Electric Field Gradient Tensor Research Articles

Drop That Activation Energy: Tetragonal to Cubic Transformations in Na3PS4−xSex for Solid State Sodium Ion Battery Materials

AbstractSodium‐containing chalcogenide materials are emerging as a class of solid electrolytes for application in inexpensive all‐solid‐state sodium‐ion batteries due to their high ionic conductivity, abundance, and degree of synthetic and structural variability. Members of the solid solution Na3PS4−xSex, which are promising solid electrolytes for sodium‐ion batteries, are prepared by reaction at high temperature. With increasing substitution of S by Se, the structure transforms from tetragonal (space group P21c for x = 0, 1) to cubic (space group I3m for x = 2, 3, 4). Within the solid solution, the S and Se atoms are completely disordered in the environments around the P atoms, in accordance with a binomial distribution, as inferred by the 31P nuclear magnetic resonance (NMR) spectra. In 23Na NMR experiments conducted at different magnetic fields and temperatures, quadrupolar lineshapes are observed that are influenced by sodium ion dynamics; the activation energies decrease from 0.21 to 0.15 eV on progressing from the S‐ to the Se‐rich members. A dynamic model is proposed to account for the changes in the 23Na quadrupolar lineshapes by switching the orientations of the electric field gradient and chemical shift anisotropy tensors when Na+ ions hop to the four nearest Na sites.

An Intensity Tensor and Electric Field Gradient Tensor for Fe3+ at M1 Sites of Aegirine–Augite Using Single-Crystal Mössbauer Spectroscopy

An intensity tensor of quadrupole doublets and an electric field gradient tensor for Fe3+ at M1 sites in aegirine–augite ((Ca0.16Na0.86)∑1.02(Mg0.13Fe2+0.04Fe3+0.72 Al0.07)∑0.96Si2.01O6) are determined using single-crystal Mössbauer spectroscopy. The components of the intensity tensor are IXX = 0.670 (19), IYY = 0.353 (14), IXY = −0.113 (37) and IZZ = 0.477 (33). The components of the electric field gradient tensor (VXX, VYY and VZZ) for Fe3+ at M1 sites in aegirine–augite are −5.96 × 109, −4.65 × 1010 and 5.23 × 1010 C/m3, respectively. Comparisons of the intensity tensor of aegirine–augite with those of aegirine and augite (Wo40En45Fs16) that have already been reported and the IXX, IYY, IXY and IZZ intensity tensor components of aegirine–augite in this study are almost the same as those of aegirine, but different from those of augite. While the M2 sites of aegirine–augite and aegirine are fully occupied with Na+ and Ca2+ ions, the M2 sites of augite are not fully occupied with Ca2+. The compositional dependency of the intensity tensor components suggests that the intensity tensor components for Fe3+ at the M1 site of a solid solution between aegirine and augite are dependent on the occupancy of large cations such as Ca2+ and Na+ at M2 sites.

Can simple 'molecular' corrections outperform projector augmented-wave density functional theory in the prediction of 35 Cl electric field gradient tensor parameters for chlorine-containing crystalline systems?

Many-body expansion (MBE) fragment approaches have been applied to accurately compute nuclear magnetic resonance (NMR) parameters in crystalline systems. Recent examples demonstrate that electric field gradient (EFG) tensor parameters can be accurately calculated for 14 N and 17 O. A key additional development is the simple molecular correction (SMC) approach, which uses two one-body fragment (i.e., isolated molecule) calculations to adjust NMR parameter values established using 'benchmark' projector augmented-wave (PAW) density functional theory (DFT) values. Here, we apply a SMC using the hybrid PBE0 exchange-correlation (XC) functional to see if this can improve the accuracy of calculated 35 Cl EFG tensor parameters. We selected eight organic and two inorganic crystal structures and considered 15 chlorine sites. We find that this SMC improves the accuracy of computed values for both the 35 Cl quadrupolar coupling constant (CQ ) and the asymmetry parameter ( ) by approximately 30% compared with benchmark PAW DFT values. We also assessed a SMC that offers local improvements not only in terms of the quality of the XC functional but simultaneously in the quality of the description of relativistic effects via the inclusion of spin-orbit effects. As the inorganic systems considered contain heavy atoms bonded to the chlorine atoms, we find further improvements in the accuracy of calculated 35 Cl EFG tensor parameters when both a hybrid functional and spin-orbit effects are included in the SMC. On the contrary, for chlorine-containing organics, the inclusion of spin-orbit relativistic effects using a SMC does not improve the accuracy of computed 35 Cl EFG tensor parameters.

Temperature Dependence of Nuclear Quadrupole Resonance and the Observation of Metal-Ligand Covalency in Actinide Complexes: 35Cl in Cs2UO2Cl4.

