Spinach--a software library for simulation of spin dynamics in large spin systems

Quantum chemical package Jaguar: A survey of recent developments and unique features

This paper is dedicated to the quantum chemical package Jaguar, which is commercial software developed and distributed by Schrödinger, Inc. We discuss Jaguar's scientific features that are relevant to chemical research as well as describe those aspects of the program that are pertinent to the user interface, the organization of the computer code, and its maintenance and testing. Among the scientific topics that feature prominently in this paper are the quantum chemical methods grounded in the pseudospectral approach. A number of multistep workflows dependent on Jaguar are covered: prediction of protonation equilibria in aqueous solutions (particularly calculations of tautomeric stability and pKa), reactivity predictions based on automated transition state search, assembly of Boltzmann-averaged spectra such as vibrational and electronic circular dichroism, as well as nuclear magnetic resonance. Discussed also are quantum chemical calculations that are oriented toward materials science applications, in particular, prediction of properties of optoelectronic materials and organic semiconductors, and molecular catalyst design. The topic of treatment of conformations inevitably comes up in real world research projects and is considered as part of all the workflows mentioned above. In addition, we examine the role of machine learning methods in quantum chemical calculations performed by Jaguar, from auxiliary functions that return the approximate calculation runtime in a user interface, to prediction of actual molecular properties. The current work is second in a series of reviews of Jaguar, the first having been published more than ten years ago. Thus, this paper serves as a rare milestone on the path that is being traversed by Jaguar's development in more than thirty years of its existence.

Excitation of long-lived nuclear spin order using spin-locking: a geometrical formalism

Over the last two decades, numerous pulse sequences have been introduced for the excitation of long-lived spin order (LLS) in high fields. The long continuous wave (CW) or adiabatic pulses used in the SLIC and APSOC sequences should remind one of the spin-locking pulses that are used to induce cross-polarization (CP). Dynamics during these spin-lockings in CP experiments are explained through a geometrical formalism. However, the SLIC and APSOC sequences are described in terms of the energy-level picture or in the language of level anti-crossings. Motivated by this analogy, this work presents here a geometrical formalism for the LLS excitation by spin-locking pulses in weakly coupled systems. The formalism is similar to the one used for CP dynamics and reveals new pulse sequences involving CW or adiabatic locking. A similar formalism for the sustaining period of LLS is also provided, which reveals new features of the dynamics and suggests the usage of modulated spin-lockings for proper LLS sustaining. For strong and intermediate regimes, although a simple geometrical formalism seems infeasible, a new pulse sequence that employs a ramp-down adiabatic pulse for both LLS excitation and reconversion to observables in both these regimes is presented here. Given the similarities between LLS excitation and well-developed CP, it may be anticipated that this work would initiate the search for new LLS excitation methods and applications.

Hyperpolarized nuclear Overhauser enhancement of alanine methyl groups by doubly relayed proton exchange

Hyperpolarized water in dissolution dynamic nuclear polarization (dDNP) experiments has emerged as a promising method for enhancing nuclear magnetic resonance (NMR) signals, particularly in studies of proteins and peptides. Herein, we focus on the application of "proton exchange-doubly relayed" nuclear Overhauser effects (NOE) from hyperpolarized water to achieve positive signal enhancement of methyl groups in the side chain of an alanine-glycine peptide. In particular, we show a cascade hyperpolarization transfer. Initial proton exchange between solvent and amide introduces hyperpolarization into the peptide. Subsequently, intermolecular NOE relays the hyperpolarization first to Ala-Hα and then in a second step to the Ala-CH3 moiety. Both NOEs have negative signs. Hence, the twice-relayed NOE pathway leads to a positive signal enhancement of the methyl group with respect to the thermal equilibrium magnetization. This effect might indicate a way towards hyperpolarized water-based signal enhancement for methyl groups, which are often used for NMR studies of large proteins in solution.

Open-source magnetic resonance imaging: Improving access, science, and education through global collaboration

Open-source practices and resources in magnetic resonance imaging (MRI) have increased substantially in recent years. This trend started with software and data being published open-source and, more recently, open-source hardware designs have become increasingly available. These developments towards a culture of sharing and establishing nonexclusive global collaborations have already improved the reproducibility and reusability of code and designs, while providing a more inclusive approach, especially for low-income settings. Community-driven standardization and documentation efforts are further strengthening and expanding these milestones. The future of open-source MRI is bright and we have just started to discover its full collaborative potential. In this review we will give an overview of open-source software and open-source hardware projects in human MRI research.

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.

Conformational Analysis of 1,3-Difluorinated Alkanes

Fluorine substitution can have a profound impact on molecular conformation. Here, we present a detailed conformational analysis of how the 1,3-difluoropropylene motif (-CHF-CH2-CHF-) determines the conformational profiles of 1,3-difluoropropane, anti- and syn-2,4-difluoropentane, and anti- and syn-3,5-difluoroheptane. It is shown that the 1,3-difluoropropylene motif strongly influences alkane chain conformation, with a significant dependence on the polarity of the medium. The conformational effect of 1,3-fluorination is magnified upon chain extension, which contrasts with vicinal difluorination. Experimental evidence was obtained from NMR analysis, where polynomial complexity scaling simulation algorithms were necessary to enable J-coupling extraction from the strong second-order spectra, particularly for the large 16-spin systems of the difluorinated heptanes. These results improve our understanding of the conformational control toolkit for aliphatic chains, yield simple rules for conformation population analysis, and demonstrate quantum mechanical time-domain NMR simulations for liquid state systems with large numbers of strongly coupled spins.

DPPM-Bridged Binuclear Pt(II) Pincer Complexes: Chemistry, Structure, and Photophysics in Solution Revisited

A series of luminescent binuclear ([dppm{Pt(NNC)}2]2+) and mononuclear ([PPh3Pt(NNC)]+) complexes containing pincer ligands were synthesized and characterized. Photophysical characteristics of both types of complexes were studied in dichloromethane solution. In the solid phase, the binuclear compounds adopt a syn configuration where the {Pt(NNC)} fragments are held together due to intramolecular Pt-Pt bonding and π-stacking of the pincer ligand aromatic systems. Analysis of the complexes' molecular structure in solution by multinuclear NMR spectroscopy showed that the stacked intramolecular configuration is retained in fluid media, which is in complete agreement with a considerable red shift of the emission wavelength due to formation of the intramolecular Pt-Pt bond, leading to the transformation of an emissive excited state to 3MMLCT. It was also found that triethylamine quenches the emission of both types of complexes; the mechanism of quenching is a combination of dynamic and static channels of excited-state deactivation. In the case of binuclear complexes, deprotonation of the dppm methylene bridge by triethylamine also contributes to the chromophore quenching. To explain the observed chemistry of binuclear complex interactions with Et3N, a chemical equilibrium scheme was suggested, which was confirmed by quantitative monitoring of the 31P signal variations as a function of triethylamine concentration.

