Computer-intensive simulation of solid-state NMR experiments using SIMPSON

Comparison of methods for the NMR measurement of motionally averaged dipolar couplings

Motionally averaged dipolar couplings are an important tool for understanding the complex dynamics of catalysts, polymers, and biomolecules. While there is a plethora of solid-state NMR pulse sequences available for their measurement, in can be difficult to gauge the methods' strengths and weaknesses. In particular, there has not been a comprehensive comparison of their performance in natural abundance samples, where 1H homonuclear dipolar couplings are important and the use of large MAS rotors may be required for sensitivity reasons. In this work, we directly compared some of the more common methods for measuring C-H dipolar couplings in natural abundance samples using L-alanine (L-Ala) and the N-formyl-L-methionyl-L-leucyl-L-phenylalanine (fMLF) tripeptide as model systems. We evaluated their performance in terms of accuracy, resolution, sensitivity, and ease of implementation. We found that, despite the presence of 1H homonuclear dipolar interactions, all methods, with the exception of REDOR, were able to yield the reasonable dipolar coupling strengths for both mobile and static moieties. Of these methods, PDLF provides the most convenient workflow and precision at the expense of low sensitivity. In low-sensitivity cases, MAS-PISEMA and DIPSHIFT appear to be the better options.

Simulating multipulse NMR spectra of polycrystalline solids in the frequency domain

An approach is presented for simulating multipulse nuclear magnetic resonance (NMR) spectra of polycrystalline solids directly in the frequency domain. The approach integrates the symmetry pathway concept for multipulse NMR with efficient algorithms for calculating spinning sideband amplitudes and performing interpolated finite-element numerical integration over all crystallite orientations in a polycrystalline sample. The numerical efficiency is achieved through a set of assumptions used to approximate the evolution of a sparse density matrix through a pulse sequence as a set of individual transition pathway signals. The utility of this approach for simulating the spectra of complex materials, such as glasses and other structurally disordered materials, is demonstrated.

Red Shift in the Absorption Spectrum of Phototropin LOV1 upon the Formation of a Semiquinone Radical: Reconstructing the Orbital Architecture

Flavin mononucleotide (FMN) is a ubiquitous blue-light pigment due to its ability to drive one- and two-electron transfer reactions. In both light-oxygen-voltage (LOV) domains of phototropin from the green algae Chlamydomonas reinhardtii, FMN is noncovalently bound. In the LOV1 cysteine-to-serine mutant (C57S), light-induced electron transfer from a nearby tryptophan occurs, and a transient spin-correlated radical pair (SCRP) is formed. Within this photocycle, nuclear hyperpolarization is created by the solid-state photochemically induced dynamic nuclear polarization (photo-CIDNP) effect. In a side reaction, a stable protonated semiquinone radical (FMNH·) forms undergoing a significant bathochromic shift of the first electronic transition from 445 to 591 nm. The incorporation of phototropin LOV1-C57S into an amorphous trehalose matrix, stabilizing the radical, allows for application of various magnetic resonance experiments at ambient temperatures, which are combined with quantum-chemical calculations. As a result, the bathochromic shift of the first absorption band is explained by lifting the degeneracy of the molecular orbital energy levels for electrons with alpha and beta spins in FMNH· due to the additional electron.

High-efficiency low-power 13C-15N cross polarization in MAS NMR

Biomolecular solid-state magic angle spinning (MAS) NMR spectroscopy frequently relies on selective 13C-15N magnetization transfers, for various kinds of correlation experiments. Introduced in 1998, spectrally induced filtering in combination with cross polarization (SPECIFIC-CP) is a selective heteronuclear magnetization transfer experiment widely used for biological applications. At MAS frequencies below 20 kHz, commonly used for 13C-detected MAS NMR experiments, SPECIFIC-CP transfer between amide 15N and 13Cα atoms (NCA) is typically performed with radiofrequency (rf) fields set higher than the MAS frequency for both 13C and 15N channels, and high-power 1H decoupling rf field is simultaneously applied. Here, we experimentally explore a broad range of NCA zero-quantum (ZQ) SPECIFIC-CP matching conditions at the MAS frequency of 14 kHz and compare the best high- and low-power matching conditions with respect to selectivity, robustness, and sensitivity at lower 1H decoupling rf fields. We show that low-power NCA SPECIFIC-CP matching condition gives rise to 20% sensitivity enhancement compared to high-power conditions, in 2D NCA spectra of microcrystalline assemblies of HIV-1 CACTD-SP1 protein with inositol hexakis-phosphate (IP6).

Accelerated acquisition of wideline solid-state NMR spectra of spin 3/2 nuclei by frequency-stepped indirect detection experiments

73% of all NMR-active nuclei are quadrupolar nuclei with a nuclear spin I > 1/2. The broadening of the solid-state NMR signals by the quadrupolar interaction often leads to poor sensitivity and low resolution. In this work we present experimental and theoretical investigations of magic angle spinning (MAS) 1H{X} double-echo resonance-echo saturation-pulse double-resonance (DE-RESPDOR) and Y{X} J-resolved solid-state NMR experiments for the indirect detection of spin 3/2 quadrupolar nuclei (X = spin 3/2 nuclei, Y = spin 1/2 nuclei). In these experiments, the spectrum of the quadrupolar nucleus is reconstructed by plotting the observed dephasing of the detected spin as a function of the transmitter offset of the indirectly detected spin. Numerical simulations were used to investigate the achievable levels of dephasing and to predict the lineshapes of indirectly detected NMR spectra of the quadrupolar nucleus. We demonstrate 1H, 31P and 207Pb detection of 35Cl, 81Br, and 63Cu (I = 3/2) nuclei in trans-Cl2Pt(NH3)2 (transplatin), (CH3NH3)PbCl3 (methylammonium lead chloride, MAPbCl3), (CH3NH3)PbBr3 (methylammonium lead bromide, MAPbBr3) and CH3C(CH2PPh2)3CuI (1,1,1-tris(diphenylphosphinomethyl)ethane copper(I) iodide, triphosCuI), respectively. In all of these experiments, we were able to detect megahertz wide central transition or satellite transition powder patterns. Significant time savings and gains in sensitivity were attained in several test cases. Additionally, the indirect detection experiments provide valuable structural information because they confirm the presence of dipolar or scalar couplings between the detected nucleus and the quadrupolar nucleus of interest. Finally, numerical simulations suggest these methods are also potentially applicable to abundant spin 5/2 and spin 7/2 quadrupolar nuclei.

Fluorinated Benzimidazole-Linked Highly Conjugated Polymer Enabling Covalent Polysulfide Anchoring for Stable Sulfur Batteries

Sulfur is one of the most abundant and economical elements in the p-block family and highly redox active, potentially utilizable as a charge-storing electrode with high theoretical capacities. However, its inherent good solubility in many electrolytes inhibits its accessibility as an electrode material in typical metal-sulfur batteries. In this work, the synthetically designed fluorinated porous polymer, when treated with elemental sulfur through a well-known nucleophilic aromatic substitution mechanism (SN Ar), allows for the covalent integration of polysulfides into a highly conjugated benzimidazole polymer by replacing the fluorine atoms. Chemically robust benzimidazole linkages allow such harsh post-synthetic treatment and facilitate the electronic activation of the anchored polysulfides for redox reactions under applied potential. The electrode amalgamated with sulfurized polymer mitigates the so-called polysulfide shuttle effect in the lithium-sulfur (Li-S) battery and also enables a reversible, more environmentally friendly, and more economical aluminum-sulfur (Al-S) battery that is configured with mostly p-block elements as cathode, anode, and electrolytes. The improved cycling stabilities and reduction of the overpotential in both cases pave the way for future sustainable energy storage solutions.