We report a study of the temperature dependence of 35Cl nuclear quadrupole resonance (NQR) transition energies and spin-lattice relaxation times (T1) for 235U-depleted dicesium uranyl tetrachloride (Cs2UO2Cl4) aimed at elucidating electronic interactions between the uranium center and atoms in the equatorial plane of the UO22+ ion. The transition frequency decreases slowly with temperature below 75 K and with a more rapid linear dependence above this temperature. The spin-lattice relaxation time becomes shorter with temperature, and as temperatures increase, the T1 decrease becomes nearly quadratic. The observed trends are reproduced by a model that assumes phonon-induced fluctuations of the electric field gradient tensor and partial electron delocalization from Cl to U. The fit of the theoretical model to experimental data allows a Debye temperature of 96 K to be estimated. The generalization of this approach to investigations of covalency in actinide-ligand bonding is examined.

Exploring Partial Structural Disorder in Anhydrous Paraxanthine through Combined Experiment, Solid-State Computational Modelling, and Molecular Docking

Paraxanthine (PX), a major metabolite of caffeine, a protective agent against Alzheimer’s and Parkinson’s disease, and a promising drug for the treatment of post-COVID 2019 anosmia and ageusia, has been studied in the solid state and protein–ligand complex. Partial disorder in PX, caused by the methyl group at the N(7) position, has been modelled and discussed. The relationship between the unusual structural disorder and the propensity to form a specific system of non-covalent bonds was analyzed. Three 1H-14N NMR-NQR (nuclear magnetic resonance–nuclear quadrupole resonance) experimental techniques were used, namely multiple frequency sweeps, Larmor frequency scanning, and the two-frequency irradiation, followed by solid-state computational modelling (density functional theory, supplemented by quantum theory of atoms in molecules, 3D Hirshfeld surfaces, and reduced density gradient), and molecular docking approaches. New quantitative methods for estimating changes in the global pattern of interactions under the influence of rotation of the methyl group in N(7) based on the Pompeiu–Hausdorff and Bhattacharayya metrics and the Wasserstein distance have been proposed and applied. A spectrum consisting of 12 lines, indicating the presence of 4 chemically inequivalent nitrogen sites in the PX molecule, was recorded, and the lines’ assignment to particular sites was made. The influence of the methyl rotation on the eigenvalues and eigenvectors of the electric field gradient tensor, NQR parameters, and resonance line positions was modelled in the solid (GGA/RPBE, m-GGA/RSCAN) and cluster (Minnesota M062X hybrid). Three factors have been found to determine structural disorder in PX: larger crystal voids near the methyl at N(7) than at N(1) (opening the path for the disorder), hyperconjugation strongly affecting the density distribution in the five-membered ring, and the involvement of the methyl group at N(7) in many non-covalent bonds that intercept (capture) subsequent jumping protons. The Pompeiu–Hausdorff and Bhattacharayya metrics and the Wasserstein distance confirmed the changes in the distribution and strength of non-covalent interactions throughout the molecule as a result of methyl rotation. This effect is clearly visible regardless of the type of metric, and its order of magnitude is consistent with the modulation effect of the NQR spectra (experimental and calculated). Through molecular docking, it was discovered that the PX moiety in protein–ligand complexes adopt the same methyl group conformation at N(7) as in the solid state. It was found that the cooperation–competition between the C-H⋯O hydrogen bonds and C-H⋯H-C dispersion interactions is the crucial factor that impedes methyl rotation and induces structural disorder, as well as being an important factor in the formation of the protein–ligand complexes.

Synthesis and Characterization of Xylazine Hydrochloride Polymorphs, Hydrates, and Cocrystals: A 35Cl Solid-State NMR and DFT Study

Xylazine HCl (X) is a veterinary analgesic with many known solid forms, making it an ideal system for studying the noncovalent interactions, such as hydrogen bonding, that provide stability to polymorphs, solvates/hydrates, and cocrystal of pharmaceuticals. Herein, we report methods for the reliable preparation and interconversion of polymorphs of X (including mechanochemical pathways), the discovery of a novel polymorph, and the synthesis of three cocrystals with coformers containing amide and carboxylic acid moieties. An understanding of ball milling protocols is essential for optimizing these reactions and ensuring clean and reproducible syntheses of the products in high yields. All materials were characterized using thermal analysis, powder and single-crystal X-ray diffraction (PXRD and SCXRD), and multinuclear solid-state NMR (SSNMR) spectroscopy. 35Cl SSNMR is highlighted for its versatility for fingerprinting polymorphs, hydrates, and cocrystals (including the detection of impurity phases that are not always evident from PXRD and offering an avenue for optimizing synthetic protocols) and providing molecular-level structural information. The 35Cl electric field gradient (EFG) tensor is extremely sensitive to the unique hydrogen-bonding network in each solid form of X, resulting in distinct powder patterns. Dispersion-corrected plane-wave density functional theory (DFT) structural refinements yield better models of the hydrogen-bonding environments of the chloride ions than is possible through XRD methods alone. Calculations employing the refined structures yield 35Cl EFG tensors that agree well with experiment. PXRD and 35Cl SSNMR, in tandem with reliable calculations of EFG tensors, are essential for the development of NMR crystallographic and crystal structure prediction protocols and crucial for future studies involving HCl salts and their concomitant solid forms.