Universally Quantitative Band-Selective Pure Shift NMR Spectroscopy

NMR spectroscopy is often described as a quantitative analytical technique. Strictly, only the simple pulse-acquire experiment is universally quantitative, but the poor signal resolution of the 1H NMR pulse-acquie experiment frequently complicates quantitative analysis. Pure shift NMR techniques provide higher resolution, by reducing signal overlap, but they are susceptible to a variety of sources of site-dependent signal loss. Here, we introduce a new method that corrects for signal loss from such sources in band-selective pure shift NMR experiments, by performing different numbers of iterations of the same pulse sequence elements before acquisition to allow extrapolation back to the loss-free signal. We apply this method to both interferogram and semi-realtime acquisition modes, obtaining integrals within 1% of those acquired from a pulse-acquire experiment for a three-component mixture.

Relaxation Editing in NMR Using a New Two-Dimensional Long-Lived Coherence Method for Mixture Analysis

The exploration of metabolomics and targeted segments of proteins stands as a pivotal facet of Nuclear Magnetic Resonance (NMR) analysis, furnishing valuable insights into molecular architectures and potential therapeutic applications. The issue of spectral congestion frequently presents challenges in ascribing distinct peaks within the confines of both one-dimensional (1D) and two-dimensional (2D) NMR spectra. Numerous strategies have been proposed to resolve specific resonances in NMR spectra differentially. Among these approaches, relaxation editing emerges as a viable solution. In the realm of relaxation phenomena within NMR, Long-Lived States (LLS) and Long-Lived Coherences (LLC) manifest as promising phenomena, offering enhanced relaxation lifetimes in comparison to the traditional longitudinal (T1) and transverse (T2) relaxation times for coupled nuclear spins. Notably, LLC presents a pathway to attenuate uncoupled high-intensity peaks, effectively diminishing their impact. The foundation of this technique rests upon the premise that the relaxation lifetime in the rotating frame (T1ρ) remains smaller than TLLC. In pursuit of refining spectral assignments within complex mixtures, we introduce a new pulse sequence tailored for LLC Total Correlation Spectroscopy (LLC-TOCSY). This demonstrates efficacy in extracting LLC signals within configurations involving multiple coupled spins, thereby decluttering the spectrum and enhancing the accuracy of peak assignments. To validate the effectiveness of this method, a collection of samples was subjected to scrutiny, yielding compelling results.

Improved detection of magnetic interactions in proteins based on long-lived coherences

Living systems rely on molecular building blocks with low structural symmetry. Therefore, constituent amino acids and nucleotides yield short-lived nuclear magnetic responses to electromagnetic radiation. Magnetic signals are at the basis of molecular imaging, structure determination and interaction studies. In solution state, as the molecular weight of analytes increases, coherences with long lifetimes are needed to yield advantageous through-space magnetisation transfers. Interactions between magnetic nuclei can only be detected provided the lifetimes of spin order are sufficient. In J-coupled pairs of nuclei, long-lived coherences (LLC's) connect states with different spin-permutation symmetry. Here in, we show sustained LLC's in protein Lysozyme, weighing 14.3 kDa, with lifetimes twice as long as those of classical magnetisation for the aliphatic protons of glycine residues. We found for the first time that, in a protein of significant molecular weight, LLC's yield substantial through-space magnetisation transfers: spin-order transfer stemming from LLC's overcame transfers from classical coherences by factors > 2. Furthermore, in agreement with theory, the permutation symmetry of LLC-based transfers allows mapping interacting atoms in the protein structure with respect to the molecular plane of glycine residues in a stereospecific manner. These findings can extend the scope of liquid-state high-resolution biomolecular spectroscopy.

Controlling NMR spin systems for quantum computation

Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.

Spatially encoded pure-shift diffusion-ordered NMR spectroscopy yielded by chirp excitation

Spatially-encoded diffusion-ordered NMR spectroscopy (SPEN-DOSY) has emerged as a new time-efficient tool for the analysis of mixtures of small molecules in solution. Time efficiency is achieved using the concept of spatial parallelization of the effective gradient area, instead of the sequential incrementation used in conventional diffusion experiments. The data acquired with such sequences are then usually processed to extract diffusion coefficients, but cases when peak overlap in the 1H spectrum are difficult to address. Such limitation in conventional diffusion experiments is addressed via using the Pure Shift Yielded by CHirp Excitation (PSYCHE)-iDOSY sequence. Here we have adapted the PSYCHE-iDOSY sequence by using echo planar spectroscopic imaging (EPSI) to acquire SPEN-DOSY data. The pure shift mode of PSYCHE separates the overlapped components and a modified Stejskal-Tanner equation is used to extract the corresponding diffusion coefficient. The primary results obtained with the above-mentioned mixtures seem to open the possibility of separating complex mixtures in less time than PSYCHE-iDOSY.

Quantitative Analysis of 2D EXSY NMR Spectra of Strongly Coupled Spin Systems in Transmembrane Exchange

Solute translocation by membrane transport proteins is a vital biological process that can be tracked, on the sub-second timescale, using nuclear magnetic resonance (NMR). Fluorinated substrate analogues facilitate such studies because of high sensitivity of 19 F NMR and absence of background signals. Accurate extraction of translocation rate constants requires precise quantification of NMR signal intensities. This becomes complicated in the presence of J-couplings, cross-correlations, and nuclear Overhauser effects (NOE) that alter signal integrals through mechanisms unrelated to translocation. Geminal difluorinated motifs introduce strong and hard-to-quantify contributions from non-exchange effects, the nuanced nature of which makes them hard to integrate into data analysis methodologies. With analytical expressions not being available, numerical least squares fitting of theoretical models to 2D spectra emerges as the preferred quantification approach. For large spin systems with simultaneous coherent evolution, cross-relaxation, cross-correlation, conformational exchange, and membrane translocation between compartments with different viscosities, the only available simulation framework is Spinach. In this study, we demonstrate GLUT-1 dependent membrane transport of two model sugars featuring CF2 and CF2 CF2 fluorination motifs, with precise determination of translocation rate constants enabled by numerical fitting of 2D EXSY spectra. For spin systems and kinetic networks of this complexity, this was not previously tractable.

Colloidal pathways of amorphous calcium carbonate formation lead to distinct water environments and conductivity

CaCO3 is the most abundant biomineral and a major constituent of incrustations arising from water hardness. Polycarboxylates play key roles in controlling mineralization. Herein, we present an analytical and spectroscopic study of polycarboxylate-stabilized amorphous CaCO3 (ACC) and its formation via a dense liquid precursor phase (DLP). Polycarboxylates facilitate pronounced, kinetic bicarbonate entrapment in the DLP. Since bicarbonate is destabilized in the solid state, DLP dehydration towards solid ACC necessitates the formation of locally calcium deficient sites, thereby inhibiting nucleation. Magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy of poly-aspartate-stabilized ACC reveals the presence of two distinct environments. The first contains immobile calcium and carbonate ions and structural water molecules, undergoing restricted, anisotropic motion. In the second environment, water molecules undergo slow, but isotropic motion. Indeed, conductive atomic force microscopy (C-AFM) reveals that ACC conducts electrical current, strongly suggesting that the mobile environment pervades the bulk of ACC, with dissolved hydroxide ions constituting the charge carriers. We propose that the distinct environments arise from colloidally stabilized interfaces of DLP nanodroplets, consistent with the pre-nucleation cluster (PNC) pathway.

