Chemical Shielding Anisotropy Research Articles

The EFG Rosetta Stone: translating between DFT calculations and solid state NMR experiments.

We present a comprehensive study on the best practices for integrating first principles simulations in experimental quadrupolar solid-state nuclear magnetic resonance (SS-NMR), exploiting the synergies between theory and experiment for achieving the optimal interpretation of both. Most high performance materials (HPMs), such as battery electrodes, exhibit complex SS-NMR spectra due to dynamic effects or amorphous phases. NMR crystallography for such challenging materials requires reliable, accurate, efficient computational methods for calculating NMR observables from first principles for the transfer between theoretical material structure models and the interpretation of their experimental SS-NMR spectra. NMR-active nuclei within HPMs are routinely probed by their chemical shielding anisotropy (CSA). However, several nuclear isotopes of interest, e.g.7Li and 27Al, have a nuclear quadrupole and experience additional interactions with the surrounding electric field gradient (EFG). The quadrupolar interaction is a valuable source of information about atomistic structure, and in particular, local symmetry, complementing the CSA. As such, there is a range of different methods and codes to choose from for calculating EFGs, from all-electron to plane wave methods. We benchmark the accuracy of different simulation strategies for computing the EFG tensor of quadrupolar nuclei with plane wave density functional theory (DFT) and study the impact of the material structure as well as the details of the simulation strategy. Especially for small nuclei with few electrons, such as 7Li, we show that the choice of physical approximations and simulation parameters has a large effect on the transferability of the simulation results. To the best of our knowledge, we present the first comprehensive reference scale and literature survey for 7Li quadrupolar couplings. The results allow us to establish practical guidelines for developing the best simulation strategy for correlating DFT to experimental data extracting the maximum benefit and information from both, thereby advancing further research into HPMs.

Chemical shielding and electric field gradient tensors of disodium 5′-adenosine triphosphate trihydrate determined by solid-state NMR spectroscopy and ab initio calculations

The tri-phosphate and sodium ion environments in well crystallized disodium 5′adenosine triphosphate trihydrate (ATP•3H2O) are investigated using high-resolution solid-state NMR spectroscopy and ab initio calculations. The six inequivalent phosphorus sites resolved in 31P MAS spectra have been assigned on the basis of experimentally obtained results and theoretical ab initio quantum chemical calculations of 31P chemical shielding tensors with increased numerical accuracy. Aided by 31P-31P dipolar connectivity established in DQ-SQ correlation experiment and DFT calculations carried out at the B3LYP/(aug-cc-pDVZ(3s,2p,1d), 6–31G(d,p)) level, phosphorus resonance assignments in MAS spectra have been made and the 31P chemical shielding anisotropies and tensor orientations in the molecule-fixed frame have been determined. 31P shielding tensors are found to be oriented with the most shielded direction nearly perpendicular to the O-P-O plane involving the two adjoining oxygens. The complete resolution of the four sodium sites has been achieved from 3Q-MAS experiments performed at 7.05 T and this has enabled 23Na quadrupole parameters to be determined experimentally and compared with theoretical calculations. Besides aiding a partial resonance assignment of the 23Na 3Q-MAS spectrum, our HF/6–311++G(2d,2p) calculations of 23Na EFG tensors show that for two sodium sites which are tightly coordinated the orientation of the EFG tensor is distinct. These exhibit unique directions along which the field gradient is the smallest and largest.

Exploring Accuracy Limits of Predictions of the 1H NMR Chemical Shielding Anisotropy in the Solid State.

The 1H chemical shielding anisotropy (CSA) is an NMR parameter that is exquisitely sensitive to the local environment of protons in crystalline systems, but it is difficult to obtain it experimentally due to the need to concomitantly suppress other anisotropic interactions in the solid-state NMR (SSNMR) pulse sequences. The SSNMR measurements of the 1H CSA are particularly challenging if the fast magic-angle-spinning (MAS) is applied. It is thus important to confront the results of both the single-crystal (SC) and fast-MAS experiments with their theoretical counterparts. Here the plane-waves (PW) DFT calculations have been carried out using two functionals in order to precisely characterize the structures and the 1H NMR chemical shielding tensors (CSTs) of the solid forms of maleic, malonic, and citric acids, and of L-histidine hydrochloride monohydrate. The level of agreement between the PW DFT and either SC or fast-MAS SSNMR 1H CSA data has been critically compared. It has been found that for the eigenvalues of the 1H CSTs provided by the fast-MAS measurements, an accuracy limit of current PW DFT predictions is about two ppm in terms of the standard deviation of the linear regression model, and sources of this error have been thoroughly discussed.

