Homonuclear dipolar recoupling under ultra-fast magic-angle spinning: probing 19F-19F proximities by solid-state NMR

Solid-State NMR Double-Quantum Dipolar Recoupling Enhanced by Additional Phase Modulation

Additional phase modulation (APM) is proposed to generally enhance the theoretical efficiency of homonuclear double-quantum (DQ) recoupling in solid-state NMR. APM applies an additional phase list to DQ recoupling in steps of an entire block. The sine-based phase list can enhance the theoretical efficiency by 15-30 %, from 0.52 to 0.68 (non-γ-encoded recoupling) or from 0.73 to 0.84 (γ-encoded recoupling), with doubled recoupling time. The genetic-algorithm (GA) optimized APM can adiabatically enhance the efficiency to ∼1.0 at longer times. The concept of APM has been tested on SPR-51 , BaBa, and SPR-31 , which represent γ-encoded recoupling, non-γ-encoded recoupling, and another kind beyond the former two, respectively. Simulations reveal that enhancements from APM are due to the activation of more crystallites in the powder. Experiments on 2,3-13 C labeled alanine are used to validate the APM recoupling. This new concept shall shed light on developing more efficient homonuclear recoupling methods.

Comparison of through-space homonuclear correlations between quadrupolar nuclei in solids

Various two-dimensional (2D) homonuclear correlation experiments have been proposed to observe proximities between identical half-integer spin quadrupolar nuclei in solids. These experiments select either the single- or double-quantum coherences during the indirect evolution period, t₁. We compare here the efficiency and the robustness of the 2D double-quantum to single-quantum (DQ-SQ) and SQ-SQ homonuclear correlations for two half-integer spin quadrupolar isotopes subject to small chemical shift anisotropy (CSA): ¹¹B with a nuclear spin I = 3/2 and ²⁷Al with I = 5/2. Such a comparison is performed using experiments on two model samples: Li₂B₄O₇ for ¹¹B and AlPO₄-14 for ²⁷Al. For both isotopes, the DQ-SQ homonuclear correlations are recommended since they allow probing the proximities between nuclei with close or identical frequencies. In the case of small or moderate isotropic chemical shift differences (e.g. ¹¹B) the [SR2₂¹] or [BR2₂¹] bracketed DQ-SQ recoupling schemes are recommended; whereas it is the BR2₂¹ un-bracketed one otherwise (e.g. ²⁷Al).

Theory of frequency-selective homonuclear dipolar recoupling in solid-state NMR

In solid-state nuclear magnetic resonance, frequency-selective homonuclear dipolar recoupling is key to quantitative distance measurement or selective enhancement of correlations between atoms of interest in multiple-spin systems, which are not amenable to band-selective or broadband recoupling. Previous frequency-selective recoupling is mostly based on the so-called rotational resonance (R²) condition that restricts the application to spin pairs with resonance frequencies differing in integral multiples of the magic-angle spinning (MAS) frequency. Recently, we have proposed a series of frequency-selective homonuclear recoupling sequences called SPR (short for Selective Phase-optimized Recoupling), which have been successfully applied for selective ¹H-¹H or ¹³C-¹³C recoupling under from moderate (∼10 kHz) to ultra-fast (150 kHz) MAS frequencies. In this study, we fully analyze the average Hamiltonian theory of SPR sequences and reveal the origin of frequency selectivity in recoupling. The theoretical description, as well as numerical simulations and experiments, demonstrates that the frequency selectivity can be easily controlled by the flip angle (p) in the (p)_ϕk(p)_ϕk+π unit in the pSPR-N_n sequences. Small flip angles lead to frequency-selective recoupling, while large flip angles may lead to broadband recoupling in principle. The result shall shed new light on the design of homonuclear recoupling sequences with arbitrary frequency bandwidths.