Delivering Robust Proton-Only Sensing of Hyperpolarized [1,2-13C2]-Pyruvate Using Broad-Spectral-Range Nuclear Magnetic Resonance Pulse Sequences

Hyperpolarized [1-13C]pyruvate is the leading hyperpolarized injectable contrast agent and is currently under evaluation in clinical trials for molecular imaging of metabolic diseases, including cardiovascular disease and cancer. One aspect limiting broad scalability of the technique is that hyperpolarized 13C MRI requires specialized 13C hardware and software that are not generally available on clinical MRI scanners, which employ proton-only detection. Here, we present an approach that uses pulse sequences to transfer 13C hyperpolarization to methyl protons for detection of the 13C-13C pyruvate singlet, employing proton-only excitation and detection only. The new pulse sequences are robust to the B1 and B0 magnetic field inhomogeneities. The work focuses on singlet-to-magnetization (S2M) and rotor-synchronized (R) pulses, both relying on trains of hard pulses with broad spectral width coverage designed to effectively transform hyperpolarized 13C2-singlet hyperpolarization to 1H polarization on the CH3 group of [1,2-13C2]pyruvate. This approach may enable a broader adoption of hyperpolarized MRI as a molecular imaging technique.

Broadband Cross-Polarization to Half-Integer Quadrupolar Nuclei: Wideline Static NMR Spectroscopy

Cross-polarization (CP) is a technique commonly used for the signal enhancement of NMR spectra; however, applications to quadrupolar nuclei have heretofore been limited due to a number of problems, including poor spin-locking efficiency, inconvenient relaxation times, and reduced CP efficiencies over broad spectral bandwidths─this is unfortunate, since they constitute 73% of NMR-active nuclei in the periodic table. The Broadband Adiabatic Inversion CP (BRAIN-CP) pulse sequence has proven useful for the signal enhancement of wideline and ultra-wideline (i.e., 250 kHz to several MHz in breadth) powder patterns arising from stationary samples; however, a comprehensive investigation of its application to half-integer quadrupolar nuclei (HIQN) is currently lacking. Herein, we present theoretical and experimental considerations for applying BRAIN-CP to acquire central-transition (CT, +1/2 ↔ -1/2) powder patterns of HIQN. Consideration is given to parameters crucial to the success of the experiment, such as the Hartmann-Hahn (HH) matching conditions and the phase modulation of the contact pulse. Modifications to the BRAIN-CP sequence such as flip-back (FB) pulses and ramped contact pulses applied to the 1H spins are used for the reduction of experimental times and increased CP bandwidth capabilities, respectively. Spectra for a series of quadrupolar nuclei with broad CT powder patterns, including 35Cl (S = 3/2), 55Mn (S = 5/2), 59Co (S = 7/2), and 93Nb (S = 9/2), are acquired via direct excitation (CPMG and WCPMG) and indirect excitation (CP/CPMG and BRAIN-CP) methods. We demonstrate that proper implementation of the sequence can enable 1H-S broadband CP over a bandwidth of 1 MHz, which to the best of our knowledge is the largest CP bandwidth reported to date. Finally, we establish the basic principles necessary for simplified optimization and execution of the BRAIN-CP pulse sequence for a wide range of HIQNs.

Digital quantum simulation of NMR experiments

Simulations of nuclear magnetic resonance (NMR) experiments can be an important tool for extracting information about molecular structure and optimizing experimental protocols but are often intractable on classical computers for large molecules such as proteins and for protocols such as zero-field NMR. We demonstrate the first quantum simulation of an NMR spectrum, computing the zero-field spectrum of the methyl group of acetonitrile using four qubits of a trapped-ion quantum computer. We reduce the sampling cost of the quantum simulation by an order of magnitude using compressed sensing techniques. We show how the intrinsic decoherence of NMR systems may enable the zero-field simulation of classically hard molecules on relatively near-term quantum hardware and discuss how the experimentally demonstrated quantum algorithm can be used to efficiently simulate scientifically and technologically relevant solid-state NMR experiments on more mature devices. Our work opens a practical application for quantum computation.

Optimal control pulses for the 1.2-GHz (28.2-T) NMR spectrometers

The ability to measure nuclear magnetic resonance (NMR) spectra with a large sample volume is crucial for concentration-limited biological samples to attain adequate signal-to-noise (S/N) ratio. The possibility to measure with a 5-mm cryoprobe is currently absent at the 1.2-GHz NMR instruments due to the exceedingly high radio frequency power demands, which is four times compared to 600-MHz instruments. Here, we overcome the high-power demands by designing optimal control (OC) pulses with up to 20 times lower power requirements than currently necessary at a 1.2-GHz spectrometer. We show that multidimensional biomolecular NMR experiments constructed using these OC pulses can bestow improvement in the S/N ratio of up to 26%. With the expected power limitations of a 5-mm cryoprobe, we observe an enhancement in the S/N ratio of more than 240% using our OC sequences. This motivates the development of a cryoprobe with a larger volume than the current 3-mm cryoprobes.

Biomolecular NMR spectroscopy in the era of artificial intelligence

Biomolecular nuclear magnetic resonance (NMR) spectroscopy and artificial intelligence (AI) have a burgeoning synergy. Deep learning-based structural predictors have forever changed structural biology, yet these tools currently face limitations in accurately characterizing protein dynamics, allostery, and conformational heterogeneity. We begin by highlighting the unique abilities of biomolecular NMR spectroscopy to complement AI-based structural predictions toward addressing these knowledge gaps. We then highlight the direct integration of deep learning approaches into biomolecular NMR methods. AI-based tools can dramatically improve the acquisition and analysis of NMR spectra, enhancing the accuracy and reliability of NMR measurements, thus streamlining experimental processes. Additionally, deep learning enables the development of novel types of NMR experiments that were previously unattainable, expanding the scope and potential of biomolecular NMR spectroscopy. Ultimately, a combination of AI and NMR promises to further revolutionize structural biology on several levels, advance our understanding of complex biomolecular systems, and accelerate drug discovery efforts.

Accounting for gradient non-uniformity in spatially-encoded diffusion-ordered NMR spectroscopy

Diffusion-ordered NMR spectroscopy (DOSY) is a powerful tool for the analysis of mixtures. Spatially-encoded (SPEN) DOSY makes it possible to collect a complete DOSY data set in a single scan, through spatial parallelisation of the gradient dimension. One limitation of current SPEN DOSY experiments is that the data is analysed assuming that the field gradient is uniform over the sample. This is usually not the case for high resolution NMR probes, and even less for triple-axis gradient probes. In this work, we have developed methods to account for gradient non-uniformity in the processing of SPEN DOSY experiment. We have first mapped the field gradient, using a stimulated echo (STE) NMR sequence with a weak readout gradient. We have then modified the calculation of the position-dependent effective gradient pulse area that is used in the analysis of SPEN DOSY data. The resulting model was validated through numerical simulations. A comparison of results obtained with and without inclusion of the effect of non-uniform gradients shows that the proposed approach increases the accuracy of SPEN DOSY experiments.

