TensorView: A software tool for displaying NMR tensors

Automatic fitting of multiple-field solid-state NMR spectra

The NMR lineshapes produced by half-integer quadrupolar nuclei are sensitive to 11 distinct fit parameters per inequivalent site. To date, automatic fitting routines have failed to replace manual parameter insertion and evaluation due to the importance of local minima and the need for fitting multiple-field magic-angle spinning (MAS) and static spectra simultaneously. Herein we introduce a new tool, AMES-Fit (Automatic Multiple Experiment Simulation and Fitting), to automatically find the global best-fit simulation parameters for a series of multiple-field NMR lineshapes. AMES-Fit uses an adaptive step size random search algorithm to dynamically probe parameter space and requires minimal human input. The best fits are obtained in a few minutes of computation time that would otherwise have required several person-hours of work. The program is freely available and open-source.

13Ccarbene nuclear magnetic resonance chemical shift analysis confirms CeIV[double bond, length as m-dash]C double bonding in cerium(iv)-diphosphonioalkylidene complexes

Diphosphonioalkylidene dianions have emerged as highly effective ligands for lanthanide and actinide ions, and the resulting formal metal-carbon double bonds have challenged and developed conventional thinking about f-element bond multiplicity and covalency. However, f-element-diphosphonioalkylidene complexes can be represented by several resonance forms that render their metal-carbon double bond status unclear. Here, we report an experimentally-validated 13C Nuclear Magnetic Resonance computational assessment of two cerium(iv)-diphosphonioalkylidene complexes, [Ce(BIPMTMS)(ODipp)2] (1, BIPMTMS = {C(PPh2NSiMe3)2}2-; Dipp = 2,6-diisopropylphenyl) and [Ce(BIPMTMS)2] (2). Decomposing the experimental alkylidene chemical shifts into their corresponding calculated shielding (σ) tensor components verifies that these complexes exhibit Ce[double bond, length as m-dash]C double bonds. Strong magnetic coupling of Ce[double bond, length as m-dash]C σ/π* and π/σ* orbitals produces strongly deshielded σ11 values, a characteristic hallmark of alkylidenes, and the largest 13C chemical shift tensor spans of any alkylidene complex to date (1, 801 ppm; 2, 810 ppm). In contrast, the phosphonium-substituent shielding contributions are much smaller than the Ce[double bond, length as m-dash]C σ- and π-bond components. This study confirms significant Ce 4f-orbital contributions to the Ce[double bond, length as m-dash]C bonding, provides further support for a previously proposed inverse-trans-influence in 2, and reveals variance in the 4f spin-orbit contributions that relate to the alkylidene hybridisation. This work thus confirms the metal-carbon double bond credentials of f-element-diphosphonioalkylidenes, providing quantified benchmarks for understanding diphosphonioalkylidene bonding generally.

31P Nuclear Magnetic Resonance Spectroscopy as a Probe of Thorium-Phosphorus Bond Covalency: Correlating Phosphorus Chemical Shift to Metal-Phosphorus Bond Order

We report the use of solution and solid-state 31P Nuclear Magnetic Resonance (NMR) spectroscopy combined with Density Functional Theory calculations to benchmark the covalency of actinide-phosphorus bonds, thus introducing 31P NMR spectroscopy to the investigation of molecular f-element chemical bond covalency. The 31P NMR data for [Th(PH2)(TrenTIPS)] (1, TrenTIPS = {N(CH2CH2NSiPri3)3}3-), [Th(PH)(TrenTIPS)][Na(12C4)2] (2, 12C4 = 12-crown-4 ether), [{Th(TrenTIPS)}2(μ-PH)] (3), and [{Th(TrenTIPS)}2(μ-P)][Na(12C4)2] (4) demonstrate a chemical shift anisotropy (CSA) ordering of (μ-P)3- > (═PH)2- > (μ-PH)2- > (-PH2)1- and for 4 the largest CSA for any bridging phosphido unit. The B3LYP functional with 50% Hartree-Fock mixing produced spin-orbit δiso values that closely match the experimental data, providing experimentally benchmarked quantification of the nature and extent of covalency in the Th-P linkages in 1-4 via Natural Bond Orbital and Natural Localized Molecular Orbital analyses. Shielding analysis revealed that the 31P δiso values are essentially only due to the nature of the Th-P bonds in 1-4, with largely invariant diamagnetic but variable paramagnetic and spin-orbit shieldings that reflect the Th-P bond multiplicities and s-orbital mediated transmission of spin-orbit effects from Th to P. This study has permitted correlation of Th-P δiso values to Mayer bond orders, revealing qualitative correlations generally, but which should be examined with respect to specific ancillary ligand families rather than generally to be quantitative, reflecting that 31P δiso values are a very sensitive reporter due to phosphorus being a soft donor that responds to the rest of the ligand field much more than stronger, harder donors like nitrogen.