On the use of radio-frequency offsets for improving double-quantum homonuclear dipolar recoupling of half-integer-spin quadrupolar nuclei

Detecting proximities between nuclei is crucial for atomic-scale structure determination with nuclear magnetic resonance (NMR) spectroscopy. Different from spin-1/2 nuclei, the methodology for quadrupolar nuclei is limited for solids due to the complex spin dynamics under simultaneous magic-angle spinning (MAS) and radio-frequency irradiation. Herein, the performances of several homonuclear rotary recoupling (HORROR)-based homonuclear dipolar recoupling sequences are evaluated for ²⁷ Al (spin-5/2). It is shown numerically and experimentally on mesoporous alumina that BR 2 2 1 outperforms the supercycled S₃ sequence and its pure double-quantum (DQ) (bracketed) version, [S₃ ], both in terms of DQ transfer efficiency and bandwidth. This result is surprising since the S₃ sequence is among the best low-power recoupling schemes for spin-1/2. The superiority of BR 2 2 1 is thoroughly explained, and the crucial role of radio-frequency offsets during its spin dynamics is highlighted. The analytical approximation of BR 2 2 1 , derived in an offset-toggling frame, clarifies the interplay between offset and DQ efficiency, namely, the benefits of off-resonance irradiation and the trough in DQ efficiency for BR 2 2 1 when the irradiation is central between two resonances, both for spin-1/2 and half-integer-spin quadrupolar nuclei. Additionally, density matrix propagations show that the BR 2 2 1 sequence, applied to quadrupolar nuclei subject to quadrupolar interaction much larger than radio-frequency frequency field, can create single- and multiple-quantum coherences for near on-resonance irradiation. This significantly perturbs the creation of DQ coherences between central transitions of neighboring quadrupolar nuclei. This effect explains the DQ efficiency trough for near on-resonance irradiation, in the case of both cross-correlation and autocorrelation peaks. Overall, this work aids experimental acquisition of homonuclear dipolar correlation spectra of half-integer-spin quadrupolar nuclei and provides theoretical insights towards improving recoupling schemes at high magnetic field and fast MAS.

Efficient symmetry-based γ-encoded DQ recoupling sequences for suppression of t1-noise in solid-state NMR spectroscopy at fast MAS

Solid-state NMR spectroscopy has played a significant role in elucidating the structure and dynamics of materials and biological solids at a molecular level for decades. In particular, the ¹H double-quantum/single-quantum (DQ/SQ) chemical shift correlation experiment is widely used for probing the proximity of protons, rendering it a powerful tool for elucidating the hydrogen-bonding interactions and molecular packing of various complex molecular systems. Two factors, namely, the DQ filtering efficiency and t₁-noise, dictate the quality of the 2D ¹H DQ/SQ spectra. Experimentally different recoupling sequences show varied DQ filtering efficiencies and t₁-noise. Herein, after a systematic search of symmetry-based DQ recoupling sequences, we report that the symmetry-based γ-encoded RN_n^ν sequences show superior performance to other DQ recoupling sequences, which not only have a higher DQ recoupling efficiency but can also significantly reduce t₁-noise. The origin of t₁-noise is further discussed in detail via extensive numerical simulations. We envisage that such γ-encoded RN_n^ν sequences are superior candidates for DQ recoupling in proton-based solid-state NMR spectroscopy due to its capability of efficiently exciting DQ coherences and suppressing t₁-noise.

Optimization of band-selective homonuclear dipolar recoupling in solid-state NMR by a numerical phase search

Spin polarization transfers among aliphatic ¹³C nuclei, especially ¹³Cα-¹³Cβ transfers, permit correlations of their nuclear magnetic resonance (NMR) frequencies that are essential for signal assignments in multidimensional solid-state NMR of proteins. We derive and demonstrate a new radio-frequency (RF) excitation sequence for homonuclear dipolar recoupling that enhances spin polarization transfers among aliphatic ¹³C nuclei at moderate magic-angle spinning (MAS) frequencies. The phase-optimized recoupling sequence with five π pulses per MAS rotation period (denoted as PR5) is derived initially from systematic numerical simulations in which only the RF phases are varied. Subsequent theoretical analysis by average Hamiltonian theory explains the favorable properties of numerically optimized phase schemes. The high efficiency of spin polarization transfers in simulations is preserved in experiments, in part because the RF field amplitude in PR5 is only 2.5 times the MAS frequency so that relatively low ¹H decoupling powers are required. Experiments on a microcrystalline sample of the β1 immunoglobulin binding domain of protein G demonstrate an average enhancement factor of 1.6 for ¹³Cα → ¹³Cβ polarization transfers, compared to the standard ¹³C-¹³C spin-diffusion method, implying a two-fold time saving in relevant 2D and 3D experiments.