Steady state effects introduced by local relaxation modes on J-driven DNP-enhanced NMR

One of solution-state Nuclear Magnetic Resonance (NMR)'s main weaknesses, is its relative insensitivity. J-driven Dynamic Nuclear Polarization (JDNP) was recently proposed for enhancing solution-state NMR's sensitivity, by bypassing the limitations faced by conventional Overhauser DNP (ODNP), at the high magnetic fields where most analytical research is performed. By relying on biradicals with inter-electron exchange couplings Jex on the order of the electron Larmor frequency ωE, JDNP was predicted to introduce a transient enhancement in NMR's nuclear polarization at high magnetic fields, and for a wide range of rotational correlation times of medium-sized molecules in conventional solvents. This communication revisits the JDNP proposal, including additional effects and conditions that were not considered in the original treatment. These include relaxation mechanisms arising from local vibrational modes that often dominate electron relaxation in organic radicals, as well as the possibility of using biradicals with Jex of the order of the nuclear Larmor frequency ωN as potential polarizing agents. The presence of these new relaxation effects lead to variations in the JDNP polarization mechanism originally proposed, and indicate that triplet-to-singlet cross-relaxation processes may lead to a nuclear polarization enhancement that persists even at steady states. The physics and potential limitations of the ensuing theoretical derivations, are briefly discussed.

On the effects of quadrupolar relaxation in Earth's field NMR spectra

There is growing interest in using low-field magnetic resonance experiments for routine chemical characterization. Earth's field NMR is one such technique that can garner structural information and enable sample differentiation with low cost and highly portable designs. The resulting NMR spectra are primarily influenced by J-couplings, resulting in so-called J-coupled spectra (JCS). Many small molecules include atoms with NMR-active nuclei that are quadrupolar either at natural abundance or are often isotopically enriched (e.g.,2H, 6Li, 11B, 14N, 17O, etc.) where the effects of quadrupolar J-couplings and relaxation on JCS of strongly- and weakly-coupled spin systems have not been explored to date. Herein, using a set of seven fluoropyridine samples with unique substitution and J-couplings, we demonstrate that the 14N relaxation rates can induce drastic line-broadening in the JCS. This includes a previously unexplored unique line broadening mechanism enabled by strongly coupled spins at low-field. Numerical simulations are used to model and refine the magnitudes and signs of J-couplings, as well as indirectly determine the 14N relaxation rates in a single 1D experiment that has a higher fidelity than observed in high-field NMR experiments.

Selective filtration of NMR signals arising from weakly- and strongly-coupled spin systems

Nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for analyzing chemical and biological systems. However, in complex solutions with similar molecular components, NMR signals can overlap, making it challenging to distinguish and quantify individual species. In this paper, we introduce new spectral editing sequences that exploit the differences in nuclear spin interactions (J-couplings) between weakly- and strongly-coupled two-spin systems. These sequences selectively attenuate or nullify undesired spin magnetization while they preserve the desired signals, resulting in simplified NMR spectra and potentially facilitating single-species imaging applications. We demonstrate the effectiveness of our approach using a 31P spectral filtration method on a model system of nicotinamide dinucleotide (NAD), which exists in oxidized (NAD+) and reduced (NADH) forms. The presented sequences are robust to field inhomogeneity, do not require additional sub-spectra, and retain a significant portion of the original signal.

Meta-analysis and open-source database for in vivo brain Magnetic Resonance spectroscopy in health and disease

Proton (1H) Magnetic Resonance Spectroscopy (MRS) is a non-invasive tool capable of quantifying brain metabolite concentrations in vivo. Prioritization of standardization and accessibility in the field has led to the development of universal pulse sequences, methodological consensus recommendations, and the development of open-source analysis software packages. One on-going challenge is methodological validation with ground-truth data. As ground-truths are rarely available for in vivo measurements, data simulations have become an important tool. The diverse literature of metabolite measurements has made it challenging to define ranges to be used within simulations. Especially for the development of deep learning and machine learning algorithms, simulations must be able to produce accurate spectra capturing all the nuances of in vivo data. Therefore, we sought to determine the physiological ranges and relaxation rates of brain metabolites which can be used both in data simulations and as reference estimates. Using the Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA) guidelines, we've identified relevant MRS research articles and created an open-source database containing methods, results, and other article information as a resource. Using this database, expectation values and ranges for metabolite concentrations and T2 relaxation times are established based upon a meta-analyses of healthy and diseased brains.

Cross-Polarization Schemes for Improved Heteronuclear Transfers Involving Labile Protons in Biomolecular Solution NMR

INEPT-based experiments are widely used for 1 H→15 N transfers, but often fail when involving labile protons due to solvent exchanges. J-based cross polarization (CP) strategies offer a more efficient alternative to perform such transfers, particularly when leveraging the Hwater ↔ ${ \leftrightarrow }$ HN exchange process to boost the 1 H→15 N transfer process. This leveraging, however, demands the simultaneous spin-locking of both Hwater and HN protons by a strong 1 H RF field, while fulfilling the γH B1,H =γN B1,N Hartmann-Hahn matching condition. Given the low value of γN /γH , however, these demands are often incompatible-particularly when experiments are executed by the power-limited cryogenic probes used in contemporary high field NMR. The present manuscript discusses CP alternatives that can alleviate this limitation, and evaluates their performance on urea, amino acids, and intrinsically disordered proteins. These alternatives include new CP variants based on frequency-swept and phase-modulated pulses, designed to simultaneously fulfill the aforementioned conflicting conditions. Their performances vis-à-vis current options are theoretically analyzed with Liouville-space simulations, and experimentally tested with double and triple resonance transfer experiments.

Simulation and design of shaped pulses beyond the piecewise-constant approximation

Response functions of resonant circuits create ringing artefacts if their input changes rapidly. When physical limits of electromagnetic spectroscopies are explored, this creates two types of problems. Firstly, simulation: the system must be propagated accurately through every response transient, this may be computationally expensive. Secondly, optimal control: circuit response must be taken into account; it may be advantageous to design pulses that are resilient to such distortions. At the root of both problems is the popular piecewise-constant approximation for control sequences in the rotating frame; in magnetic resonance it has persisted since the earliest days and has become entrenched in the commercially available hardware. In this paper, we report an implementation and benchmarks of recent Lie-group methods that can efficiently simulate and optimise smooth control sequences.