Effects of surface acidity on the structure of organometallics supported on oxide surfaces

Well-defined organometallics supported on high surface area oxides are promising heterogeneous catalysts. An important design factor in these materials is how the metal interacts with the functionalities on an oxide support, commonly anionic X-type ligands derived from the reaction of an organometallic M-R with an -OH site on the oxide. The metal can either form a covalent M-O bond or form an electrostatic M⁺⋯^-O ion-pair, which impacts how well-defined organometallics will interact with substrates in catalytic reactions. A less common reaction pathway involves the reaction of a Lewis site on the oxide with the organometallic, resulting in abstraction to form an ion-pair, which is relevant to industrial olefin polymerization catalysts. This Feature Article views the spectrum of reactivity between an organometallic and an oxide through the prism of Brønsted and/or Lewis acidity of surface sites and draws analogies to the molecular frame where Lewis and Brønsted acids are known to form reactive ion-pairs. Applications of the well-defined sites developed in this article are also discussed.

TensorView for MATLAB: Visualizing tensors with Euler angle decoding

TensorView for MATLAB is a GUI-based visualization tool for depicting second-rank Cartesian tensors as surfaces on three-dimensional molecular models. Both ellipsoid and ovaloid tensor display formats are supported, and the software allows for easy conversion of Euler angles from common rotation schemes (active, passive, ZXZ, and ZYZ conventions) with visual feedback. In addition, the software displays all four orientation-equivalent Euler angle solutions for the placement of a single tensor in the molecular frame and can report relative orientations of two tensors with all 16 orientation-equivalent Euler angle sets that relate them. The salient relations are derived and illustrated through several examples. TensorView for MATLAB expands and complements the earlier implementation of TensorView within the Mathematica programming environment and can be run without a MATLAB license. TensorView for MATLAB is available through github at https://github.com/LeoSvenningsson/TensorViewforMatlab, and can also be accessed directly via the NMRbox resource.

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.

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).

Cross-correlation effects in the solution NMR spectra of near-equivalent spin-1/2 pairs

The nuclear magnetic resonance (NMR) spectra of spin-1/2 pairs contain four peaks, with two inner peaks much stronger than the outer peaks in the near-equivalence regime. We have observed that the strong inner peaks have significantly different linewidths when measurements were performed on a 13C2-labelled triyne derivative. This linewidth difference may be attributed to strong cross-correlation effects. We develop the theory of cross-correlated relaxation in the case of near-equivalent homonuclear spin-1/2 pairs, in the case of a molecule exhibiting strongly anisotropic rotational diffusion. Good agreement is found with the experimental NMR lineshapes.

Solid-state 17O NMR study of α-d-glucose: exploring new frontiers in isotopic labeling, sensitivity enhancement, and NMR crystallography

We report the first “total synthesis” of 17O-labeled d-glucose and its solid-state 17O NMR characterization with unprecedented sensitivity and resolution.

Weak nuclear spin singlet relaxation mechanisms revealed by experiment and computation

Nuclear spin singlet states are often found to allow long-lived storage of nuclear magnetization, which can form the basis of novel applications in spectroscopy, imaging, and in studies of dynamic...

Solid-state 11B NMR studies of coinage metal complexes containing a phosphine substituted diboraanthracene ligand

Transition metal interactions with Lewis acids (M → Z linkages) are fundamentally interesting and practically important. The most common Z-type ligands contain boron, which contains an NMR active ¹¹B nucleus. We measured solid-state ¹¹B{¹H} NMR spectra of copper, silver, and gold complexes containing a phosphine substituted 9,10-diboraanthracene ligand (B₂P₂) that contain planar boron centers and weak M → BR₃ linkages ([(B₂P₂)M][BAr^F₄] (M = Cu (1), Ag (2), Au (3)) characterized by large quadrupolar coupling (C_Q) values (4.4-4.7 MHz) and large span (Ω) values (93-139 ppm). However, the solid-state ¹¹B{¹H} NMR spectrum of K[Au(B₂P₂)]^- (4), which contains tetrahedral borons, is narrow and characterized by small C_Q and Ω values. DFT analysis of 1-4 shows that C_Q and Ω are expected to be large for planar boron environments and small for tetrahedral boron, and that the presence of a M → BR₃ linkage relates to the reduction in C_Q and ¹¹B NMR shielding properties. Thus solid-state ¹¹B NMR spectroscopy contains valuable information about M → BR₃ linkages in complexes containing the B₂P₂ ligand.