A facile approach for estimating radio-frequency field strength of low-receptivity nuclei

Radio-frequency (RF) field calibration is essential in NMR spectroscopy. A common practice is to collect a nutation curve by varying the pulse length in a direct single-pulse excitation experiment or in a cross-polarization magic-angle spinning with a flip-back pulse experiment. From the null points on this curve, one can calculate the RF field strength. Nevertheless, the practical implementation is not always straightforward or can even be unrealizable, especially for low-receptivity nuclei owing to their associated low sensitivity. Several researchers used an approach that involves utilizing other nuclei with more sensitivity but nearly identical Larmor frequencies to that of the nucleus of interest. However, such an approach has not been a common practice so far. In this work, we have systematically revisited this approach using 3.2 mm rotors on different sets of nuclei covering a Larmor frequency range up to 80 MHz. The effect of solid- and solution-states on RF field strength measurements has been investigated. The detection of each set of nuclei is then carried out with a resonant circuit in the NMR probe consisting of identical coils and capacitors. Our methodology is illustrated by recording 135/137Ba NMR spectra of BaTiO3 without prior 135/137Ba RF field calibration.

Hydrogen bonding in duplex DNA probed by DNP enhanced solid-state NMR N-H bond length measurements

Numerous biological processes and mechanisms depend on details of base pairing and hydrogen bonding in DNA. Hydrogen bonds are challenging to quantify by X-ray crystallography and cryo-EM due to difficulty of visualizing hydrogen atom locations but can be probed with site specificity by NMR spectroscopy in solution and the solid state with the latter particularly suited to large, slowly tumbling DNA complexes. Recently, we showed that low-temperature dynamic nuclear polarization (DNP) enhanced solid-state NMR is a valuable tool for distinguishing Hoogsteen base pairs (bps) from canonical Watson-Crick bps in various DNA systems under native-like conditions. Here, using a model 12-mer DNA duplex containing two central adenine-thymine (A-T) bps in either Watson-Crick or Hoogsteen confirmation, we demonstrate DNP solid-state NMR measurements of thymine N3-H3 bond lengths, which are sensitive to details of N-H···N hydrogen bonding and permit hydrogen bonds for the two bp conformers to be systematically compared within the same DNA sequence context. For this DNA duplex, effectively identical TN3-H3 bond lengths of 1.055 ± 0.011 Å and 1.060 ± 0.011 Å were found for Watson-Crick A-T and Hoogsteen A (syn)-T base pairs, respectively, relative to a reference amide bond length of 1.015 ± 0.010 Å determined for N-acetyl-valine under comparable experimental conditions. Considering that prior quantum chemical calculations which account for zero-point motions predict a somewhat longer effective peptide N-H bond length of 1.041 Å, in agreement with solution and solid-state NMR studies of peptides and proteins at ambient temperature, to facilitate direct comparisons with these earlier studies TN3-H3 bond lengths for the DNA samples can be readily scaled appropriately to yield 1.083 Å and 1.087 Å for Watson-Crick A-T and Hoogsteen A (syn)-T bps, respectively, relative to the 1.041 Å reference peptide N-H bond length. Remarkably, in the context of the model DNA duplex, these results indicate that there are no significant differences in N-H···N A-T hydrogen bonds between Watson-Crick and Hoogsteen bp conformers. More generally, high precision measurements of N-H bond lengths by low-temperature DNP solid-state NMR based methods are expected to facilitate detailed comparative analysis of hydrogen bonding for a range of DNA complexes and base pairing environments.

Regulating polystyrene glass transition temperature by varying the hydration levels of aromatic ring/Li+ interaction

Polymer properties can be altered via lithium ion doping, whereby adsorbed Li+ binds with H2O within the polymer chain. However, direct spectroscopic evidence of the tightness of Li+/H2O binding in the solid state is limited, and the impact of Li+ on polymer sidechain packing is rarely reported. Here, we investigate a polystyrene/H2O/LiCl system using solid-state NMR, from which we determined a dipolar coupling of 11.4 kHz between adsorbed Li+ and H2O protons. This coupling corroborates a model whereby Li+ interacts with the oxygen atom in H2O via charge affinity, which we believe is the main driving force of Li+ binding. We demonstrated the impact of hydrated Li+ on sidechain packing and dynamics in polystyrene using proton-detected solid-state NMR. Experimental data and density functional theory (DFT) simulations revealed that the addition of Li+ and the increase in the hydration levels of Li+, coupled with aromatic ring binding, change the energy barrier of sidechain packing and dynamics and, consequently, changes the glass transition temperature of polystyrene.

Performance of the cross-polarization experiment in conditions of radiofrequency field inhomogeneity and slow to ultrafast magic angle spinning (MAS)

In this paper, we provide an analytical description of the performance of the cross-polarization (CP) experiment, including linear ramps and adiabatic tangential sweeps, using effective Hamiltonians and simple rotations in 3D space. It is shown that radiofrequency field inhomogeneity induces a reduction in the transfer efficiency at increasing magic angle spinning (MAS) frequencies for both the ramp and the adiabatic CP experiments. The effect depends on the ratio of the dipolar coupling constant and the sample rotation frequency. In particular, our simulations show that for small dipolar couplings (1 kHz ) and ultrafast MAS (above 100 kHz ) the transfer efficiency is below 40 % when extended contact times up to 20 ms are used and relaxation losses are ignored. New recoupling and magnetization transfer techniques that are designed explicitly to account for inhomogeneous radiofrequency fields are needed.

The Structure of Boron Monoxide

Boron monoxide (BO), prepared by the thermal condensation of tetrahydroxydiboron, was first reported in 1955; however, its structure could not be determined. With the recent attention on boron-based two-dimensional materials, such as borophene and hexagonal boron nitride, there is renewed interest in BO. A large number of stable BO structures have been computationally identified, but none are supported by experiments. The consensus is that the material likely forms a boroxine-based two-dimensional material. Herein, we apply advanced 11B NMR experiments to determine the relative orientations of B(B)O2 centers in BO. We find that the material is composed of D2h-symmetric O2B-BO2 units that organize to form larger B4O2 rings. Further, powder diffraction experiments additionally reveal that these units organize to form two-dimensional layers with a random stacking pattern. This observation is in agreement with earlier density functional theory (DFT) studies that showed B4O2-based structures to be the most stable.

Determination of the mutual orientation between proton CSA tensors mediated through band-selective 1H-1H recoupling under fast MAS

The mutual orientation of nuclear spin interaction tensors provides critical information on the conformation and arrangement of molecules in chemicals, materials, and biological systems at an atomic level. Proton is a ubiquitous and important element in a variety of substances, and its NMR is highly sensitive due to their virtually 100% natural abundance and large gyromagnetic ratio. Nevertheless, the measurement of mutual orientation between the ¹H CSA tensors has remained largely untouched in the past due to strong ¹H-¹H homonuclear interactions in a dense network of protons. In this study, we have developed a proton-detected 3D ¹H CSA/¹H CSA/¹H CS correlation method that utilizes three techniques to manage homonuclear interactions, namely fast magic-angle spinning, windowless C-symmetry-based CSA recoupling (windowless-ROCSA), and a band-selective ¹H-¹H polarization transfer. The asymmetric ¹H CSA/¹H CSA correlated powder patterns produced by the C-symmetry-based methods are highly sensitive to the sign and asymmetry parameter of the ¹H CSA, and the Euler angle β as compared to the symmetric pattern obtained by the existing γ-encoded R-symmetry-based CSA/CSA correlation methods and allows a larger spectral area for data fitting. These features are beneficial for determining the mutual orientation between the nuclear spin interaction tensors with improved accuracy.