Multiple quantum filtered nuclear magnetic resonance of 23Na+ in uniformly stretched and compressed hydrogels

Stretching or compressing hydrogels creates anisotropic environments that lead to motionally averaged alignment of embedded guest quadrupolar nuclear spins such as 23Na+. These distorted hydrogels can elicit a residual quadrupolar coupling that gives an oscillation in the trajectories of single quantum coherences (SQCs) as a function of the evolution time during a spin-echo experiment. We present solutions to equations of motion derived with a Liouvillian superoperator approach, which encompass the coherent quadrupolar interaction in conjunction with relaxation, to give a full analytical description of the evolution trajectories of rank-1 (T^1±1), rank-2 (T^2±1), and rank-3 (T^3±1) SQCs. We performed simultaneous numerical fitting of the experimental 23Na nuclear magnetic resonance (NMR) spectra and rank-2 (T^2±1) and rank-3 (T^3±1) SQC evolution trajectories measured in double and triple quantum filtered experiments, respectively. We estimated values of the quadrupolar coupling constant CQ, rotational correlation time τC, and 3 × 3 Saupe order matrix. We performed simultaneous fitting of the analytical expressions to the experimental data to estimate values of the quadrupolar coupling frequency ωQ/2π, residual quadrupolar coupling ωQ/2π, and corresponding spherical order parameter S0*, which showed a linear dependence on the extent of uniform hydrogel stretching and compression. The analytical expressions were completely concordant with the numerical approach. The insights gained here can be extended to more complicated (biological) systems such as 23Na+ bound to proteins or located inside and outside living cells in high-field NMR experiments and, by extension, to the anisotropic environments found in vivo with 23Na magnetic resonance imaging.

Spin dynamics of [1,2-13C2]pyruvate hyperpolarization by parahydrogen in reversible exchange at micro Tesla fields

Hyperpolarization of 13C-pyruvate via Signal Amplificaton By Reversibble Exchange (SABRE) is an important recent discovery because of both the relative simplicity of hyperpolarization and the central biological relevance of pyruvate as a biomolecular probe for in vitro or in vivo studies. Here, we analyze the [1,2-13C2]pyruvate-SABRE spin system and its field dependence theoretically and experimentally. We provide first-principles analysis of the governing 4-spin dihydride-13C2 Hamiltonian and numerical spin dynamics simulations of the 7-spin dihydride-13C2-CH3 system. The analytical and the numerical results are compared to matching systematic experiments. With these methods we unravel the observed spin state mixing of singlet states and triplet states at microTesla fields and we also analyze the dynamics during transfer from micro-Tesla field to high field for detection to understand the resulting spectra from the [1,2-13C2]pyruvate-SABRE system.

Meta-analysis and Open-source Database for In Vivo Brain Magnetic Resonance Spectroscopy in Health and Disease

Proton ( 1 H) Magnetic Resonance Spectroscopy (MRS) is a non-invasive tool capable of quantifying brain metabolite concentrations in vivo . Prioritization of standardization and accessibility in the field has led to the development of universal pulse sequences, methodological consensus recommendations, and the development of open-source analysis software packages. One on-going challenge is methodological validation with ground-truth data. As ground-truths are rarely available for in vivo measurements, data simulations have become an important tool. The diverse literature of metabolite measurements has made it challenging to define ranges to be used within simulations. Especially for the development of deep learning and machine learning algorithms, simulations must be able to produce accurate spectra capturing all the nuances of in vivo data. Therefore, we sought to determine the physiological ranges and relaxation rates of brain metabolites which can be used both in data simulations and as reference estimates. Using the Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA) guidelines, we've identified relevant MRS research articles and created an open-source database containing methods, results, and other article information as a resource. Using this database, expectation values and ranges for metabolite concentrations and T 2 relaxation times are established based upon a meta-analyses of healthy and diseased brains.

Indirectly detected satellite-transition quadrupolar NMR via progressive saturation of the proton reservoir

Static satellite-transitions (ST) NMR line shapes from half-integer quadrupolar nuclei could be very informative: they can deliver insight about local motions over a wide range of timescales, and can report on small changes in the local electronic environments as reflected by variations in the quadrupolar parameters. Satellite transitions, however, are typically "invisible" for half-integer quadrupolar nuclei due to their sheer breadth, leading to low signal-to-noise ratio -especially for unreceptive low-gamma or dilute quadrupolar nuclei. Very recently we have introduced a method for enhancing the NMR sensitivity of unreceptive X nuclei in static solids dubbed PROgressive Saturation of the Proton Reservoir (PROSPR), which opens the possibility of magnifying the signals from such spins by repeatedly imprinting frequency-selective X-driven depolarizations on the much more sensitive ¹H NMR signal. Here, we show that PROSPR's efficacy is high enough for enabling the detection of static ST NMR for challenging species like ³⁵Cl, ³³S and even ¹⁷O -all at natural-abundance. The ensuing ST-PROSPR NMR experiment thus opens new approaches to probe ultra-wideline (6-8 MHz wide) spectra. These highly pronounced anisotropies can in turn deliver new vistas about dynamic changes in solids, as here illustrated by tracking ST line shapes as a function of temperature during thermally-driven events.

Multiple Stroboscopic Detection of Long-Lived Nuclear Magnetization for Glutathione Oxidation Kinetics

Imaging the molecular kinetics of antioxidants by magnetic resonance can contribute to the mechanistic understanding of therapeutic approaches. Magnetic resonance detection of the response to flashes of oxidative stress requires sequential spectroscopy on the same time scale on which reactive oxygen species are generated. To this effect, we propose a single-polarization multiple-detection stroboscopic experiment. We demonstrate this experiment for the follow-up of glutathione oxidation kinetics. On-the-fly stroboscopic detection minimizes the durations necessary for single acquisitions yet necessitates sustaining of magnetization lifetimes. Long-lived proton spin states (LLS) in the cysteine and glycine residues of glutathione with T_LLS up to 16 s are reached. Based on ¹H LLS, we followed fast oxidation kinetics in the glutathione redox pair GSH/GSSG. This new detection method allows sampling of long-lived spin order multiple times via small flip-angle excitations. This establishes the ground for the follow-up of redox processes detecting GSH/GSSG kinetics as magnetic-resonance biomarker of FLASH oxidative processes on time scales of tens of seconds.

Simulation of NMR spectra at zero and ultralow fields from A to Z - a tribute to Prof. Konstantin L'vovich Ivanov

Simulating NMR experiments may appear mysterious and even daunting for those who are new to the field. Yet, broken down into pieces, the process may turn out to be easier than expected. Quite the opposite, it is in fact a powerful and playful means to get insights into the spin dynamics of NMR experiments. In this tutorial paper, we show step by step how some NMR experiments can be simulated, assuming as little prior knowledge from the reader as possible. We focus on the case of NMR at zero and ultralow fields, an emerging modality of NMR in which the spin dynamics are dominated by spin-spin interactions rather than spin-field interactions, as is usually the case with conventional high-field NMR. We first show how to simulate spectra numerically. In a second step, we detail an approach to construct an eigenbasis for systems of spin-1 / 2 nuclei at zero field. We then use it to interpret the numerical simulations.