Determination of Long-Range Distances by Fast Magic-Angle-Spinning Radiofrequency-Driven 19F-19F Dipolar Recoupling NMR

Nanometer-range distances are important for restraining the three-dimensional structure and oligomeric assembly of proteins and other biological molecules. Solid-state NMR determination of protein structures typically utilizes ¹³C-¹³C and ¹³C-¹⁵N distance restraints, which can only be measured up to ∼7 Å because of the low gyromagnetic ratios of these nuclear spins. To extend the distance reach of NMR, one can harvest the power of ¹⁹F, whose large gyromagnetic ratio in principle allows distances up to 2 nm to be measured. However, ¹⁹F possesses large chemical shift anisotropies (CSAs) as well as large isotropic chemical shift dispersions, which pose challenges to dipolar coupling measurements. Here, we demonstrate ¹⁹F-¹⁹F distance measurements at high magnetic fields under fast magic-angle spinning (MAS) using radiofrequency-driven dipolar recoupling (RFDR). We show that ¹⁹F-¹⁹F cross-peaks for distances up to 1 nm can be readily observed in two-dimensional ¹⁹F-¹⁹F correlation spectra using less than 5 ms of RFDR mixing. This efficient ¹⁹F-¹⁹F dipolar recoupling is achieved using practically accessible MAS frequencies of 15-55 kHz, moderate ¹⁹F radio frequency field strengths, and no ¹H decoupling. Experiments and simulations show that the fastest polarization transfer for aromatic fluorines with the highest distance accuracy is achieved using either fast MAS (e.g., 60 kHz) with large pulse duty cycles (>50%) or slow MAS with strong ¹⁹F pulses. Fast MAS considerably reduces relaxation losses during the RFDR π-pulse train, making finite-pulse RFDR under fast-MAS the method of choice. Under intermediate MAS frequencies (25-40 kHz) and intermediate pulse duty cycles (15-30%), the ¹⁹F CSA tensor orientation has a quantifiable effect on the polarization transfer rate; thus, the RFDR buildup curves encode both distance and orientation information. At fast MAS, the impact of CSA orientation is minimized, allowing pure distance restraints to be extracted. We further investigate how relayed transfer and dipolar truncation in multifluorine environments affect polarization transfer. This fast-MAS ¹⁹F RFDR approach is complementary to ¹⁹F spin diffusion for distance measurements and will be the method of choice under high-field fast-MAS conditions that are increasingly important for protein structure determination by solid-state NMR.

Fast Magic-Angle-Spinning 19F Spin Exchange NMR for Determining Nanometer 19F-19F Distances in Proteins and Pharmaceutical Compounds

Internuclear distances measured using NMR provide crucial constraints of three-dimensional structures but are often restricted to about 5 Å due to the weakness of nuclear-spin dipolar couplings. For studying macromolecular assemblies in biology and materials science, distance constraints beyond 1 nm will be extremely valuable. Here we present an extensive and quantitative analysis of the feasibility of 19F spin exchange NMR for precise and robust measurements of interatomic distances up to 1.6 nm at a magnetic field of 14.1 T, under 20-40 kHz magic-angle spinning (MAS). The measured distances are comparable to those achievable from paramagnetic relaxation enhancement but have higher precision, which is better than ±1 Å for short distances and ±2 Å for long distances. For 19F spins with the same isotropic chemical shift but different anisotropic chemical shifts, intermediate MAS frequencies of 15-25 kHz without 1H irradiation accelerate spin exchange. For spectrally resolved 19F-19F spin exchange, 1H-19F dipolar recoupling significantly speeds up 19F-19F spin exchange. On the basis of data from five fluorinated synthetic, pharmaceutical, and biological compounds, we obtained two general curves for spin exchange between CF groups and between CF3 and CF groups. These curves allow 19F-19F distances to be extracted from the measured spin exchange rates after taking into account 19F chemical shifts. These results demonstrate the robustness of 19F spin exchange NMR for distance measurements in a wide range of biological and chemical systems.

