acquisition of constant-time experiments at ultra-fast MAS (CT-MAS) which verifies this hypothesis. The combination of this experiment with the two-dimensional one pulse (TOP) transformation reduces the experimental time to a fraction of the original cost while retaining the narrowing effects. Results obtained with TOP-CT-MAS at 111 kHz MAS on a sample of β-AspAla yield up to 30% higher resolution spectra than the equivalent one-pulse experiment, in less than 10 min.

Refocused linewidths less than 10 Hz in 1H solid-state NMR

Coherence lifetimes in homonuclear dipolar decoupled ¹H solid-state NMR experiments are usually on the order of a few ms. We discover an oscillation that limits the lifetime of the coherences by recording spin-echo dephasing curves. We find that this oscillation can be removed by the application of a double spin-echo experiment, leading to coherence lifetimes of more than 45 ms in adamantane and more that 22 ms in β-AspAla, corresponding to refocused linewidths of less than 7 and 14 Hz respectively.

1H line width dependence on MAS speed in solid state NMR - Comparison of experiment and simulation

Recent developments in magic angle spinning (MAS) technology permit spinning frequencies of ≥100 kHz. We examine the effect of such fast MAS rates upon nuclear magnetic resonance proton line widths in the multi-spin system of β-Asp-Ala crystal. We perform powder pattern simulations employing Fokker-Plank approach with periodic boundary conditions and ¹H-chemical shift tensors calculated using the bond polarization theory. The theoretical predictions mirror well the experimental results. Both approaches demonstrate that homogeneous broadening has a linear-quadratic dependency on the inverse of the MAS spinning frequency and that, at the faster end of the spinning frequencies, the residual spectral line broadening becomes dominated by chemical shift distributions and susceptibility effects even for crystalline systems.

Minimizing the t1-noise when using an indirect 1H high-resolution detection of unlabeled samples

The most utilized through-space correlation ¹H-{X} methods with proton indirect detection use two consecutive transfers, ¹H → X and then X → ¹H, with the evolution time t₁ in the middle. When the X isotope is not 100% naturally abundant (NA), only the signal of the protons close to these isotopes is modulated by the ¹H-X dipolar interactions. This signal is theoretically disentangled with phase-cycling from the un-modulated one. However, this separation is never perfect and it may lead to t₁-noise in case of isotopes with very small NA, such as ¹³C or even worse ¹⁵N. One way to reduce this t₁-noise is to minimize, 'purge', during t₁ the un-modulated ¹H magnetization before trying to suppress it with phase-cycling. We analyze experimentally several sequences following the HORROR condition, which allow purging the ¹H transverse magnetization. The comparison is made at three spinning speeds, including very fast ones for ¹H resolution: 27.75, 55.5 and 111 kHz. We show (i) that the efficiency of this purging process increases with the spinning speed, and (ii) that the best recoupling sequences are the two simplest ones: XY and S₁ = SR2¹₂. We then compare the S/N that can be achieved with the two most used ¹H-{X} 2D methods, called D-HMQC and CP-CP. The only difference in between these two methods is that the transfers are done with either two π/2-pulses on X channel (D-HMQC), or two Cross-Polarization (CP) transfers (CP-CP). The first method, D-HMQC, is very robust and should be preferred when indirectly detecting nuclei with high NA. The second method, CP-CP, (i) requires experimental precautions to limit the t₁-noise, and (ii) is difficult to use with quadrupolar nuclei because the two CP transfers are then not efficient nor robust. However, CP-CP is presently the best method to indirectly detect isotopes with small NA, such as ¹³C and ¹⁵N.

Five decades of homonuclear dipolar decoupling in solid-state NMR: Status and outlook

It has been slightly more than fifty years since the first homonuclear spin decoupling scheme, Lee-Goldburg decoupling, was proposed for removing homonuclear dipolar interactions in solid-state nuclear magnetic resonance. A family of such schemes has made observation of high-resolution NMR spectra of abundant spins possible in various applications in solid state. This review outlines the strategies used in this field and the future prospects of homonuclear spin decoupling in solid-state NMR.

High resolution triple resonance micro magic angle spinning NMR spectroscopy of nanoliter sample volumes

To be able to study mass-limited samples and small single crystals, a triple resonance micro-magic angle spinning (μMAS) probehead for the application of high-resolution solid-state NMR of nanoliter samples was developed. Due to its excellent rf performance this allows us to explore the limits of proton NMR resolution in strongly coupled solids. Using homonuclear decoupling we obtain unprecedented (1)H linewidths for a single crystal of glycine (Δν(CH2) = 0.14 ppm) at high field (20 T) in a directly detected spectrum. The triple channel design allowed the recording of high-resolution μMAS (13)C-(15)N correlations of [U-(13)C-(15)N] arginine HCl and shows that the superior (1)H resolution opens the way for high-sensitivity inverse detection of heteronuclei even at moderate spinning speeds and rf-fields. Efficient decoupling leads to long coherence times which can be exploited in many correlation experiments.