Magneto-Structural Correlations in a Mixed Porphyrin(Cu2+ )/Trityl Spin System: Magnitude, Sign, and Distribution of the Exchange Coupling Constant

Tetrathiatriarylmethyl radicals (TAM or trityl) are receiving increasing attention in various fields of magnetic resonance such as imaging, dynamic nuclear polarization, spin labeling, and, more recently, molecular magnetism and quantum information technology. Here, a trityl radical attached via a phenyl bridge to a copper(II)tetraphenylporphyrin was synthesized, and its magnetic properties studied by multi-frequency continuous-wave electron paramagnetic resonance (EPR) spectroscopy and magnetic measurements. EPR revealed that the electron spin-spin coupling constant J between the trityl and Cu²⁺ spin centers is ferromagnetic with a magnitude of -2.3 GHz (-0.077 cm^-1 , + J S → 1 S → 2 ${+J{\vec{S}}_{1}{\vec{S}}_{2}}$ convention) and a distribution width of 1.2 GHz (0.040 cm^-1 ). With the help of density functional theory (DFT) calculations, the obtained ferromagnetic exchange coupling, which is unusual for para-substituted phenyl-bridged biradicals, could be related to the almost perpendicular orientation of the phenyl linker with respect to the porphyrin and trityl ring planes in the energy minimum, while the J distribution was rationalized by the temperature weighted rotation of the phenyl bridge about the molecular axis connecting both spin centers. This study exemplifies the importance of molecular dynamics for the homogeneity (or heterogeneity) of the magnetic properties of trityl-based systems.

Microwave-free J-driven dynamic nuclear polarization: A proposal for enhancing the sensitivity of solution-state NMR

J-driven dynamic nuclear polarization (JDNP) was recently proposed for enhancing the sensitivity of solution-state nuclear magnetic resonance (NMR), while bypassing the limitations faced by conventional (Overhauser) DNP at magnetic fields of interest in analytical applications. Like Overhauser DNP, JDNP also requires saturating the electronic polarization using high-frequency microwaves known to have poor penetration and associated heating effects in most liquids. The present microwave-free JDNP (MF-JDNP) proposal seeks to enhance solution NMR's sensitivity by shuttling the sample between higher and lower magnetic fields, with one of these fields providing an electron Larmor frequency that matches the interelectron exchange coupling J_{ex}. If spins cross this so-called JDNP condition sufficiently fast, we predict that a sizable nuclear polarization will be created without microwave irradiation. This MF-JDNP proposal requires radicals whose singlet-triplet self-relaxation rates are dominated by dipolar hyperfine relaxation, and shuttling times that can compete with these electron relaxation processes. This paper discusses the theory behind the MF-JDNP, as well as proposals for radicals and conditions that could enable this new approach to NMR sensitivity enhancement.

The effect of the zero-field splitting in light-induced pulsed dipolar electron paramagnetic resonance (EPR) spectroscopy

Laser-induced magnetic dipole (LaserIMD) spectroscopy and light-induced double electron-electron resonance (LiDEER) spectroscopy are important techniques in the emerging field of light-induced pulsed dipolar electron paramagnetic resonance (EPR) spectroscopy (light-induced PDS). These techniques use the photoexcitation of a chromophore to the triplet state and measure its dipolar coupling to a neighboring electron spin, which allows the determination of distance restraints. To date, LaserIMD and LiDEER have been analyzed with software tools that were developed for a pair of two S = 1 / 2 spins and that neglected the zero-field splitting (ZFS) of the excited triplet. Here, we explore the limits of this assumption and show that the ZFS can have a significant effect on the shape of the dipolar trace. For a detailed understanding of the effect of the ZFS, a theoretical description for LaserIMD and LiDEER is derived, taking into account the non-secular terms of the ZFS. Simulations based on this model show that the effect of the ZFS is not that pronounced in LiDEER for experimentally relevant conditions. However, the ZFS leads to an additional decay in the dipolar trace in LaserIMD. This decay is not that pronounced in Q-band but can be quite noticeable for lower magnetic field strengths in X-band. Experimentally recorded LiDEER and LaserIMD data confirm these findings. It is shown that ignoring the ZFS in the data analysis of LaserIMD traces can lead to errors in the obtained modulation depths and background decays. In X-band, it is additionally possible that the obtained distance distribution is plagued by long distance artifacts.

Effects of inter-radical interactions and scavenging radicals on magnetosensitivity: spin dynamics simulations of proposed radical pairs

Although the magnetosensitivity to weak magnetic fields, such as the geomagnetic field, which was exhibited by radical pairs that are potentially responsible for avian navigation, has been previously investigated by spin dynamics simulations, understanding this behavior for proposed radical pairs in other species is limited. These include, for example, radical pairs formed in the single-cell green alga Chlamydomonas reinhardtii (CraCRY) and in Columba livia (ClCRY4). In addition, the radical pair of FADH^• with the one-electron reduced cyclobutane thymine dimer that was shown to be sensitive to weak magnetic fields has been of interest. In this work, we investigated the directional magnetosensitivity of these radical pairs to a weak magnetic field by spin dynamics simulations. We find significant reduction in the magnetosensitivity by inclusion of dipolar and exchange interactions, which can be mitigated by a scavenging radical, as demonstrated for the [FAD^•- TyrD^•] radical pair in CraCRY, but not for the [FADH^• T□T^•-] radical pair because of the large exchange coupling. The directional magnetosensitivity of the ClCRY4 [FAD^•- TyrE^•] radical pair can survive this adverse effect even without the scavenging reaction, possibly motivating further experimental exploration.

Theoretical analysis of flow effects in spatially encoded diffusion NMR

The measurement of translational diffusion coefficients by nuclear magnetic resonance (NMR) spectroscopy is essential in a broad range of fields, including organic, inorganic, polymer, and supramolecular chemistry. It is also a powerful method for mixture analysis. Spatially encoded diffusion NMR (SPEN DNMR)" is a time efficient technique to collect diffusion NMR data, which is particularly relevant for the analysis of samples that evolve in time. In many cases, motion other than diffusion is present in NMR samples. This is, for example, the case of flow NMR experiments, such as in online reaction monitoring and in the presence of sample convection. Such motion is deleterious for the accuracy of DNMR experiments in general and for SPEN DNMR in particular. Limited theoretical understanding of flow effects in SPEN DNMR experiments is an obstacle for their broader experimental implementation. Here, we present a detailed theoretical analysis of flow effects in SPEN DNMR and of their compensation, throughout the relevant pulse sequences. This analysis is validated by comparison with numerical simulation performed with the Fokker-Planck formalism. We then consider, through numerical simulation, the specific cases of constant, laminar, and convection flow and the accuracy of SPEN DNMR experiments in these contexts. This analysis will be useful for the design and implementation of fast diffusion NMR experiments and for their applications.

High-resolution NMR spectroscopy for measuring complex samples based on chemical-shift-difference selection

NMR spectroscopy serves as an immensely powerful tool for component assignments and molecular structure elucidations. However, proton NMR spectra are generally trapped with spectral congestion caused by limited frequency differences and complex multiplets. 2D NMR can effectively relieve spectral congestion, but its resolution and acquisition efficiency are restricted by the broad spectral bandwidth. Herein, we introduce an NMR method based on chemical-shift-difference selection by chirp excitation to record high-resolution 2D NMR spectra for extracting coupling correlation networks and multiplet structures, suitable for measurements on complex samples. The performance of the proposed method is illustrated in determining diastereotopic methylene protons, small frequency-difference coupled proton pairs of furanose, pyranose and benzene rings. This study is expected to benefit molecular structure elucidation and composition analysis of complex samples in chemistry, biochemistry and metabonomics.