NMR Crystallography of the Polymorphs of Metergoline

Two polymorphs of the drug compound metergoline (C25H29N3O2) were investigated in detail by solid-state NMR measurements. The results have been analysed by an advanced procedure, which uses experimental input together with the results of quantum chemical calculations that were performed for molecular crystals. In this way, it was possible to assign the total of 40 1H–13C correlation pairs in a highly complex system, namely, in the dynamically disordered polymorph with two independent molecules in the unit cell of a large volume of 4234 Å3. For the simpler polymorph, which exhibits only small-amplitude motions and has just one molecule in the unit cell with a volume of 529.0 Å3, the values of the principal elements of the 13C chemical shift tensors were measured. Additionally, for this polymorph, a set of crystal structure predictions were generated, and the {13C, 1H} isotropic and 13C anisotropic chemical shielding data were computed while using the gauge-including projector augmented-wave approach combined with the “revised Perdew-Burke-Ernzerhof“ exchange-correlation functional (GIPAW-RPBE). The experimental and theoretical results were combined in an application of the newly developed strategy to polymorph discrimination. This research thus opens up new routes towards more accurate characterization of the polymorphism of drug formulations.

Accurate 13-C and 15-N molecular crystal chemical shielding tensors from fragment-based electronic structure theory

Standard nuclear magnetic resonance (NMR) spectroscopy experiments measure isotropic chemical shifts, but measuring the chemical shielding anisotropy (CSA) tensor can provide additional insights into solid state chemical structures. Interpreting the principal components of these tensors is facilitated by first-principles chemical shielding tensor predictions. Here, the ability to predict molecular crystal CSA tensor components for 13C and 15N nuclei with fragment-based electronic structure techniques is explored. Similar to what has been found previously for isotropic chemical shifts, the benchmarking demonstrates that fragment-based techniques can accurately reproduce CSA tensor components. The use of hybrid density functionals like PBE0 or B3LYP provide higher accuracy than generalized gradient approximation functionals like PBE. Unlike for planewave density functional techniques, hybrid density functionals can be employed routinely with modest computational cost in fragment approaches. Finally, good consistency between the regression parameters used to map either isotropic shieldings or CSA tensor components is demonstrated, providing further evidence for the quality of the models and highlighting that models trained for isotropic shifts can also be applied to CSA tensor components.

Refocusing CSA during magic angle spinning rotating-frame relaxation experiments

We examine coherent evolution of spin-locked magnetization during magic-angle spinning (MAS), in the context of relaxation experiments designed to probe chemical exchange (rotating-frame relaxation (R1ρ)). Coherent evolution is expected in MAS based rotating-frame relaxation decay experiments if matching conditions are met (such as, ω1 = nωr) and if the chemical shielding anisotropy (CSA) is substantial. We show here using numerical simulations and experiments that even when such matching requirements are avoided (e.g., ω1 < 0.5ωr, ∼1.5ωr, >2.5ωr), coherent evolution of spin-locked magnetization with large CSA is still considerable. The coherent evolution has important consequences on the analysis of relaxation decay and the ability to extract accurate information of interest about dynamics. We present a pulse sequence that employs rotary echoes and refocuses CSA contributions, allowing for more sensitive measurement of rotating-frame relaxation with less interference from coherent evolution. In practice, the proposed pulse sequence, REfocused CSA Rotating-frame Relaxation (RECRR) is robust to carrier frequency offset, B1-field inhomogeneity, and slight miscalibrations of the refocusing pulses.