Nuclear spin diffusion under fast magic-angle spinning in solid-state NMR

Solid-state nuclear spin diffusion is the coherent and reversible process through which spin order is transferred via dipolar couplings. With the recent increases in magic-angle spinning (MAS) frequencies and magnetic fields becoming routinely applied in solid-state nuclear magnetic resonance, understanding how the increased 1H resolution obtained affects spin diffusion is necessary for interpretation of several common experiments. To investigate the coherent contributions to spin diffusion with fast MAS, we have developed a low-order correlation in Liouville space model based on the work of Dumez et al. (J. Chem. Phys. 33, 224501, 2010). Specifically, we introduce a new method for basis set selection, which accounts for the resonance-offset dependence at fast MAS. Furthermore, we consider the necessity of including chemical shift, both isotropic and anisotropic, in the modeling of spin diffusion. Using this model, we explore how different experimental factors change the nature of spin diffusion. Then, we show case studies to exemplify the issues that arise in using spin diffusion techniques at fast spinning. We show that the efficiency of polarization transfer via spin diffusion occurring within a deuterated and 100% back-exchanged protein sample at 60 kHz MAS is almost entirely dependent on resonance offset. We additionally identify temperature-dependent magnetization transfer in beta-aspartyl L-alanine, which could be explained by the influence of an incoherent relaxation-based nuclear Overhauser effect.

Determination of the relative orientation between 15N-1H dipolar coupling and 1H chemical shift anisotropy tensors under fast MAS solid-state NMR

In this work, we have proposed a proton-detected three-dimensional (3D) ¹⁵N-¹H dipolar coupling (DIP)/¹H chemical shift anisotropy (CSA)/¹H chemical shift (CS) correlation experiment to measure the relative orientation between the ¹⁵N-¹H dipolar coupling and the ¹H CSA tensors under fast magic angle spinning (MAS) solid-state NMR. In the 3D correlation experiment, the ¹⁵N-¹H dipolar coupling and ¹H CSA tensors are recoupled using our recently developed windowless C-symmetry-based C3₃¹-ROCSA (recoupling of chemical shift anisotropy) DIPSHIFT and C3₃¹-ROCSA pulse-based methods, respectively. The 2D ¹⁵N-¹H DIP/¹H CSA powder lineshapes extracted using the proposed 3D correlation method are shown to be sensitive to the sign and asymmetry of the ¹H CSA tensor, a feature that allows the determination of the relative orientation between the two correlating tensors with improved accuracy. The experimental method developed in this study is demonstrated on a powdered U-¹⁵N L-Histidine.HCl·H₂O sample.

Comparison of methods for 14N-1H recoupling in 14N-1H HMQC MAS NMR

¹H-detected ¹⁴N heteronuclear multiple-quantum coherence (HMQC) magic-angle-spinning (MAS) NMR experiments performed at fast magic-angle spinning (≥50 kHz) are finding increasing application, e.g., to pharmaceuticals. Of importance to the efficacy of these techniques is the recoupling technique applied to reintroduce the ¹H-¹⁴N dipolar coupling. In this paper, we compare, by experiment and 2-spin density matrix simulations, two classes of recoupling scheme: first, those based on n = 2 rotary resonance, namely R³ and spin-polarisation inversion SPI-R³, and the symmetry based SR4₁² method and, second, the TRAPDOR method. Both classes require optimisation depending on the magnitude of the quadrupolar interaction, and thus there is a compromise choice for samples with more than one nitrogen site, as is the case for the studied dipeptide β-AspAla that contains two nitrogen sites with a small and large quadrupolar coupling constant. Considering this, we observe better sensitivity for the TRAPDOR method, though noting the marked sensitivity of TRAPDOR to the ¹⁴N transmitter offset, with both SPI-R³ and SR4₁² giving similar recoupling performance.

Acceleration of indirect detection 195Pt solid-state NMR experiments by sideband selective excitation or alternative indirect sampling schemes

The measurement of the of chemical shift (CS) tensors via solid-state NMR (ssNMR) spectroscopy has proven to be a powerful probe of structure for organic molecules, biomolecules, and inorganic materials. However, when measuring the NMR spectra of heavy spin-1/2 isotopes the chemical shift anisotropy (CSA) is commonly on the order of thousands of parts per million, which makes acquisition of NMR spectra difficult due to the low NMR sensitivity imposed by the breadth of the signals and challenges in uniformly exciting the NMR spectrum. We have recently shown that complete ¹⁹⁵Pt NMR spectra could be rapidly measured by using ¹⁹⁵Pt saturation or excitation selective long pulses (SLP) with multiple rotor-cycle durations and RF fields less than 50 kHz into ¹H{¹⁹⁵Pt} or ¹H-³¹P{¹⁹⁵Pt} PE S-RESPDOR, TONE D-HMQC-4, J-resolved, and J-HMQC pulse sequences. The SLP only provide signal or dephasing when they are applied on resonance with a spinning sideband. The magic angle spinning ¹⁹⁵Pt NMR spectrum is reconstructed in the sideband selective NMR experiments by acquiring 1D NMR spectra at variable ¹⁹⁵Pt pulse offsets. In this work, we present a detailed investigation of the specific pulse conditions required for the ideal performance of sideband selective experiments. Sideband selective experiments are shown to be able to accurately reproduce MAS NMR spectra with minimal distortions of relative sideband intensities. It is also demonstrated that a ¹⁹⁵Pt NMR spectrum indirectly detected with HMQC can be rapidly obtained by acquiring a single rotor cycle of indirect dimension evolution points. We dub this method One Rotor Cycle of Acquisition (ORCA) HMQC. Sideband selective experiments and ORCA HMQC experiments are shown to provide a one order of magnitude improvement in experiment times as compared to conventional wideline HMQC experiments.

Asynchronising five-fold symmetry sequence for better homonuclear polarisation transfer in magic-angle-spinning solid-state NMR

Recoupling, decoupling, and multidimensional correlation experiments in magic-angle-spinning (MAS) solid-state NMR can be designed by exploiting the symmetry of internal spin interactions. One such scheme, namely, C5₂¹, and its supercycled version SPC5₂¹, notated as a five-fold symmetry sequence, is widely used for double-quantum dipole-dipole recoupling. Such schemes are generally rotor synchronised by design. We demonstrate an asynchronous implementation of the SPC5₂¹ sequence leading to higher double-quantum homonuclear polarisation transfer efficiency compared to the normal synchronous implementation. Rotor-synchronisation is broken in two different ways: lengthening the duration of one of the pulses, denoted as pulse-width variation (PWV), and mismatching the MAS frequency denoted as MAS variation (MASV). The application of this asynchronous sequence is shown on three different samples, namely, U-¹³C-alanine and 1,4-¹³C-labelled ammonium phthalate which include ¹³C_α-¹³C_β, ¹³C_α-¹³C_o, and ¹³C_o-¹³C_o spin systems, and adenosine 5'- triphosphate disodium salt trihydrate (ATP⋅3H₂O). We show that the asynchronous version performs better for spin pairs with small dipole-dipole couplings and large chemical-shift anisotropies, for example, ¹³C_o-¹³C_o. Simulations and experiments are shown to corroborate the results.