Revealing the Local Proton Network through Three-Dimensional 13C/1H Double-Quantum/1H Single-Quantum and 1H Double-Quantum/13C/1H Single-Quantum Correlation Fast Magic-Angle Spinning Solid-State NMR Spectroscopy at Natural Abundance

¹H double quantum (DQ)/¹H single quantum (SQ) correlation solid-state NMR spectroscopy is widely used to obtain internuclear ¹H-¹H proximities, especially at fast magic-angle spinning (MAS) rate (>60 kHz). However, to date, ¹H signals are not well-resolved because of intense ¹H-¹H homonuclear dipolar interactions even at the attainable maximum MAS frequencies of ∼100 kHz and/or under ¹H-¹H homonuclear dipolar decoupling irradiations. Here we introduce novel three-dimensional (3D) experiments to resolve the ¹H DQ/¹H SQ correlation peaks using the additional ¹³C dimension. Although the low natural abundance of ¹³C (1.1%) significantly reduces the sensitivities, the ¹H indirect measurements alleviate this issue and make this experiment possible even in naturally abundant samples. The two different implementations of ¹³C/¹H DQ/¹H SQ correlations and ¹H DQ/¹³C/¹H SQ correlations are discussed and demonstrated using l-histidine·HCl·H₂O at natural abundance to reveal the local ¹H-¹H networks near each ¹³C. In addition, the complete ¹H resonance assignments are achieved from a single 3D ¹³C/¹H DQ/¹H SQ experiment. We have also demonstrated the applicability of our proposed method on a biologically relevant molecule, capsaicin.

Composite pulses in directly and indirectly detected 14N MAS overtone spectroscopy

¹⁴N MAS overtone spectroscopy is mainly limited by narrow excitation bandwidths owing to the use of very long pulses to get stronger signals. We previously reported the use of modified 90° composite pulses for broadband excitation in ¹H-{NOTDQ14}D-HMQC experiments at ultra-fast MAS. In this work, we modified the 180° composite pulses, which are originally designed for spin 1/2 nuclei, for both indirect detection in ¹H-{NOTDQ14}D-HMQC experiment and direct detection in one-pulse experiment, and found that the modified 180° composite pulses are useful for broadband excitation. Furthermore, we found that the bandwidth can be tailored by simply adjusting the total pulse length.

Fast magic-angle sample spinning solid-state NMR at 60-100kHz for natural abundance samples

In spite of tremendous progress made in pulse sequence designs and sophisticated hardware developments, methods to improve sensitivity and resolution in solid-state NMR (ssNMR) are still emerging. The rate at which sample is spun at magic angle determines the extent to which sensitivity and resolution of NMR spectra are improved. To this end, the prime objective of this article is to give a comprehensive theoretical and experimental framework of fast magic angle spinning (MAS) technique. The engineering design of fast MAS rotors based on spinning rate, sample volume, and sensitivity is presented in detail. Besides, the benefits of fast MAS citing the recent progress in methodology, especially for natural abundance samples are also highlighted. The effect of the MAS rate on (1)H resolution, which is a key to the success of the (1)H inverse detection methods, is described by a simple mathematical factor named as the homogeneity factor k. A comparison between various (1)H inverse detection methods is also presented. Moreover, methods to reduce the number of spinning sidebands (SSBs) for the systems with huge anisotropies in combination with (1)H inverse detection at fast MAS are discussed.

Structure determination of Ba5AlF13 by coupling electron, synchrotron and neutron powder diffraction, solid-state NMR and ab initio calculations

The structure and dynamics of Ba₅AlF₁₃ are resolved by combining complementary information from powder diffraction, ²⁷Al and ¹⁹F ultra-fast MAS NMR and DFT calculations.

Observation of 1H-13C and 1H-1H proximities in a paramagnetic solid by NMR at high magnetic field under ultra-fast MAS

The assignment of NMR signals in paramagnetic solids is often challenging since: (i) the large paramagnetic shifts often mask the diamagnetic shifts specific to the local chemical environment, and (ii) the hyperfine interactions with unpaired electrons broaden the NMR spectra and decrease the coherence lifetime, thus reducing the efficiency of usual homo- and hetero-nuclear NMR correlation experiments. Here we show that the assignment of (1)H and (13)C signals in isotopically unmodified paramagnetic compounds with moderate hyperfine interactions can be facilitated by the use of two two-dimensional (2D) experiments: (i) (1)H-(13)C correlations with (1)H detection and (ii) (1)H-(1)H double-quantum↔single-quantum correlations. These methods are experimentally demonstrated on isotopically unmodified copper (II) complex of l-alanine at high magnetic field (18.8 T) and ultra-fast Magic Angle Spinning (MAS) frequency of 62.5 kHz. Compared to (13)C detection, we show that (1)H detection leads to a 3-fold enhancement in sensitivity for (1)H-(13)C 2D correlation experiments. By combining (1)H-(13)C and (1)H-(1)H 2D correlation experiments with the analysis of (13)C longitudinal relaxation times, we have been able to assign the (1)H and (13)C signals of each l-alanine ligand.