A Multifaceted Study of Methane Adsorption in Metal–Organic Frameworks by Using Three Complementary Techniques

Methane is a promising clean and inexpensive energy alternative to traditional fossil fuels, however, its low volumetric energy density at ambient conditions has made devising viable, efficient methane storage systems very challenging. Metal-organic frameworks (MOFs) are promising candidates for methane storage. In order to improve the methane storage capacity of MOFs, a better understanding of the methane adsorption, mobility, and host-guest interactions within MOFs must be realized. In this study, methane adsorption within α-Mg3 (HCO2 )6 , α-Zn3 (HCO2 )6 , SIFSIX-3-Zn, and M-MOF-74 (M=Mg, Zn, Ni, Co) has been comprehensively examined. Single-crystal X-ray diffraction (SCXRD) experiments and DFT calculations of the methane adsorption locations were performed for α-Mg3 (HCO2 )6 , α-Zn3 (HCO2 )6 , and SIFSIX-3-Zn. The SCXRD thermal ellipsoids indicate that methane possesses significant mobility at the adsorption sites in each system. 2 H solid-state NMR (SSNMR) experiments targeting deuterated CH3 D guests in α-Mg3 (HCO2 )6 , α-Zn3 (HCO2 )6 , SIFSIX-3-Zn, and MOF-74 yield an interesting finding: the 2 H SSNMR spectra of methane adsorbed in these MOFs are significantly influenced by the chemical shielding anisotropy in addition to the quadrupolar interaction. The chemical shielding anisotropy contribution is likely due mainly to the nuclear independent chemical shift effect on the MOF surfaces. In addition, the 2 H SSNMR results and DFT calculations strongly indicate that the methane adsorption strength is linked to the MOF pore size and that dispersive forces are responsible for the methane adsorption in these systems. This work lays a very promising foundation for future studies of methane adsorption locations and dynamics within adsorbent MOF materials.

The C-, Si-, Ge-Doped (6,3) Chiral BNNTs: A Computational Study

Abstract Electronic structure properties including bond lengths, bond angles, dipole moments (μ), energies, band gaps, nuclear magnetic resonance (NMR) parameters of the isotropic and anisotropic chemical shielding parameters for the sites of various atoms were calculated using density functional theory for C-, Si-, and Ge-doped (6,3) chiral BNNTs. The calculations indicated that average bond lengths were as follows: Ge–N&gt;Si–N&gt;C–N and Ge–B&gt;Si–B&gt;C–B. The dipole moments for C-, Si-, and Ge-doped (6,3) chiral BNNTs structures show fairly large changes with respect to the pristine model.

Chemical Shielding Anisotropies for Chloroform Exchanging between a Free Site and a Complex with Cryptophane-D: A Cross-Correlated NMR Relaxation Study.

The case of (13)C-labeled chloroform exchanging between a free site in solution and the encaged site within the cryptophane-D cavity is investigated using the measurements of longitudinal cross-correlated relaxation rates, involving the interference of the dipole-dipole and chemical shielding anisotropy interactions. A compact theoretical expression is provided, along with an experimental protocol, based on INEPT (insensitive nuclei enhanced by polarization)-enhanced double-quantum-filtered inversion recovery measurements. The analysis of the build-up curves results in a set of cross-correlated relaxation rates for both the (13)C and (1)H spins at the two sites. It is demonstrated that the results can be given a consistent interpretation in terms of molecular-level properties, such as rotational correlation times, the Lipari-Szabo order parameter, and interaction strength constants. The analysis yields the bound-site carbon-13 chemical shielding anisotropy, ΔσC = -58 ± 8 ppm, in good agreement with most recent liquid-crystal measurements and the corresponding proton shielding anisotropy, ΔσH = 14 ± 2 ppm.