Simultaneous recoupling of chemical shift tensors of two nuclei by R-symmetry sequences

Chemical shift tensors (CSTs) are sensitive probes of structure and dynamics. R-symmetry pulse sequences (RNCSA) can efficiently recouple CSTs of varying magnitudes in magic angle spinning (MAS) NMR experiments, for a broad range of conditions and MAS frequencies. Herein, we introduce dual-channel R-symmetry pulse sequences for simultaneously recording CSTs of two different nuclei in a single experiment (DORNE-CSA). We demonstrate the performance of DORNE-CSA sequences for simultaneous measurement of 13C and 15N CSTs, on a U-13C,15N-labeled microcrystalline l-histidine. We show that the DORNE-CSA method is robust, provides accurate CST parameters, and takes only half of the measurement time compared to a pair of RNCSA experiments otherwise required for recording the CSTs of individual nuclei. DORNE-CSA approach is broadly applicable to a wide range of biological and inorganic systems.

Internuclear distance measurements between 1H and 14N in multi-component rigid solids at fast MAS

¹H-¹⁴N internuclear distances are readily and accurately measured using the symmetry-based phase-modulated resonance-echo saturation-pulse double-resonance (PM-S-RESPDOR) method in rigid solids. The fraction curve, (S₀ - S')/S₀, is represented by a single variable of a ¹H-¹⁴N heteronuclear dipolar coupling, where S₀ and S' are the PM-S-RESPDOR signal intensity with and without ¹⁴N PM saturation pulse, respectively. Analytical equation of the fraction curve easily provides ¹H-¹⁴N couplings. This treatment is only applicable when NH proton resonance is well separated from the other proton peaks. With the limited ¹H resolution even at fast MAS > 60 kHz, unfortunately, this condition is not necessarily satisfied especially in multi-component systems which often appear in pharmaceutical applications. To overcome this problem, T-HMQC filtering is applied to suppress the ¹H signals other than NH proton prior to the PM-S-RESPDOR experiments. The method is well demonstrated on two components acetaminophen-oxalic acid (APAP-OXA) systems. Further analysis of orientation dependence of T-HMQC and PM-S-RESPDOR shows that the analytical equation can be safely applied in the analysis of T-HMQC filtered PM-S-RESPDOR experiments.

DESPERATE: A Python library for processing and denoising NMR spectra

NMR spectroscopy is an inherently insensitive technique with respect to the amount of observable signal. A common element in all NMR spectra is random thermal noise that is often characterized by a signal-to-noise ratio (SNR). SNR can be generically improved experimentally with repetitive signal averaging or during post-processing with apodization; the former of which often results in long experimental times and the latter results in the loss of spectral resolution. Denoising techniques can instead be used during post-processing to enhance SNR without compromising resolution. The most common approach relies on the singular-value decomposition (SVD) to discard noisy components of NMR data. SVD-based approaches work well, such as Cadzow and PCA, but are computationally expensive when used for large datasets that are often encountered in NMR (e.g., Carr-Purcell/Meiboom-Gill and nD datasets). Herein, we describe the implementation of a new wavelet transform (WT) routine for the fast and robust denoising of 1D and 2D NMR spectra. Several simulated and experimental datasets are denoised with both SVD-based Cadzow or PCA and WT's, and the resulting SNR enhancements and spectral uniformity are compared. WT denoising offers similar and improved denoising compared with SVD and operates faster by several orders-of-magnitude in some cases. All denoising and processing routines used in this work are included in a free and open-source Python library called DESPERATE.

Assignment of aromatic side-chain spins and characterization of their distance restraints at fast MAS

The assignment of aromatic side-chain spins has always been more challenging than assigning backbone and aliphatic spins. Selective labeling combined with mutagenesis has been the approach for assigning aromatic spins. This manuscript reports a method for assigning aromatic spins in a fully protonated protein by connecting them to the backbone atoms using a low-power TOBSY sequence. The pulse sequence employs residual polarization and sequential acquisitions techniques to record H^N- and H^C-detected spectra in a single experiment. The unambiguous assignment of aromatic spins also enables the characterization of ¹H-¹H distance restraints involving aromatic spins. Broadband (RFDR) and selective (BASS-SD) recoupling sequences were used to generate H^N-Η^C, H^C-H^N and H^C-H^C restraints involving the side-chain proton spins of aromatic residues. This approach has been demonstrated on a fully protonated U-[¹³C,¹⁵N] labeled GB1 sample at 95-100 kHz MAS.

Sensitivity-Enhanced Multidimensional Solid-State NMR Spectroscopy by Optimal-Control-Based Transverse Mixing Sequences

Recently, proton-detected magic-angle spinning (MAS) solid-state nuclear magnetic resonance (NMR) spectroscopy has become an attractive tool to study the structure and dynamics of insoluble proteins at atomic resolution. The sensitivity of the employed multidimensional experiments can be systematically improved when both transversal components of the magnetization are transferred simultaneously after an evolution period. The method of preservation of equivalent pathways has been explored in solution-state NMR; however, it does not find widespread application due to relaxation issues connected with increased molecular size. We present here for the first time heteronuclear transverse mixing sequences for correlation experiments at moderate and fast MAS frequencies. Optimal control allows to boost the signal-to-noise ratio (SNR) beyond the expected factor of 2 for each indirect dimension. In addition to the carbon-detected sensitivity-enhanced 2D NCA experiment, we present a novel proton-detected, doubly sensitivity-enhanced 3D hCANH pulse sequence for which we observe a 3-fold improvement in SNR compared to the conventional experimental implementation. The sensitivity gain turned out to be essential to unambiguously characterize a minor fibril polymorph of a human lambda-III immunoglobulin light chain protein that escaped detection so far.

t1-noise elimination by continuous chemical shift anisotropy refocusing

Due to their high gyromagnetic ratio, there is considerable interest in measuring distances and correlations involving protons, but such measurements are compounded by the simultaneous recoupling of chemical shift anisotropy (CSA). This secondary recoupling adds additional modulations to the signal intensities that ultimately lead to t₁-noise and signal decay. Recently, Venkatesh et al. demonstrated that the addition of CSA refocusing periods during ¹H-X dipolar recoupling led to sequences with far higher stability and performance. Herein, we describe a related effort and develop a symmetry-based recoupling sequence that continually refocuses the ¹H CSA. This sequence shows superior performance to the regular and t₁-noise eliminated D-HMQC sequences in the case of spin-1/2 nuclei and comparable performance to the later for half-integer quadrupoles.