Proton-Only Sensing of Hyperpolarized [1,2-13C2]Pyruvate

Hyperpolarized MRI is emerging as a next-generation molecular imaging modality that can detect metabolic transformations in real time deep inside tissue and organs. 13C-hyperpolarized pyruvate is the leading hyperpolarized contrast agent that can probe cellular energetics in real time. Currently, hyperpolarized MRI requires specialized "multinuclear" MRI scanners that have the ability to excite and detect 13C signals. The objective of this work is the development of an approach that works on conventional (i.e., proton-only) MRI systems while taking advantage of long-lived 13C hyperpolarization. The long-lived singlet state of [1,2-13C2]pyruvate is hyperpolarized with parahydrogen in reversible exchange, and subsequently, the polarization is transferred from the 13C2 spin pair to the methyl protons of pyruvate for detection. This polarization transfer is accomplished with spin-lock induced crossing pulses that are only applied to the methyl protons yet access the hyperpolarization stored in the 13C2 singlet state. Theory and first experimental demonstrations are provided for our method, which obviates 13C excitation and detection for proton sensing of 13C-hyperpolarized pyruvate with an overall experimental-polarization transfer efficiency of ∼22% versus a theoretically predicted polarization transfer efficiency of 25%.

Adaptive optimal control of entangled qubits

Developing fast, robust, and accurate methods for optimal control of quantum systems comprising interacting particles is one of the most active areas of current science. Although a valuable repository of algorithms is available for numerical applications in quantum control, the high computational cost is somewhat overlooked. Here, we present a fast and accurate optimal control algorithm for systems of interacting qubits, QOALA (quantum optimal control by adaptive low-cost algorithm), which is predicted to offer [Formula: see text](M2) speedup for an M-qubit system, compared to the state-of-the-art exact methods, without compromising overall accuracy of the optimal solution. The method is general and compatible with diverse Hamiltonian structures. The proposed approach uses inexpensive low-accuracy approximations of propagators far from the optimum, adaptively switching to higher accuracy, higher-cost propagators when approaching the optimum. In addition, the utilization of analytical Lie algebraic derivatives that do not require computationally expensive matrix exponential brings even better performance.

Geometrization for Energy Levels of Isotropic Hyperfine Hamiltonian Block and Related Central Spin Problems for an Arbitrarily Complex Set of Spin-1/2 Nuclei

Description of interacting spin systems relies on understanding the spectral properties of the corresponding spin Hamiltonians. However, the eigenvalue problems arising here lead to algebraic problems too complex to be analytically tractable. This is already the case for the simplest nontrivial (Kmax−1) block for an isotropic hyperfine Hamiltonian for a radical with spin-12 nuclei, where n nuclei produce an n-th order algebraic equation with n independent parameters. Systems described by such blocks are now physically realizable, e.g., as radicals or radical pairs with polarized nuclear spins, appear as closed subensembles in more general radical settings, and have numerous counterparts in related central spin problems. We provide a simple geometrization of energy levels in this case: given n spin-12 nuclei with arbitrary positive couplings ai, take an n-dimensional hyper-ellipsoid with semiaxes ai, stretch it by a factor of n+1 along the spatial diagonal (1, 1, …, 1), read off the semiaxes of thus produced new hyper-ellipsoid qi, augment the set {qi} with q0=0, and obtain the sought n+1 energies as Ek=−12qk2+14∑iai. This procedure provides a way of seeing things that can only be solved numerically, giving a useful tool to gain insights that complement the numeric simulations usually inevitable here, and shows an intriguing connection to discrete Fourier transform and spectral properties of standard graphs.

Sensing Magnetic Field and Intermolecular Interactions in Diamagnetic Solution Using Residual Dipolar Couplings of Zephycandidine

An unusual residual dipolar coupling of methylene protons was recorded in NMR spectra because aromatic zephycandidine has preferential orientation at the external magnetic field. The observed splitting contains contribution from the dipole-dipole D-coupling and the anisotropic component of J-coupling. Absolute values of the anisotropy of magnetic susceptibility |Δχ_ax| are larger for protic solvents because of the hydrogen-bonding compared to aprotic solvents for which polar and dispersion forces are more important. The energy barrier for the reorientation due to hydrogen-bonding is 1.22 kJ/mol in methanol-d_4, 0.85 kJ/mol in ethanol-d₆ and 0.87 kJ/mol in acetic acid-d₆. In dimethyl sulfoxide-d₆, 1.08 kJ/mol corresponds to the interaction of solvent lone pair electrons with π-electrons of zephycandidine. This energy barrier decreases for acetone-d₆ which has smaller electric dipole moment. In acetonitrile-d₃, there is no energy barrier which suggests solvent ordering around the solute due to the solvent-solvent interactions. The largest absolute values of the magnetic anisotropy are observed for aromatic benezene-d₆ and tolune-d₈ which have their own preferential orientation and enhance the order in the solution. The magnetic anisotropy of "isolated" zephycandidine, not hindered by intermolecular interaction could be estimated from the correlation between Δχ_ax and cohesion energy density.

Signal-to-Noise Ratio Enhancement of Single-Voxel In Vivo 31P and 1H Magnetic Resonance Spectroscopy in Mice Brain Data Using Low-Rank Denoising

Magnetic resonance spectroscopy (MRS) is a noninvasive technique for measuring metabolite concentration. It can be used for preclinical small animal brain studies using rodents to provide information about neurodegenerative diseases and metabolic disorders. However, data acquisition from small volumes in a limited scan time is technically challenging due to its inherently low sensitivity. To mitigate this problem, this study investigated the feasibility of a low-rank denoising method in enhancing the quality of single voxel multinuclei (³¹P and ¹H) MRS data at 9.4 T. Performance was evaluated using in vivo MRS data from a normal mouse brain (³¹P and ¹H) and stroke mouse model (¹H) by comparison with signal-to-noise ratios (SNRs), Cramer-Rao lower bounds (CRLBs), and metabolite concentrations of a linear combination of model analysis results. In ³¹P MRS data, low-rank denoising resulted in improved SNRs and reduced metabolite quantification uncertainty compared with the original data. In ¹H MRS data, the method also improved the SNRs, CRLBs, but it performed better for ³¹P MRS data with relatively simpler patterns compared to the ¹H MRS data. Therefore, we suggest that the low-rank denoising method can improve spectra SNR and metabolite quantification uncertainty in single-voxel in vivo ³¹P and ¹H MRS data, and it might be more effective for ³¹P MRS data. The main contribution of this study is that we demonstrated the effectiveness of the low-rank denoising method on small-volume single-voxel MRS data. We anticipate that our results will be useful for the precise quantification of low-concentration metabolites, further reducing data acquisition voxel size, and scan time in preclinical MRS studies.