Spectroscopic (FT-IR, FT-Raman and UV–Visible) investigations, NMR chemical shielding anisotropy (CSA) parameters of 2,6-Diamino-4-chloropyrimidine for dye sensitized solar cells using density functional theory

The molecular structure, geometry optimization, vibrational frequencies of organic dye sensitizer 2,6-Diamino-4-chloropyrimidine (DACP) were studied based on Hartree–Fock (HF) and density functional theory (DFT) using B3LYP methods with 6-311++G(d,p) basis set. Ultraviolet–Visible (UV–Vis) spectrum was investigated by time dependent DFT (TD-DFT). Features of the electronic absorption spectrum in the UV–Visible regions were assigned based on TD-DFT calculation. The absorption bands are assigned to transitions. The interfacial electron transfer between semiconductor TiO2 electrode and dye sensitizer DACP is due to an electron injection process from excited dye to the semiconductor’s conduction band. The observed and the calculated frequencies are found to be in good agreement. The energies of the frontier molecular orbitals (FMOS) have also been determined. The chemical shielding anisotropic (CSA) parameters are calculated from the NMR analysis, Stability of the molecule arising from hyperconjugative interactions and charge delocalization has been analyzed using natural bond orbital (NBO) analysis.

Electronic and Structural Properties of Ga-Doped (4,4) armchair SiCNT as a p-Semiconductor

The properties of pristine and Ga-doped silicon carbide nanotubes (SiCNTs) in two models (GaSi and GaC) as a p-semiconductor were investigated by density functional theory (DFT) calculations. The investigated structures were optimized, and quantum molecular descriptors and isotropic (CSI) and anisotropic (CSA) chemical shielding parameters were calculated for the optimized structures. We extended the DFT calculation to predict the electronic and structural properties of Ga-doped silicon carbide nanotubes, which are important for the production of solid-state devices and other applications. According to the calculations, the GaSi model is a better p-semiconductor than the GaC model in the production of solid-state devices.

Disiline-doped boron nitride nanotubes: A computational study

The properties of the electronic structure of the Disiline-doped boron nitride nanotubes (Disiline-BNNTs) are investigated by a density functional theory (DFT) calculation. The structural forms are firstly optimized and the CS tensors calculated. Subsequently, the chemical-shielding isotropic (CSI) and chemical shielding anisotropic (CSA) parameters are found. The shielding values of boron (B) and nitrogen (N) atoms were calculated by Gauge-Including Atomic Orbital (GIAO), Continuous Set of Gauge Transformations (CSGT) and Individual Gauges for Atoms in Molecules (IGAIM) methods, using B3LYP/6-311+G*. The B3LYP level of theory with IGAIM was the best method to evaluate the theoretical chemical shifts for studied models. The results reveal a significant effect of Disiline doping on the chemical shielding tensors at the sites of those 11B and 15N nuclei located in the nearest neighborhood of the Disiline-doped ring. Furthermore, the values of dipole moments and HOMO-LUMO gaps change in the Disiline-doped models in comparison with the original pristine model.

Singularities in the lineshape of a second-order perturbed quadrupolar nucleus and their use in data fitting

Even for large quadrupolar interactions, the powder spectrum of the central transition for a half-integral spin is relatively narrow, because it is unperturbed to first order. However, the second-order perturbation is still orientation dependent, so it generates a characteristic lineshape. This lineshape has both finite step discontinuities and singularities where the spectrum is infinite, in theory. The relative positions of these features are well-known and they play an important role in fitting experimental data. However, there has been relatively little discussion of how high the steps are, so we present explicit formulae for these heights. This gives a full characterization of the features in this lineshape which can lead to an analysis of the spectrum without the usual laborious powder average.The transition frequency, as a function of the orientation angles, shows critical points: maxima, minima and saddle points. The maxima and minima correspond to the step discontinuities and the saddle points generate the singularities. Near a maximum, the contours are ellipses, whose dimensions are determined by the second derivatives of the frequency with respect to the polar and azimuthal angles. The density of points is smooth as the contour levels move up and down, but then drops to zero when a maximum is passed, giving a step. The height of the step is determined by the Hessian matrix—the matrix of all partial second derivatives. The points near the poles and the saddle points require a more detailed analysis, but this can still be done analytically. The resulting formulae are then compared to numerical simulations of the lineshape.We expand this calculation to include a relatively simple case where there is chemical shielding anisotropy and use this to fit experimental 139La spectra of La2O3.