Nuclear singlet relaxation by chemical exchange

The population imbalance between nuclear singlet states and triplet states of strongly coupled spin-1/2 pairs, also known as nuclear singlet order, is well protected against several common relaxation mechanisms. We study the nuclear singlet relaxation of ¹³C pairs in aqueous solutions of 1,2-¹³C₂ squarate over a range of pH values. The ¹³C singlet order is accessed by introducing ¹⁸O nuclei in order to break the chemical equivalence. The squarate dianion is in chemical equilibrium with hydrogen-squarate (SqH^-) and squaric acid (SqH₂) characterized by the dissociation constants pK₁ = 1.5 and pK₂ = 3.4. Surprisingly, we observe a striking increase in the singlet decay time constants T_S when the pH of the solution exceeds ∼10, which is far above the acid-base equilibrium points. We derive general rate expressions for chemical-exchange-induced nuclear singlet relaxation and provide a qualitative explanation of the T_S behavior of the squarate dianion. We identify a kinetic contribution to the singlet relaxation rate constant, which explicitly depends on kinetic rate constants. Qualitative agreement is achieved between the theory and the experimental data. This study shows that infrequent chemical events may have a strong effect on the relaxation of nuclear singlet order.

31P nuclear spin singlet lifetimes in a system with switchable magnetic inequivalence: experiment and simulation

³¹P NMR spectroscopy and the study of nuclear spin singlet relaxation phenomena are of interest in particular due to the importance of phosphorus-containing compounds in physiology. We report the generation and measurement of relaxation of ³¹P singlet order in a chemically equivalent but magnetically inequivalent case. Nuclear magnetic resonance singlet state lifetimes of ³¹P pairs have heretofore not been reported. Couplings between ¹H and ³¹P nuclei lead to magnetic inequivalence and serve as a mechanism of singlet state population conversion within this molecule. We show that in this molecule singlet relaxation occurs at a rate significantly faster than spin-lattice relaxation, and that anticorrelated chemical shift anisotropy can account for this observation. Calculations of this mechanism, with the help of molecular dynamics simulations and ab initio calculations, provide excellent agreement with the experimental findings. This study could provide guidance for the study of ³¹P singlets within other compounds, including biomolecules.

Bridging photochemistry and photomechanics with NMR crystallography: the molecular basis for the macroscopic expansion of an anthracene ester nanorod

Crystals composed of photoreactive molecules represent a new class of photomechanical materials with the potential to generate large forces on fast timescales. An example is the photodimerization of 9-tert-butyl-anthracene ester (9TBAE) in molecular crystal nanorods that leads to an average elongation of 8%. Previous work showed that this expansion results from the formation of a metastable crystalline product. In this article, it is shown how a novel combination of ensemble oriented-crystal solid-state NMR, X-ray diffraction, and first principles computational modeling can be used to establish the absolute unit cell orientations relative to the shape change, revealing the atomic-resolution mechanism for the photomechanical response and enabling the construction of a model that predicts an elongation of 7.4%, in good agreement with the experimental value. According to this model, the nanorod expansion does not result from an overall change in the volume of the unit cell, but rather from an anisotropic rearrangement of the molecular contents. The ability to understand quantitatively how molecular-level photochemistry generates mechanical displacements allows us to predict that the expansion could be tuned from +9% to -9.5% by controlling the initial orientation of the unit cell with respect to the nanorod axis. This application of NMR-assisted crystallography provides a new tool capable of tying the atomic-level structural rearrangement of the reacting molecular species to the mechanical response of a nanostructured sample.

NMR crystallography of molecular organics

Developments of NMR methodology to characterise the structures of molecular organic structures are reviewed, concentrating on the previous decade of research in which density functional theory-based calculations of NMR parameters in periodic solids have become widespread. With a focus on demonstrating the new structural insights provided, it is shown how "NMR crystallography" has been used in a spectrum of applications from resolving ambiguities in diffraction-derived structures (such as hydrogen atom positioning) to deriving complete structures in the absence of diffraction data. As well as comprehensively reviewing applications, the different aspects of the experimental and computational techniques used in NMR crystallography are surveyed. NMR crystallography is seen to be a rapidly maturing subject area that is increasingly appreciated by the wider crystallographic community.