Molecular and Electronic Structure of Isolated Platinum Sites Enabled by the Expedient Measurement of 195Pt Chemical Shift Anisotropy

Techniques that can characterize the molecular structures of dilute surface species are required to facilitate the rational synthesis and improvement of Pt-based heterogeneous catalysts. ¹⁹⁵Pt solid-state NMR spectroscopy could be an ideal tool for this task because ¹⁹⁵Pt isotropic chemical shifts and chemical shift anisotropy (CSA) are highly sensitive probes of the local chemical environment and electronic structure. However, the characterization of Pt surface-sites is complicated by the typical low Pt loadings that are between 0.2 and 5 wt% and broadening of ¹⁹⁵Pt solid-state NMR spectra by CSA. Here, we introduce a set of solid-state NMR methods that exploit fast MAS and indirect detection using a sensitive spy nucleus (¹H or ³¹P) to enable the rapid acquisition of ¹⁹⁵Pt MAS NMR spectra. We demonstrate that high-resolution wideline ¹⁹⁵Pt MAS NMR spectra can be acquired in minutes to a few hours for a series of molecular and single-site Pt species grafted on silica with Pt loading of only 3-5 wt%. Low-power, long-duration, sideband-selective excitation, and saturation pulses are incorporated into t₁-noise eliminated dipolar heteronuclear multiple quantum coherence, perfect echo resonance echo saturation pulse double resonance, or J-resolved pulse sequences. The complete ¹⁹⁵Pt MAS NMR spectrum is then reconstructed by recording a series of 1D NMR spectra where the offset of the ¹⁹⁵Pt pulses is varied in increments of the MAS frequency. Analysis of the ¹⁹⁵Pt MAS NMR spectra yields the ¹⁹⁵Pt chemical shift tensor parameters. Zeroth order approximation density functional theory calculations accurately predict ¹⁹⁵Pt CS tensor parameters. Simple and predictive orbital models relate the CS tensor parameters to the Pt electronic structure and coordination environment. The methodology developed here paves the way for the detailed structural and electronic analysis of dilute platinum surface-sites.

Determination of accurate 19F chemical shift tensors with R-symmetry recoupling at high MAS frequencies (60-100 kHz)

Fluorination is a versatile and valuable modification for numerous systems, and ¹⁹F NMR spectroscopy is the premier method for their structural characterization. ¹⁹F chemical shift anisotropy is a sensitive probe of structure and dynamics, even though ¹⁹F chemical shift tensors have been reported for only a handful of systems to date. Here, we explore γ-encoded R-symmetry based recoupling sequences for the determination of ¹⁹F chemical shift tensors in fully protonated organic solids at high, 60-100 kHz MAS frequencies. We show that the performance of ¹⁹F-RNCSA experiments improves with increasing MAS frequencies, and that ¹H decoupling is required to determine accurate chemical shift tensor parameters. In addition, these sequences are tolerant to B₁-field inhomogeneity making them suitable for a wide range of systems and experimental conditions.

Field and magic angle spinning frequency dependence of proton resonances in rotating solids

Proton detection in solid state NMR is continuously developing and allows one to gain new insights in structural biology. Overall, this progress is a result of the synergy between hardware development, new NMR methodology and new isotope labeling strategies, to name a few factors. Even though current developments are rapid, it is worthwhile to summarize what can currently be achieved employing proton detection in biological solids. We illustrate this by analysing the signal-to-noise ratio (SNR) for spectra obtained for a microcrystalline α-spectrin SH3 domain protein sample by (i) employing different degrees of chemical dilution to replace protons by incorporating deuterons in different sites, by (ii) variation of the magic angle spinning (MAS) frequencies between 20 and 110 kHz, and by (iii) variation of the static magnetic field B₀. The experimental SNR values are validated with numerical simulations employing up to 9 proton spins. Although in reality a protein would contain far more than 9 protons, in a deuterated environment this is a sufficient number to achieve satisfactory simulations consistent with the experimental data. The key results of this analysis are (i) with current hardware, deuteration is still necessary to record spectra of optimum quality; (ii) 13CH3 isotopomers for methyl groups yield the best SNR when MAS frequencies above 100 kHz are available; and (iii) sensitivity increases with a factor beyond B0 3/2 with the static magnetic field due to a transition of proton-proton dipolar interactions from a strong to a weak coupling limit.

NMR Assignment of Methyl Groups in Immobilized Proteins Using Multiple-Bond 13C Homonuclear Transfers, Proton Detection, and Very Fast MAS

In nuclear magnetic resonance spectroscopy of proteins, methyl protons play a particular role as extremely sensitive reporters on dynamics, allosteric effects, and protein–protein interactions, accessible even in high-molecular-weight systems approaching 1 MDa. The notorious issue of their chemical shift assignment is addressed here by a joint use of solid-state 1H-detected methods at very fast (nearly 100 kHz) magic-angle spinning, partial deuteration, and high-magnetic fields. The suitability of a series of RF schemes is evaluated for the efficient coherence transfer across entire 13C side chains of methyl-containing residues, which is key for establishing connection between methyl and backbone 1H resonances. The performance of ten methods for recoupling of either isotropic 13C–13C scalar or anisotropic dipolar interactions (five variants of TOBSY, FLOPSY, DIPSI, WALTZ, RFDR, and DREAM) is evaluated experimentally at two state-of-the-art magic-angle spinning (55 and 94.5 kHz) and static magnetic field conditions (18.8 and 23.5 T). Model isotopically labeled compounds (alanine and Met-Leu-Phe tripeptide) and ILV-methyl and amide-selectively protonated, and otherwise deuterated chicken α-spectrin SH3 protein are used as convenient reference systems. Spin dynamics simulations in SIMPSON are performed to determine optimal parameters of these RF schemes, up to recently experimentally attained spinning frequencies (200 kHz) and B0 field strengths (28.2 T). The concept of linearization of 13C side chain by appropriate isotope labeling is revisited and showed to significantly increase sensitivity of methyl-to-backbone correlations. A resolution enhancement provided by 4D spectroscopy with non-uniform (sparse) sampling is demonstrated to remove ambiguities in simultaneous resonance assignment of methyl proton and carbon chemical shifts.

Double echo symmetry-based REDOR and RESPDOR pulse sequences for proton detected measurements of heteronuclear dipolar coupling constants

¹H{X} symmetry-based rotational echo double resonance pulse sequences (S-REDOR) and symmetry-based rotational echo saturation pulse double resonance (S-RESPDOR) solid-state NMR experiments have found widespread application for ¹H detected measurements of difference NMR spectra, dipolar coupling constants, and internuclear distances under conditions of fast magic angle spinning (MAS). In these experiments the supercycled R4₁² (SR4₁²) symmetry-based recoupling pulse sequence is typically applied to the ¹H spins to reintroduce heteronuclear dipolar couplings. However, the timing of SR4₁² and other symmetry-based pulse sequences must be precisely synchronized with the rotation of the sample, otherwise, the evolution of ¹H CSA and other interactions will not be properly refocused. For this reason, significant distortions are often observed in experimental dipolar dephasing difference curves obtained with S-REDOR or S-RESPDOR pulse sequences. Here we introduce a family of double echo (DE) S-REDOR/S-RESPDOR pulse sequences that function in an analogous manner to the recently introduced t₁-noise eliminated (TONE) family of dipolar heteronuclear multiple quantum coherence (D-HMQC) pulse sequences. Through numerical simulations and experiments the DE S-REDOR/S-RESPDOR sequences are shown to provide dephasing difference curves similar to those obtained with S-REDOR/S-RESPDOR. However, the DE sequences are more robust to the deviations of the MAS frequency from the ideal value that occurs during typical solid-state NMR experiments. The DE sequences are shown to provide more reliable ¹H detected dipolar dephasing difference curves for nuclei such as ¹⁵N (with isotopic labelling), ¹⁸³W and ³⁵Cl. The double echo sequences are therefore recommended to be used in place of conventional S-REDOR/S-RESPDOR sequences for measurement of weak dipolar coupling constants and long-range distances.