Oxygen decorating at the one ring and at the N-mouth of (10, 0) aluminum nitride nanotube: A DFT investigation

Abstract We have investigated oxygen decorating in the (10, 0) aluminum nitride nanotube (AlNNT) by density functional theory. Band gaps, total (TDOS) and partial (PDOS) densities of state and chemical-shielding isotropic (CSI) and chemical-shielding anisotropic (CSA) have been calculated or determined in three models of the investigated (10, 0) AlNNT: pristine (model.0), O-decorating at the one ring in the middle of AlNNT (Model.1) and O-decorating at the nitrogen mouth of AlNNT (Model.2). The results indicated that the dipole moment does not detect the significant effects of dopant whereas TDOS, PDOS and band gap energies detect notable effects. The CSI and CSA values for the Al and N atoms-contributed to the Al-O bonds or those atoms close to the decorated region, in both models of O-decorated AlNNTs are changed.

Fully and partially exohydrogenated Si80 fullerene cage: a DFT study

We have performed a density functional study to investigate electronic and magnetic properties of fully and partially exohydrogenation in the Si80 fullerene cage based on NMR parameters, nucleus-independent chemical shift (NICS) indices and natural population analysis. Hydrogenation of 20 silicons inside and 60 silicons outside results in two distinct values for the 29Si σ iso, and also for 29Si Δσ. NICS yields negative value of −1.5 ppm at the cage center of the fully exohydrogenated fullerene, Si80H80. However, NICS yields positive value of 1.5 ppm at the cage center of the partially exohydrogenated fullerene, H20@Si80H60, then becomes more negative along the axis toward the center of pentagon until reaching −3.0 ppm at the ring center (and −4.3 at the point 1 A away from the ring center outside), suggesting that in this case pentagons can be considered as aromatic fragments. H20@Si80H60 cage is composed of negatively charged hydrogen atoms and positively charged silicon atoms, indicating electron transfer from silicon atoms on the surfaces of the cage to the chemically bonded hydrogen atoms. A decreasing trend is observed for 1H σ iso values as the natural charges of hydrogen sites in these fullerenes increase while no regular trend is observed for the chemical shielding anisotropy Δσ of hydrogen atoms. .

A DFT study of NMR parameters for MgO nanotubes

Magnesium oxide nanotubes of finite length are investigated by the Density Functional Theory (DFT) at the B3LYP/6-31G (d) level. The (6, 0) zigzag and (4, 4) armchair of MgO nanotubes were considered and nuclear magnetic resonance properties including isotropic and anisotropic chemical shielding parameters (CSI and CSA) were calculated for 25 Mg and 17 O atoms of the optimized structures for the first time. The calculated CS parameters indicated that the Mg atoms cause slight changes of electronic environment in the MgONT structures, but the changes for the O atoms are more significant. Results indicated that the zigzag MgONTs could be considered a more reactive material than the armchair model for interactions with other atoms or molecules.

The Si, Ge, Sn, Pb doped (6,3) Chiral single-walled carbon nanotubes: A computational study

Electronic structure properties including bond lengths, bond angles, dipole moments (μ), energies, band gaps, NMR parameters of the isotropic and anisotropic chemical shielding parameters for the sites of various atoms were calculated using the density functional theory for Si, Ge, Sn, Pb doped (6,3) Chiral single-walled carbon nanotubes (SWCNTs). The calculations indicated that average bond lengths were as: Pb3C>Sn3C>Ge3C>Si3C>C3C. The dipole moments for Si, Ge, Sn, Pb doped (6,3) Chiral single-walled carbon nanotubes structures show fairly large changes with respect to the pristine model.