Influence of proton coupling on symmetry-based homonuclear (19)F dipolar recoupling experiments

We study the efficiency of two symmetry based homonuclear (19)F double-quantum recoupling sequences for moderate (R142(6)) and ultra-fast (R144(5)) MAS under the influence of strong (1)H-(1)H and (1)H-(19)F dipolar interactions and (1)H continuous wave decoupling. Simulations based on various spin systems derived from the organic solid 1,3,5-tris(2-fluoro-2-methylpropionylamino)benzene (F-BTA), used as a model system, reveal that the strong-decoupling limit is not accessible even for moderate spinning speeds. Additionally, for the no-decoupling limit improved DQ efficiencies are predicted for both moderate and ultra-fast MAS. Strong perturbations of build-up curves can be avoided by additional stabilisation through supercycling. Additional (1)H cw decoupling during (19)F recoupling rapidly reduces the maximum DQ efficiency when deviating from the no-decoupling limit. These effects were confirmed by experimental data on F-BTA. For moderate spinning the influence of (1)H-(1)H and (1)H-(19)F couplings is markedly stronger compared to ultra-fast MAS. For the latter case those influences reduce to a constant scaling if only short excitation times up to the first minimum are taken into account. Based on this analysis the experimental build-up curves of 1,3,5-tris(2-fluoro-2-methylpropionylamino)benzene can be refined with homonuclear (19)F spin systems which allow to probe even subtle structural differences for the fluorine atoms of F-BTA.

Achieving high resolution dipolar NMR information without fast sample spinning: combining magic angle turning with dipolar based NMR methods

In this article we present a new approach to high resolution NMR combining the concepts of magic angle hopping (MAH)/magic angle turning (MAT) and dipolar based NMR methods such as SEDOR, REDOR or cross polarization (CP). Employing aluminophosphates as model systems we demonstrate that No MAS needed (NOMAS) is capable of supplying high resolution dipolar information without the need of fast MAS.

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.

BaBa-xy16: robust and broadband homonuclear DQ recoupling for applications in rigid and soft solids up to the highest MAS frequencies

We here present a substantially improved version of the popular Back-to-Back (BaBa) homonuclear double-quantum (DQ) MAS recoupling pulse sequence. By combining the original pulse sequence with a virtual π pulse train with xy-16 phase cycling along with time-reversed DQ reconversion, a truly broadband and exceptionally robust pulse sequence is obtained. The sequence has moderate radio-frequency power requirements, amounting to only one 360° nutation per rotor cycle, it is robust with respect to rf power and tune-up errors, and its broadband performance increases with increasing spinning frequency, here tested up to 63 kHz. The experiment can be applied to many spin-1/2 nuclei in rigid solids with substantial frequency offsets and CSAs, which is demonstrated on the example of 31P NMR of a magnesium ultraphosphate, comparing experimental data with multi-spin simulations, and we also show simulations addressing the performance in 13C NMR of bio(macro)molecules. 1H-based studies of polymer dynamics are highlighted for the example of a rigid solid with strongly anisotropic mobility, represented by a polymer inclusion compound, and for the example of soft materials with weak residual dipole-dipole couplings, represented by homogeneous and inhomogeneous elastomers. We advocate the use of normalized (relaxation-corrected) DQ build-up curves for a quantitative assessment of weak average dipole-dipole couplings and even distributions thereof.

Distance measurement between a spin-1/2 and a half-integer quadrupolar nuclei by solid-state NMR using exact analytical expressions

We show that the S-RESPDOR NMR method can be used to measure distances between spin-1/2 and half-integer quadrupolar nuclei, and that a general analytical formula describes its dephasing curve for all spin values. We demonstrate the method on the C4-O4 spin pair of L-tyrosine·HCl, with 13C natural abundance and 30% 17O enrichment, using a moderate magnetic field (9.4 T), a moderate 17O rf-field (40 kHz) and a fast spinning speed (22 kHz). It is shown that S-RESPDOR is much more robust and accurate than previous methods.