A Modified Townes-Dailey Model for Interpretation and Visualization of Nuclear Quadrupole Coupling Tensors in Molecules

We propose a modified Townes-Dailey (TD) model to help interpret and visualize experimentally measurable nuclear quadrupole coupling tensors (thus the electric field gradient tensors) in molecules. We show that within the framework of the TD model each principal component of the nuclear quadrupole coupling tensor is directly related to a new quantity termed as the valence p-orbital population anisotropy (VPPA or ΔP) in the same direction. Although the proposed model is a simple reformulation of the original TD model thus does not introduce new physics, the concept of VPPA makes it possible to directly interpret as well as visualize in a much straightforward way the experimentally determined nuclear quadrupole coupling tensors in molecules. We illustrate the utilization of VPPA using nuclear quadrupole coupling tensors for ¹¹B, ¹⁴N, ¹⁷O, ³⁵Cl, ⁷⁹Br, and ¹²⁷I nuclei in a variety of molecules. We propose to use VPPA or ΔP ellipsoid representation as a means of visualizing/displaying nuclear quadrupole coupling tensors in the molecular frame. We show the usefulness of the VPPA concept in providing a unifying explanation for seemingly different types of molecular interactions such as hydrogen bonding, halogen bonding, and frustrated Lewis pairs. We further suggest that VPPA can be used as a universal measure of the ability of any element in the entire p-block of the periodic table (groups 13-16) to interact with nucleophiles (e.g., formation of chalcogen, pnictogen, tetrel, and triel bonds).

31P MAS NMR and DFT study of crystalline phosphate matrices

We present the study of the phosphorus local environment by using ³¹P MAS NMR in a series of seven double monophosphates M^IIM^IV(PO₄)₂ (M^II and M^IV being divalent and tetravalent cations, respectively) of yavapaiite and low-yavapaiite type crystal structures. Solid-state and cluster DFT calculations were found to be efficient for predicting the ³¹P isotropic chemical shift and chemical shift anisotropy. To achieve this performance, however, a proper computational optimisation of the experimental structural data was required. From the three optimisation methods tested, the full optimisation provided the best reference structure for the calculation of the NMR parameters of the studied phosphates. Also, a better prediction of the chemical shifts was possible by using a correction to the GIPAW calculated shielding.

Origin of the 29Si NMR chemical shift in R3Si–X and relationship to the formation of silylium (R3Si+) ions

The origin in deshielding of ²⁹Si NMR chemical shifts in R₃Si–X, where X = H, OMe, Cl, OTf, [CH₆B₁₁X₆], toluene, and O_X (O_X = surface oxygen), as well as ⁱPr₃Si⁺ and Mes₃Si⁺ were studied using DFT methods.

Fast electron paramagnetic resonance magic angle spinning simulations using analytical powder averaging techniques

Simulations describing the spin physics underpinning nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) spectroscopy play an important role in the design of new experiments. When experiments are performed in the solid state, samples are commonly composed of powders or glasses, with molecules oriented at a large number of angles with respect to the laboratory frame. These powder angles must be represented in simulations to account for anisotropic interactions. Numerical techniques are typically used to accurately compute such powder averages. A large number of Euler angles are usually required, leading to lengthy simulation times. This is particularly true in broad spectra, such as those observed in EPR. The combination of the traditionally separate techniques of EPR and magic angle spinning (MAS) NMR could play an important role in future electron detected experiments, combined with dynamic nuclear polarization, which will allow for exceptional detection sensitivity of NMR spin coherences. Here, we present a method of reducing the required number of Euler angles in magnetic resonance simulations by analytically performing the powder average over one of the Euler angles in the static and MAS cases for the TEMPO nitroxide radical in a 7 T field. In the static case, this leads to a 97.5% reduction in simulation time over the fully numerical case and reproduces the expected spinning sideband manifold when simulated with a MAS frequency of 150 kHz. This technique is applicable to more traditional NMR experiments as well, such as those involving quadrupolar nuclei or multiple dimensions.

19F NMR relaxation studies of fluorosubstituted tryptophans

We present ¹⁹F longitudinal and transverse relaxation studies for four differently fluorosubstituted L-tryptophans, which carry single F atoms in the indole ring, both in the context of the free amino acid and when located in the cyclophilin A protein. For the free 4F-, 5F-, 6F-, 7F-L-Trp, satisfactory agreement between experimentally measured and calculated relaxation rates was obtained, suggesting that the parameters used for calculating the rates for the indole frame are sufficiently accurate. We also measured and calculated relaxation rates for four differently ¹⁹F-tryptophan labeled cyclophilin A proteins, transferring the parameters from the free amino acid to the protein-bound moiety. Our results suggest that ¹⁹F relaxation data of the large and rigid indole ring in Trp are only moderately affected by protein motions and provide critical reference points for evaluating fluorine NMR relaxation in the future, especially in fluorotryptophan labeled proteins.