GALLIUM AND ARSENIC DOPED ON (4, 4) ARMCHAIR AND (8, 0) ZIGZAG MODELS OF BORON PHOSPHIDE NANOTUBES: NMR STUDY

Abstract The structural and electrostatic properties of the single-walled two representative (8, 0) zigzag and (4, 4) armchair models of pristine and GaAs-doped on boron phosphide nanotubes (BPNTs) was investigated by calculating the nuclear magnetic resonance tensors and with performing the density function theory. The geometrical structures of all representative pristine and GaAs-doped models of BPNTs have been allowed to relax by optimization and then the isotropic and anisotropic chemical shielding (CS) parameters (CSI and CSA) of 11B and 31P have been calculated. The results reveal that with doping gallium and arsenic atoms in spite of boron and phosphorus atoms, the geometrical structure, the band gape energy between Homo and Lumo orbital and NMR parameters of the boron and phosphorus sites changed. The comparisons of results reveal that the variation NMR parameters and band gape energy of zigzag model are more than armchair model. The NMR properties of boron atoms only detect slight changes but those of phosphorous atoms are more notable

Vibrational spectra, NBO analysis, first order hyperpolarizabilities, thermodynamic functions and NMR chemical shielding anisotropy (CSA) parameters of 5-nitro-2-furoic acid by ab initio HF and DFT calculations

In this work, FT-IR and FT-Raman spectra are recorded on the solid phase of 5-nitro-2-furoic acid (abbreviated as NFA) in the regions 4000–400cm−1 and 3500–100cm−1 respectively. The geometrical parameters, vibrational assignments, HOMO–LUMO energies and NBO calculations are obtained for the monomer and dimer of NFA from HF and DFT (B3LYP) with 6-311++G (d, p) basis set calculations. Second order perturbation energies and electron density (ED) transfer from filled lone pairs of Lewis base to unfilled Lewis acid sites of NFA are discussed on the basis of NBO analysis. Intermolecular hydrogen bonds exist through COOH groups; give the evidence for the formation of dimer entities in the title molecule. The theoretically calculated harmonic frequencies are scaled by common scale factor. The observed and the calculated frequencies are found to be in good agreement. The thermodynamic functions were obtained for the range of temperature 100–1000K. The polarizability, first hyperpolarizability, anisotropy polarizability invariant has been computed using quantum chemical calculations. The chemical parameters were calculated from the HOMO and LUMO values. The NMR chemical shielding anisotropy (CSA) parameters were also computed for the title molecule.

Designing Dipolar Recoupling and Decoupling Experiments for Biological Solid-State NMR Using Interleaved Continuous Wave and rf Pulse Irradiation

Rapid developments in solid-state NMR methodology have boosted this technique into a highly versatile tool for structural biology. The invention of increasingly advanced rf pulse sequences that take advantage of better hardware and sample preparation have played an important part in these advances. In the development of these new pulse sequences, researchers have taken advantage of analytical tools, such as average Hamiltonian theory or lately numerical methods based on optimal control theory. In this Account, we focus on the interplay between these strategies in the systematic development of simple pulse sequences that combines continuous wave (CW) irradiation with short pulses to obtain improved rf pulse, recoupling, sampling, and decoupling performance. Our initial work on this problem focused on the challenges associated with the increasing use of fully or partly deuterated proteins to obtain high-resolution, liquid-state-like solid-state NMR spectra. Here we exploit the overwhelming presence of (2)H in such samples as a source of polarization and to gain structural information. The (2)H nuclei possess dominant quadrupolar couplings which complicate even the simplest operations, such as rf pulses and polarization transfer to surrounding nuclei. Using optimal control and easy analytical adaptations, we demonstrate that a series of rotor synchronized short pulses may form the basis for essentially ideal rf pulse performance. Using similar approaches, we design (2)H to (13)C polarization transfer experiments that increase the efficiency by one order of magnitude over standard cross polarization experiments. We demonstrate how we can translate advanced optimal control waveforms into simple interleaved CW and rf pulse methods that form a new cross polarization experiment. This experiment significantly improves (1)H-(15)N and (15)N-(13)C transfers, which are key elements in the vast majority of biological solid-state NMR experiments. In addition, we demonstrate how interleaved sampling of spectra exploiting polarization from (1)H and (2)H nuclei can substantially enhance the sensitivity of such experiments. Finally, we present systematic development of (1)H decoupling methods where CW irradiation of moderate amplitude is interleaved with strong rotor-synchronized refocusing pulses. We show that these sequences remove residual cross terms between dipolar coupling and chemical shielding anisotropy more effectively and improve the spectral resolution over that observed in current state-of-the-art methods.