Maximizing efficiency of dipolar recoupling in solid-state NMR using optimal control sequences

Dipolar recoupling is a central concept in the nuclear magnetic resonance spectroscopy of powdered solids and is used to establish correlations between different nuclei by magnetization transfer. The efficiency of conventional cross-polarization methods is low because of the inherent radio frequency (rf) field inhomogeneity present in the magic angle spinning (MAS) experiments and the large chemical shift anisotropies at high magnetic fields. Very high transfer efficiencies can be obtained using optimal control–derived experiments. These sequences had to be optimized individually for a particular MAS frequency. We show that by adjusting the length and the rf field amplitude of the shaped pulse synchronously with sample rotation, optimal control sequences can be successfully applied over a range of MAS frequencies without the need of reoptimization. This feature greatly enhances their applicability on spectrometers operating at differing external fields where the MAS frequency needs to be adjusted to avoid detrimental resonance effects.

Refined Structures of O-Phospho-l-serine and Its Calcium Salt by New Multinuclear Solid-State NMR Crystallography Methods

O-phospho-l-serine (Pser) and its Ca salt, Ca[O-phospho-l-serine]·H2O (CaPser), play important roles for bone mineralization and were recently also proposed to account for the markedly improved bone-adhesive properties of Pser-doped calcium phosphate-based cements for biomedical implants. However, the hitherto few proposed structural models of Pser and CaPser were obtained by X-ray diffraction, thereby leaving the proton positions poorly defined. Herein, we refine the Pser and CaPser structures by density functional theory (DFT) calculations and contrast them with direct interatomic-distance constraints from two-dimensional (2D) nuclear magnetic resonance (NMR) correlation experimentation at fast magic-angle spinning (MAS), encompassing double-quantum-single-quantum (2Q-1Q) 1H NMR along with heteronuclear 13C{1H} and 31P{1H} correlation NMR experiments. The Pser and CaPser structures before and after refinements by DFT were validated against sets of NMR-derived effective 1H-1H, 1H-31P, and 1H-13C distances, which confirmed the improved accuracy of the refined structures. Each distance set was derived from one sole 2D NMR experiment applied to a powder without isotopic enrichment. The distances were extracted without invoking numerical spin-dynamics simulations or approximate phenomenological models. We highlight the advantages and limitations of the new distance-extraction procedure. Isotropic 1H, 13C, and 31P chemical shifts obtained by DFT calculations using the gauge including projector augmented wave (GIPAW) method agreed very well with the experimental results. We discuss the isotropic and anisotropic 13C and 31P chemical-shift parameters in relation to the previous literature, where most data on CaPser are reported herein for the first time.

Broadband adiabatic inversion cross-polarization to integer-spin nuclei with application to deuterium NMR

Solid-state NMR (SSNMR) spectroscopy of integer-spin quadrupolar nuclei is important for the molecular-level characterization of a variety of materials and biological solids; of the integer spins, ² H (S = 1) is by far the most widely studied, due to its usefulness in probing dynamical motions. SSNMR spectra of integer-spin nuclei often feature very broad powder patterns that arise largely from the effects of the first-order quadrupolar interaction; as such, the acquisition of high-quality spectra continues to remain a challenge. The broadband adiabatic inversion cross-polarization (BRAIN-CP) pulse sequence, which is capable of cross-polarization (CP) enhancement over large bandwidths, has found success for the acquisition of SSNMR spectra of integer-spin nuclei, including ¹⁴ N (S = 1), especially when coupled with Carr-Purcell/Meiboom-Gill pulse sequences featuring frequency-swept WURST pulses (WURST-CPMG) for T₂ -based signal enhancement. However, to date, there has not been a systematic investigation of the spin dynamics underlying BRAIN-CP, nor any concrete theoretical models to aid in its parameterization for applications to integer-spin nuclei. In addition, the BRAIN-CP/WURST-CPMG scheme has not been demonstrated for generalized application to wideline or ultra-wideline (UW) ² H SSNMR. Herein, we provide a theoretical description of the BRAIN-CP pulse sequence for spin-1/2 → spin-1 CP under static conditions, featuring a set of analytical equations describing Hartmann-Hahn matching conditions and numerical simulations that elucidate a CP mechanism involving polarization transfer, coherence exchange, and adiabatic inversion. Several experimental examples are presented for comparison with theoretical models and previously developed integer-spin CP methods, demonstrating rapid acquisition of ² H NMR spectra from efficient broadband CP.

Field-stepped ultra-wideline NMR at up to 36 T: On the inequivalence between field and frequency stepping

Field-stepped NMR spectroscopy at up to 36 T using the series-connected hybrid (SCH) magnet at the U.S. National High Magnetic Field Laboratory is demonstrated for acquiring ultra-wideline powder spectra of nuclei with very large quadrupolar interactions. Historically, NMR evolved from the continuous-wave (cw) field-swept method in the early days to the pulsed Fourier-transform method in the modern era. Spectra acquired using field sweeping are generally considered to be equivalent to those acquired using the pulsed method. Here, it is shown that field-stepped wideline spectra of half-integer spin quadrupolar nuclei acquired using WURST/CPMG methods can be significantly different from those acquired with the frequency-stepped method commonly used with superconducting magnets. The inequivalence arises from magnetic field-dependent NMR interactions such as the anisotropic chemical shift and second-order quadrupolar interactions; the latter is often the main interaction leading to ultra-wideline powder patterns of half-integer spin quadrupolar nuclei. This inequivalence needs be taken into account to accurately and correctly determine the quadrupolar coupling and chemical shift parameters. A simulation protocol is developed for spectral fitting to facilitate analysis of field-stepped ultra-wideline NMR spectra acquired using powered magnets. A MATLAB program which implements this protocol is available on request.

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.

Structure Solution of Nano-Crystalline Small Molecules Using MicroED and Solid-State NMR Dipolar-Based Experiments

Three-dimensional electron diffraction crystallography (microED) can solve structures of sub-micrometer crystals, which are too small for single crystal X-ray crystallography. However, R factors for the microED-based structures are generally high because of dynamic scattering. That means R factor may not be reliable provided that kinetic analysis is used. Consequently, there remains ambiguity to locate hydrogens and to assign nuclei with close atomic numbers, like carbon, nitrogen, and oxygen. Herein, we employed microED and ssNMR dipolar-based experiments together with spin dynamics numerical simulations. The NMR dipolar-based experiments were ¹H-¹⁴N phase-modulated rotational-echo saturation-pulse double-resonance (PM-S-RESPDOR) and ¹H-¹H selective recoupling of proton (SERP) experiments. The former examined the dephasing effect of a specific ¹H resonance under multiple ¹H-¹⁴N dipolar couplings. The latter examined the selective polarization transfer between a ¹H-¹H pair. The structure was solved by microED and then validated by evaluating the agreement between experimental and calculated dipolar-based NMR results. As the measurements were performed on ¹H and ¹⁴N, the method can be employed for natural abundance samples. Furthermore, the whole validation procedure was conducted at 293 K unlike widely used chemical shift calculation at 0 K using the GIPAW method. This combined method was demonstrated on monoclinic l-histidine.