Minimizing the effects of RF inhomogeneity and phase transients allows resolution of two peaks in the (1)H CRAMPS NMR spectrum of adamantane

One of the limiting factors to achieving highly resolved (1)H NMR spectra with (1)H homonuclear decoupling sequences is imperfections in the applied radiofrequency (RF) pulses, most notably phase transients and RF inhomogeneity. Through a series of simulations and solid-state NMR experiments, it is demonstrated that the combined effects of phase transients and RF inhomogeneity can be minimized by a combination of (i) restricting the sample to small volume of the rotor, (ii) by employing a super-cycled version of the DUMBO decoupling sequence, and (iii) by carefully adjusting the probe tuning such that the asymmetric component of phase transients is minimized. Under these optimal conditions, it was possible to clearly resolve two signals in the (1)H CRAMPS NMR spectrum of adamantane arising from the CH and CH2 protons in the molecule. It is proposed that adamantane could be a very useful setup sample for (1)H CRAMPS NMR as the two peaks are only resolved when the effects of RF inhomogeneity and phase transients are minimized.

Selective excitation enables assignment of proton resonances and (1)H-(1)H distance measurement in ultrafast magic angle spinning solid state NMR spectroscopy

Remarkable developments in ultrafast magic angle spinning (MAS) solid-state NMR spectroscopy enabled proton-based high-resolution multidimensional experiments on solids. To fully utilize the benefits rendered by proton-based ultrafast MAS experiments, assignment of (1)H resonances becomes absolutely necessary. Herein, we propose an approach to identify different proton peaks by using dipolar-coupled heteronuclei such as (13)C or (15)N. In this method, after the initial preparation of proton magnetization and cross-polarization to (13)C nuclei, transverse magnetization of desired (13)C nuclei is selectively prepared by using DANTE (Delays Alternating with Nutations for Tailored Excitation) sequence and then, it is transferred to bonded protons with a short-contact-time cross polarization. Our experimental results demonstrate that protons bonded to specific (13)C atoms can be identified and overlapping proton peaks can also be assigned. In contrast to the regular 2D HETCOR experiment, only a few 1D experiments are required for the complete assignment of peaks in the proton spectrum. Furthermore, the finite-pulse radio frequency driven recoupling sequence could be incorporated right after the selection of specific proton signals to monitor the intensity buildup for other proton signals. This enables the extraction of (1)H-(1)H distances between different pairs of protons. Therefore, we believe that the proposed method will greatly aid in fast assignment of peaks in proton spectra and will be useful in the development of proton-based multi-dimensional solid-state NMR experiments to study atomic-level resolution structure and dynamics of solids.

Improving the resolution in proton-detected through-space heteronuclear multiple quantum correlation NMR spectroscopy

Connectivities and proximities between protons and low-gamma nuclei can be probed in solid-state NMR spectroscopy using two-dimensional (2D) proton-detected heteronuclear correlation, through Heteronuclear Multiple Quantum Correlation (HMQC) pulse sequence. The indirect detection via protons dramatically enhances the sensitivity. However, the spectra are often broadened along the indirect F1 dimension by the decay of heteronuclear multiple-quantum coherences under the strong (1)H-(1)H dipolar couplings. This work presents a systematic comparison of the performances of various decoupling schemes during the indirect t1 evolution period of dipolar-mediated HMQC (D-HMQC) experiment. We demonstrate that (1)H-(1)H dipolar decoupling sequences during t1, such as symmetry-based schemes, phase-modulated Lee-Goldburg (PMLG) and Decoupling Using Mind-Boggling Optimization (DUMBO), provide better resolution than continuous wave (1)H irradiation. We also report that high resolution requires the preservation of (1)H isotropic chemical shifts during the decoupling sequences. When observing indirectly broad spectra presenting numerous spinning sidebands, the D-HMQC sequence must be fully rotor-synchronized owing to the rotor-synchronized indirect sampling and dipolar recoupling sequence employed. In this case, we propose a solution to reduce artefact sidebands caused by the modulation of window delays before and after the decoupling application during the t1 period. Moreover, we show that (1)H-(1)H dipolar decoupling sequence using Smooth Amplitude Modulation (SAM) minimizes the t1-noise. The performances of the various decoupling schemes are assessed via numerical simulations and compared to 2D (1)H-{(13)C} D-HMQC experiments on [U-(13)C]-L-histidine⋅HCl⋅H2O at various magnetic fields and Magic Angle spinning (MAS) frequencies. Great resolution and sensitivity enhancements resulting from decoupling during t1 period enable the detection of heteronuclear correlation between aliphatic protons and ammonium (14)N sites in L-histidine⋅HCl⋅H2O.