Triplet Photosensitized para-Hydrogen Induced Polarization

Despite its enormous utility in structural characterization, nuclear magnetic resonance (NMR) spectroscopy is inherently limited by low spin polarization. One method to address the low polarization is para-hydrogen (p-H₂) induced polarization (PHIP) which uses the singlet spin isomer of H₂ to generate disparate nuclear spin populations to amplify the associated NMR signals. PHIP often relies on thermal catalysis or, more infrequently, UV-activated catalytic hydrogenation. Light-activated hydrogenation enables direct and timed control over the hyperpolarization of target substrates, critical for identifying short-lived intermediates. Here, we use an established Ir(III) triplet photosensitizer (PS) to visible light sensitize the triplet ligand-field states in the d⁶-transition metal dihydride Ru(CO)(PPh₃)₃(H)₂ (1). Excitation inside a 9.4 T NMR spectrometer with the PS and a 420 nm blue LED, under 3 atm of p-H₂, successfully photosensitized hyperpolarization in 1 and in a range of unsaturated substrates at and below room temperature, up to 1630-fold. In otherwise identical experimental conditions without light activation, no polarization was realized in 1 or the substrates evaluated. We believe triplet-sensitized PHIP (Trip-PHIP) represents a facile experimental means for probing triplet sensitized light activation in transition metal catalysts possessing low-lying triplet ligand-field states, providing mechanistic insight of potentially tremendous value in chemical catalysis.

Adiabatic Passage through Level Anticrossings in Systems of Chemically Inequivalent Protons Incorporating Parahydrogen: Theory, Experiment, and Prospective Applications

Level anticrossings (LACs) are ubiquitous in quantum systems and have been exploited for spin-order transfer in hyperpolarized nuclear magnetic resonance spectroscopy. This paper examines the manifestations of adiabatic passage through a specific type of LAC found in homonuclear systems of chemically inequivalent coupled protons incorporating parahydrogen (pH₂). Adiabatic passage through such a LAC is shown to elicit translation of the pH₂ spin order. As an example, with prospective applications in biomedicine, proton spin polarizations of at least 19.8 ± 2.6% on the methylene protons and 68.7 ± 0.5% on the vinylic protons of selectively deuterated allyl pyruvate ester are demonstrated experimentally. After ultrasonic spray injection of a precursor solution containing propargyl pyruvate and a dissolved Rh catalyst into a chamber pressurized with 99% para-enriched H₂, the products are collected and transported to a high magnetic field for NMR detection. The LAC-mediated hyperpolarization of the methylene protons is significant because of the stronger spin coupling to the pyruvate carbonyl ¹³C, setting up an ideal initial condition for subsequent coherence transfer by selective INEPT. Furthermore, the selective deuteration of the propargyl side arm increases the efficiency and polarization level. LAC-mediated translation of parahydrogen spin order completes the first step toward a new and highly efficient route for the ¹³C NMR signal enhancement of pyruvate via side-arm hydrogenation with parahydrogen.

The ABC transporter MsbA adopts the wide inward-open conformation in E. coli cells

Membrane proteins are currently investigated after detergent extraction from native cellular membranes and reconstitution into artificial liposomes or nanodiscs, thereby removing them from their physiological environment. However, to truly understand the biophysical properties of membrane proteins in a physiological environment, they must be investigated within living cells. Here, we used a spin-labeled nanobody to interrogate the conformational cycle of the ABC transporter MsbA by double electron-electron resonance. Unexpectedly, the wide inward-open conformation of MsbA, commonly considered a nonphysiological state, was found to be prominently populated in Escherichia coli cells. Molecular dynamics simulations revealed that extensive lateral portal opening is essential to provide access of its large natural substrate core lipid A to the binding cavity. Our work paves the way to investigate the conformational landscape of membrane proteins in cells.

31P spin-lattice and singlet order relaxation mechanisms in pyrophosphate studied by isotopic substitution, field shuttling NMR, and molecular dynamics simulation

Nuclear spin relaxation mechanisms are often difficult to isolate and identify, especially in molecules with internal flexibility. Here we combine experimental work with computation in order to determine the major mechanisms responsible for ³¹P spin-lattice and singlet order (SO) relaxation in pyrophosphate, a physiologically relevant molecule. Using field-shuttling relaxation measurements (from 2 μT to 9.4 T) and rates calculated from molecular dynamics (MD) trajectories, we identified chemical shift anisotropy (CSA) and spin-rotation as the major mechanisms, with minor contributions from intra- and intermolecular coupling. The significant spin-rotation interaction is a consequence of the relatively rapid rotation of the -PO₃^2- entities around the bridging P-O bonds, and is treated by a combination of MD simulations and quantum chemistry calculations. Spin-lattice relaxation was predicted well without adjustable parameters, and for SO relaxation one parameter was extracted from the comparison between experiment and computation (a correlation coefficient between the rotational motion of the groups).

An initial investigation of accuracy required for the identification of small molecules in complex samples using quantum chemical calculated NMR chemical shifts

The majority of primary and secondary metabolites in nature have yet to be identified, representing a major challenge for metabolomics studies that currently require reference libraries from analyses of authentic compounds. Using currently available analytical methods, complete chemical characterization of metabolomes is infeasible for both technical and economic reasons. For example, unambiguous identification of metabolites is limited by the availability of authentic chemical standards, which, for the majority of molecules, do not exist. Computationally predicted or calculated data are a viable solution to expand the currently limited metabolite reference libraries, if such methods are shown to be sufficiently accurate. For example, determining nuclear magnetic resonance (NMR) spectroscopy spectra in silico has shown promise in the identification and delineation of metabolite structures. Many researchers have been taking advantage of density functional theory (DFT), a computationally inexpensive yet reputable method for the prediction of carbon and proton NMR spectra of metabolites. However, such methods are expected to have some error in predicted ¹³C and ¹H NMR spectra with respect to experimentally measured values. This leads us to the question–what accuracy is required in predicted ¹³C and ¹H NMR chemical shifts for confident metabolite identification? Using the set of 11,716 small molecules found in the Human Metabolome Database (HMDB), we simulated both experimental and theoretical NMR chemical shift databases. We investigated the level of accuracy required for identification of metabolites in simulated pure and impure samples by matching predicted chemical shifts to experimental data. We found 90% or more of molecules in simulated pure samples can be successfully identified when errors of ¹H and ¹³C chemical shifts in water are below 0.6 and 7.1 ppm, respectively, and below 0.5 and 4.6 ppm in chloroform solvation, respectively. In simulated complex mixtures, as the complexity of the mixture increased, greater accuracy of the calculated chemical shifts was required, as expected. However, if the number of molecules in the mixture is known, e.g., when NMR is combined with MS and sample complexity is low, the likelihood of confident molecular identification increased by 90%.

Rotating Frame Relaxation in Magic Angle Spinning Solid State NMR, a Promising Tool for Characterizing Biopolymer Motion

Magic angle spinning NMR rotating frame relaxation measurements provide a unique experimental window into biomolecules dynamics, as is illustrated by numerous recent applications. We discuss experimental strategies for this class of experiments, with a particular focus on systems where motion-driven modulation of the chemical shift interaction is the main mechanism for relaxation. We also explore and describe common strategies for interpreting the data sets to extract motion time scale, activation energy, and angle or order parameters from rotating frame relaxation data. Using model free analysis and numerical simulations, including time domain treatment, we explore conditions under which it is possible to obtain accurate and precise information about the time scales of motions. Overall, with rapid technical advances in solid state NMR, there is a bright future for this class of studies.