Selective 1H-1H recoupling via symmetry sequences in fully protonated samples at fast magic angle spinning

Proton-detected solid-state NMR at fast Magic Angle Spinning (MAS) is becoming the norm to characterize molecules. Routinely ¹H-¹H and ¹H-X dipolar couplings are used to characterize the structure and dynamics of molecules. Selective proton recoupling techniques are emerging as a method for structural characterization via estimation of qualitative and quantitative distances. In the present study, we demonstrate through numerical simulations and experiments that the well-characterized CN^v_n sequences can also be tailored for selective recoupling of proton spins by employing C elements of the type (β)_Φ(4β)_Φ+π(3β)_Φ. Herein, several CN^v_n sequences were examined through numerical simulations and experiments. C6¹₄ recoupling sequence with a modified POST-element ((β)_Φ(4β)_Φ+π(3β)_Φ) shows selective polarization transfer efficiencies on the order of 40-50% between various proton spin pairs in fully protonated samples at rf amplitudes ranging from 0.3 to 0.8 times the MAS frequency. These selective recoupling sequences have been labeled as frequency-selective-CN^v_n sequences. The extent of selectivity, polarization transfer efficiency and the feasibility of experimentally measuring proton-proton distances in fully protonated samples are explored here. The development of efficient and robust selective ¹H-¹H recoupling experiments is required to structurally characterize molecules without artificial isotope enrichment or the need for diffracting crystals.

Analytical models of probe dynamics effects on NMR measurements

This paper provides a detailed analysis of three common NMR probe circuits (untuned, tuned, and impedance-matched) and studies their effects on multi-pulse experiments, such as those based on the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. The magnitude of probe dynamics effects on broadband refocusing pulses are studied as a function of normalized RF bandwidth. Finally, the probe circuit models are integrated with spin dynamics simulations to design hardware-specific RF excitation and refocusing pulses for optimizing user-specified metrics such as signal-to-noise ratio (SNR) in grossly inhomogeneous fields. Preliminary experimental results on untuned probes are also presented.

Dipolar dephasing for structure determination in a paramagnetic environment

We demonstrate the efficacy of the REDOR-type sequences in determining dipolar coupling strength in a paramagnetic environment. Utilizing paramagnetic effects of enhanced relaxation rates and rapid electronic fluctuations in Cu(II)-(DL-Ala)₂.H₂O, the dipolar coupling for the methyl C-H that is 4.20 ​Å (methyl carbon) away from the Cu²⁺ ion, was estimated to be 8.8 ​± ​0.6 ​kHz. This coupling is scaled by a factor of ~0.3 in comparison to the rigid limit value of ~32 ​kHz, in line with partial averaging of the dipolar interaction by rotational motion of the methyl group. Limited variation in the scaling factor of the dipolar coupling strength at different temperatures is observed. The C-H internuclear distance derived from the size of the dipolar coupling is similar to that observed in the crystal structure. The errors in the dipolar coupling strength observed in the REDOR-type experiments are similar to those reported for diamagnetic systems. Increase in resolution due to the Fermi contact shifts, coupled with MAS frequencies of 30-35 ​kHz allowed to estimate the hyperfine coupling strengths for protons and carbons from the temperature dependence of the chemical shift and obtain a high resolution ¹H-¹H spin diffusion spectrum. This study shows the utility of REDOR-type sequences in obtaining reliable structural and dynamical information from a paramagnetic complex. We believe that this can help in studying the active site of paramagnetic metalloproteins at high resolution.

Proton-detected solid-state NMR spectroscopy of spin-1/2 nuclei with large chemical shift anisotropy

Constant-time (CT) dipolar heteronuclear multiple quantum coherence (D-HMQC) has previously been demonstrated as a method for proton detection of high-resolution wideline NMR spectra of spin-1/2 nuclei with large chemical shift anisotropy (CSA). However, ¹H transverse relaxation and t₁-noise often reduce the sensitivity of D-HMQC experiments, preventing the theoretical gains in sensitivity provided by ¹H detection from being realized. Here we demonstrate a series of improved pulse sequences for ¹H detection of spin-1/2 nuclei under fast MAS, with ¹⁹⁵Pt SSNMR experiments on cisplatin as an example. First, a t₁-incrementation protocol for D-HMQC dubbed Arbitrary Indirect Dwell (AID) is demonstrated. AID allows the use of arbitrary, rotor asynchronous t₁-increments, but removes the constant time period from CT D-HMQC, resulting in improved sensitivity by reducing transverse relaxation losses. Next, we show that short high-power adiabatic pulses (SHAPs), which efficiently invert broad MAS sideband manifolds, can be effectively incorporated into ¹H detected symmetry-based resonance echo double resonance (S-REDOR) and t₁-noise eliminated (TONE) D-HMQC experiments. The S-REDOR experiments with SHAPs provide approximately double the dipolar dephasing, as compared to experiments with rectangular inversion pulses. We lastly show that sensitivity and resolution can be further enhanced with the use of swept excitation pulses as well as adiabatic magic angle turning (aMAT).

Single-crystal NMR spectroscopy

Single-crystal (SC) NMR spectroscopy is a solid-state NMR method that has been used since the early days of NMR to study the magnitude and orientation of tensorial nuclear spin interactions in solids. This review first presents the field of SC NMR instrumentation, then provides a survey of software for analysis of SC NMR data, and finally it highlights selected applications of SC NMR in various fields of research. The aim of the last part is not to provide a complete review of all SC NMR literature but to provide examples that demonstrate interesting applications of SC NMR.

Orientation of immobilized antigens on common surfaces by a simple computational model: Exposition of SARS-CoV-2 Spike protein RBD epitopes

The possibility of immobilizing a protein with antigenic properties on a solid support offers significant possibilities in the development of immunosensors and vaccine formulations. For both applications, the orientation of the antigen should ensure ready accessibility of the antibodies to the epitope. However, an experimental assessment of the orientational preferences necessarily proceeds through the preparation/isolation of the antigen, the immobilization on different surfaces and one or more biophysical characterization steps. To predict a priori whether favorable orientations can be achieved or not would allow one to select the most promising experimental routes, partly mitigating the time cost towards the final product. In this manuscript, we apply a simple computational model, based on united-residue modelling, to the prediction of the orientation of the receptor binding domain of the SARS-CoV-2 spike protein on surfaces commonly used in lateral-flow devices. These calculations can account for the experimental observation that direct immobilization on gold gives sufficient exposure of the epitope to obtain a response in immunochemical assays.

Large-scale magnetic resonance simulations: A tutorial

Computational modeling is becoming an essential tool in magnetic resonance to design and optimize experiments, test the performance of theoretical models, and interpret experimental data. Recent theoretical research and software development made possible simulations of large spin systems, for example, proteins with thousands of spins, in reasonable time. In the last few years, the Fokker-Planck formalism also re-emerged due to its ability to handle spatial dynamics. The purpose of this tutorial is to describe advantages and disadvantages of the most common formalisms, the latest developments and strategies to improve the computational efficiency, and to guide users in the setting up of a simulation using the Spinach software.