Detailed analysis of the TIMES and TIMES0 high-resolution MAS methods for high-resolution proton NMR

We analyze and compare the specifications of TIMES and TIMES(0) proton high-resolution NMR methods for solid-state samples. This comparison is performed in terms of resolution versus magic-angle spinning (MAS) spinning speed, ν(R), rf-field amplitude, ν(1), and tilt-angle for the effective rf-field, θ(p). The chemical-shift and homo-nuclear dipolar scaling factors are calculated for both methods. For all MAS speeds, the best resolution is always observed with rf-field of ν(1)≈120-130 kHz. At slow MAS speed (ν(R)≤10 kHz), the best resolution is observed for a tilt-angle of θ(P)≈90°. At moderate spinning speed (15≤ν(R)≤35 kHz), θ(P)≈55° gives the best resolution. At higher MAS speed (ν(R)≥60 kHz), with TIMES and TIMES(0) the best resolution is obtained for θ(P)≤40°; but we then recommend TIMES(0), owing to its simpler set-up. We also show that in addition to the usual high rf-field regime (ν(1)≈120-130 kHz), another low rf-regime (ν(1)≈40-50 kHz) exists at MAS speed higher than ν(R)≥60 kHz, which also gives a good (1)H resolution. This low rf-regime should be useful for multi-dimensional analyses of bio-molecules with (1)H detection under high-resolution, in order to limit the heating of the sample.

Improved 1H amide resonance line narrowing in oriented sample solid-state NMR of membrane proteins in phospholipid bilayers

We demonstrate (1)H amide resonance line widths <300 Hz in (1)H/(15)N heteronuclear correlation (HETCOR) spectra of membrane proteins in aligned phospholipid bilayers. This represents a substantial improvement over typically observed line widths of ∼1 kHz. Furthermore, in a proton detected local field (PDLF) version of the experiment that measures heteronuclear dipolar couplings, line widths <130 Hz are observed. This dramatic line narrowing of (1)H amide resonances enables many more individual signals to be resolved and assigned from uniformly (15)N labeled membrane proteins in phospholipid bilayers under physiological conditions of temperature and pH. Finding that the decrease in line widths occurs only for membrane proteins that undergo fast rotational diffusion around the bilayer normal, but not immobile molecules, such as peptide single crystals, identifies a potential new direction for pulse sequence development that includes overall molecular dynamics in their design.

Practical choice of ¹H-¹H decoupling schemes in through-bond ¹H-{X} HMQC experiments at ultra-fast MAS

Three (1)H-(1)H homonuclear dipolar decoupling schemes for (1)H indirect detection measurements at very fast MAS are compared. The sequences require the following conditions: (i) being operable at very fast MAS, (ii) a long T(2)(') value, (iii) a large scaling factor, (iv) a small number of adjustable parameters, (v) an acquisition window, (vi) a low rf-power requirement, and (vii) a z-rotation feature. To satisfy these conditions a modified sequence named TIlted Magic-Echo Sandwich with zero degree sandwich pulse (TIMES(0)) is introduced. The basic elements of TIMES(0) consist of one sampling window and two phase-ramped irradiations, which realize alternating positive and negative 360° rotations of (1)H magnetization around an effective field tilted with an angle θ from the B(0) axis. The TIMES(0) sequence benefits from very large chemical shift scaling factors at ultra-fast MAS that reach κ(cs)=0.90 for θ=25° at ν(r)=80kHz MAS and only four adjustable parameters, resulting in easy setup. Long κ(cs)T(2)(') values, where T(2)(') is a irreversible proton transverse relaxation time, greatly enhance the sensitivity in (1)H-{(13)C} through-bond J-HMQC (Heteronuclear Multiple-Quantum Coherence) measurements with (1)H-(1)H decoupling during magnetization transfer periods. Although similar sensitivity can be obtained with through-space D-HMQC sequences, in which (13)C-(1)H dipolar interactions are recoupled, J-HMQC experiments incorporating (1)H-(1)H decoupling benefit from lower t(1)-noise, more uniform excitation of both CH, CH(2) and CH(3) moieties, and easier identification of through-bond connectivities.

Progress in correlation spectroscopy at ultra-fast magic-angle spinning: basic building blocks and complex experiments for the study of protein structure and dynamics

Recent progress in multi-dimensional solid-state NMR correlation spectroscopy at high static magnetic fields and ultra-fast magic-angle spinning is discussed. A focus of the review is on applications to protein resonance assignment and structure determination as well as on the characterization of protein dynamics in the solid state. First, the consequences of ultra-fast spinning on sensitivity and sample heating are considered. Recoupling and decoupling techniques at ultra-fast MAS are then presented, as well as more complex experiments assembled from these basic building blocks. Furthermore, we discuss new avenues in biomolecular solid-state NMR spectroscopy that become feasible in the ultra-fast spinning regime, such as sensitivity enhancement based on paramagnetic doping, and the prospect of direct proton detection.

A scaling factor theorem for homonuclear dipolar decoupling in solid-state NMR spectroscopy

A relationship between the dipolar and the chemical-shift scaling factors of cyclic radio-frequency irradiation schemes is introduced. This scaling factor theorem is derived analytically using Average Hamiltonian Theory, and its validity is illustrated numerically with homonuclear dipolar decoupling sequences generated randomly, and with the analysis of existing sequences. While derived for a static sample, the theorem provides insight into homonuclear dipolar decoupling schemes that combine radio-frequency irradiation with fast rotation of the sample at the magic-angle with respect to the static magnetic field.