Computer-generated pulse sequences for 1H-15N and 1Hα-13Cα separated local-field experiments

High-resolution separated local field (SLF) experiments are employed in oriented-sample solid state NMR to measure angular-dependent heteronuclear dipolar couplings for structure determination. While traditionally these experiments have been designed analytically by determining cycles of pulses with specific phases and durations to achieve cancellation of the homonuclear dipolar terms in the average Hamiltonian, recent work has introduced a computational approach to optimizing linewidths of the ¹H-¹⁵N dipolar resonances. Accelerated by GPU processors, a computer algorithm searches for the optimal parameters by simulating numerous ¹H-¹⁵N NMR spectra. This approach, termed ROULETTE, showed promising results by developing a new pulse sequence (ROULETTE-1.0) exhibiting 18% sharper mean linewidths than SAMPI4 for an N-acetyl Leucine (NAL) crystal. Herein, we expand on this previous work to improve the performance of the ¹H-¹⁵N SLF experiment and extend the work beyond the original approach to new SLF experiments. The new algorithm, in addition to finding pulse durations and phases, now searches for the optimal on/off application scheme of radio frequency irradiation on each channel. This constitutes true de novo optimization, effectively optimizing every aspect of a pulse sequence instead of just phases and durations. With an improved ROULETTE algorithm, we have found a new ¹H-¹⁵N pulse sequence, termed ROULETTE-2.0, yielding 32% sharper mean linewidths than SAMPI4 for NAL crystal at 500 MHz ¹H frequency. Whereas both SAMPI4 and ROULETTE-1.0 have a window where the rf power on the I-channel is turned off, the new pulse sequence is entirely windowless. Furthermore, the reliability of the algorithm has been greatly improved in terms of avoiding false positives, i.e. well-performing pulse sequences in silica that fail to render narrow resonances in experiment. The program has been extended to the ¹³C_α-¹H_α SLF experiments, using a 6 subdwell architecture similar to the ¹H-¹⁵N optimization. Compared to the PISEMA pulse sequence, the mean ¹³C_α-¹H_α linewidth is 17% sharper for the new pulse sequence, termed ROULETTE-CAHA. In addition to superior performance, the work demonstrates the broad applicability of the algorithm and its adaptability to different NMR experiments and spin systems.

Atomic-Scale Description of Interfaces between Antigen and Aluminum-Based Adjuvants Used in Vaccines by Dynamic Nuclear Polarization (DNP) Enhanced NMR Spectroscopy

The addition of aluminum-based adjuvants in vaccines enhances the immune response to antigens. The strength of antigen adsorption on adjuvant gels is known to modulate vaccine efficacy. However, a detailed understanding of the mechanisms of interaction between aluminum gels and antigens is still missing. Herein, a new analytical approach based on dynamic nuclear polarization (DNP) enhanced NMR spectroscopy under magic angle spinning (MAS) is implemented to provide a molecular description of the antigen-adjuvant interface. This approach is demonstrated on hepatitis B surface antigen particles in combination with three aluminum gels obtained from different suppliers. Both noncovalent and covalent interactions between the phospholipids of the antigen particles and the surface of the aluminum gels are identified by using MAS DNP NMR ²⁷ Al and ³¹ P correlation experiments. Although covalent interactions were detected for only one of the formulations, dipolar recoupling rotational echo adiabatic passage double resonance (REAPDOR) experiments reveal significant differences in the strength of weak interactions.

Assessment of new symmetry-based dipolar recoupling schemes for homonuclear magnetization exchange between quadrupolar nuclei in two-dimensional correlation MAS NMR

We provide an extensive experimental and numerical evaluation of MQ-phase (S)M supercycles with M={3,4} of three groups of symmetry-based homonuclear dipolar recoupling rf-pulse sequences, [Formula: see text] , for establishing proximities among half-integer spin quadrupolar nuclei under moderately fast magic-angle-spinning (MAS) conditions in single-quantum-single-quantum (1Q-1Q) correlation NMR experiments. The relative merits of the (S)M schemes for variations in resonance offsets and rf-amplitude errors were assessed by numerically simulated magnetization transfers in spin-3/2 pairs with variable isotropic chemical shifts and quadrupolar coupling constants. Experimental demonstrations of ²³Na (spin-3/2) NMR on Na₂MoO₄·2H₂O and ²⁷Al (spin-5/2) NMR on AlPO-CJ19 [(NH₄)₂Al₄(PO₄)₄HPO₄·H₂O] are presented at 14.1 T and 24 kHz MAS. We recommend using the (SR2₂¹)3 or (SR2₂¹)4 supercycles for samples that exhibit small chemical-shift dispersions (<3 kHz), and any (SRN_N^N/2)3 scheme with N⩾10 for larger spreads of isotropic chemical shifts. However, because the (SRN_N^N/2)3 sequences recouple heteronuclear dipolar interactions, their application to proton-bearing samples requires high-power proton decoupling during the mixing period. Alternatively, the (SR2₄¹)3 and (SR2₄¹)4 schemes may be employed in the absence of proton decoupling, but with poorer compensation to resonance-offsets and rf-amplitude errors.

Direct Observation of the Exciton Self-Trapping Process in CsCu2I3 Thin Films

Low-dimensional copper halides, such as CsCu₂I₃, have emerged as promising LED materials featuring strongly Stokes-shifted photoluminescence with high quantum yield. Previous calculations suggest an exciton self-trapping mechanism; however, direct experimental evidence for this process is still lacking. Here, we present femtosecond UV-vis transient absorption experiments of CsCu₂I₃ thin films. The films were analyzed by SEM, XRD, and ¹³³Cs/⁶³Cu NMR for crystallinity and defects. Unique spectral dynamics is observed. The band gap absorption exhibits a characteristic double-peak structure arising from the 130 meV spin-orbit splitting of the copper d electrons. Emission at the direct band gap disappears because of the formation of the lowest-energy self-trapped exciton state. We determined the time constant of 12 ps for the trapping process of thermally relaxed free excitons, with an energy barrier of at least 60 meV. The data are successfully modeled by global kinetic analysis, providing also accurate time constants for charge carrier cooling processes.

MAS NMR Investigation of Molecular Order in an Ionic Liquid Crystal

The structure and molecular order in the thermotropic ionic liquid crystal (ILC), [choline][geranate(H)octanoate], an analogue of Choline And GEranate (CAGE), which has potential for use as a broad-spectrum antimicrobial and transdermal and oral delivery agent, were investigated by magic-angle spinning (MAS) nuclear magnetic resonance (NMR), polarizing optical microscopy, small-angle X-ray scattering (SAXS), and mass spectrometry. Mass spectrometry and the ¹H NMR chemical shift reveal that CAGE-oct is a dynamic system, with metathesis (the exchange of interacting ions) and hydrogen exchange occurring between hydrogen-bonded/ionic complexes such as [(choline)(geranate)(H)(octanoate)], [(choline)(octanoate)₂(H)], and [(choline)(geranate)₂(H)]. These clusters, which are shown by mass spectrometry to be significantly more stable than expected for typical electrostatic ion clusters, involve hydrogen bonding between the carboxylic acid, carboxylate, and hydroxyl groups, with rapid hydrogen bond breaking and re-formation observed to average the ¹H chemical shifts. The formation of a partial bilayer liquid crystal (LC) phase was identified by SAXS and polarizing optical microscopy at temperatures below ∼293 K. The occurrence of this transition close to room temperature could be utilized as a potential temperature-induced "switch" of the anisotropic properties for particular applications. The presence of an isotropic component of approximately 23% was observed to coexist with the LC phase, as detected by polarizing optical microscopy and quantified by both ¹H-¹³C dipolar-chemical shift correlation (DIPSHIFT) and ¹H double-quantum (DQ) MAS NMR experiments. At temperatures above the LC-to-isotropic transition, intermediate-range order (clustering of polar and nonpolar domains), a feature of many ILs, persists. Site-specific order parameters for the LC phase of CAGE-oct were obtained from the MAS NMR measurement of the partially averaged ¹³C-¹H dipolar couplings (D_CH) by cross-polarization (CP) build-up curves and DIPSHIFT experiments, and ¹H-¹H dipolar couplings (D_HH) by double-quantum (DQ) build-up curves. The corresponding order parameters, S_CH and S_HH, are in the range 0-0.2 and are lower compared to those for smectic (i.e., layered) phases of conventional nonionic liquid crystals, resembling those of lamellar phases formed by lyotropic surfactant-solvent systems.