Do Models beyond Hybrid Density Functionals Increase the Agreement with Experiment for Predicted NMR Chemical Shifts or Electric Field Gradient Tensors in Organic Solids?

Ab initio predictions of chemical shifts and electric field gradient (EFG) tensor components are frequently used to help interpret solid-state nuclear magnetic resonance (NMR) experiments. Typically, these predictions employ density functional theory (DFT) with generalized gradient approximation (GGA) functionals, though hybrid functionals have been shown to improve accuracy relative to experiment. Here, the performance of a dozen models beyond the GGA approximation are examined for the prediction of solid-state NMR observables, including meta-GGA, hybrid, and double-hybrid density functionals and second-order Møller-Plesset perturbation theory (MP2). These models are tested on organic molecular crystal data sets containing 169 experimental 13C and 15N chemical shifts and 114 17O and 14N EFG tensor components. To make these calculations affordable, gauge-including projector augmented wave (GIPAW) Perdew-Burke-Ernzerhof (PBE) calculations with periodic boundary conditions are combined with a local intramolecular correction computed at the higher level of theory. Within the context of typical NMR property calculations performed on a static, DFT-optimized crystal structure, the benchmarking finds that the double-hybrid DFT functionals produce errors versus experiment that are no smaller than those of hybrid functionals in the best cases, and they can be larger. MP2 errors versus experiment are even bigger. Overall, no practical advantages are found for using any of the tested double-hybrid functionals or MP2 to predict experimental solid-state NMR chemical shifts and EFG tensor components for routine organic crystals, especially given the higher computational cost of those methods. This finding likely reflects error cancellation benefiting the hybrid functionals. Improving the accuracy of the predicted chemical shifts and EFG tensors relative to experiment would probably require more robust treatments of the crystal structures, their dynamics, and other factors.

Benchmark accuracy of predicted NMR observables for quadrupolar 14 N and 17 O nuclei in molecular crystals.

Nuclear quadrupole resonances for and 17 O nuclei are exquisitely sensitive to interactions with surrounding atoms. As a result, nitrogen and oxygen solid-state nuclear magnetic resonance (ssNMR) provides a powerful tool for investigating structure and dynamics in complex systems. First-principles calculations are increasingly used to facilitate spectral assignment and to evaluate and adjust crystal structures. Recent work combining the strengths of planewave density functional theory (DFT) calculations with a single molecule correction obtained using a higher level of theory has proven successful in improving the accuracy of predicted chemical shielding (CS) tensors and 17 O quadrupolar coupling constants ( ). Here we extend this work by examining the accuracy of predicted 14 N and 17 O electric field gradient (EFG) tensor components obtained using alternative planewave-corrections involving cluster and two-body fragment-based calculations. We benchmark the accuracy of CS and EFG tensor predictions for both nitrogen and oxygen using planewave, two-body fragment, and enhanced planewave-corrected techniques. Combining planewave and two-body fragment calculations reduces the error in predicted 17 O values by 35% relative to traditional planewave calculations. These enhanced planewave-correction methods improve the accuracy of 17 O and 14 N EFG tensor components by 15% relative to planewave DFT but yield minimal improvement relative to a simple molecular correction. However, in structural environments involving either high symmetry or strong intermolecular interactions, enhanced planewave-corrected methods provide a distinct advantage.

On the Observation of 14N Quadrupole Resonance Transitions in Water Proton NMR Relaxometry Dispersion Curves: The Case of a Labile NH Grouping in a Semirigid Molecular Moiety.

The electric field gradient tensor (considered here at the level of a nitrogen nucleus) can be described by two parameters: the largest element in the (X,Y,Z) principal axis system, denoted by VZZ (leading to the nuclear quadrupole coupling), and the asymmetry parameter η = (|VYY| - |VXX|)/|VZZ| with |VZZ| > |VYY| > |VXX|. The frequencies of the three nitrogen-14 nuclear quadrupole resonance (NQR) transitions depend on both parameters but, for sensitivity reasons, their determination may be especially difficult and time consuming. For a partly rigid NH grouping with a labile proton, water nuclear magnetic resonance (NMR) relaxometry curves may exhibit these three transitions (dubbed quadrupolar dips or quadrupole relaxation enhancement (QRE)), provided that the NH grouping belongs to a moiety possessing a sufficient degree of ordering. Their line shape leads to the correlation time describing mainly the motion of the NH grouping (the proton of which being in exchange with water protons), and their amplitude can be interpreted in terms of an effective NH distance. This approach is applied to a hydrogel, where separate NQR lines are observed for the different types of water existing in this system. Furthermore, the analysis of experimental data allows one to determine the nuclear quadrupole coupling in the protonated and deprotonated forms of this molecular moiety involving a labile NH grouping.

Al27 NMR local study of the Al0.5TiZrPdCuNi alloy in high-entropy alloy and metallic glass forms

We report a $^{27}\mathrm{Al}$ nuclear magnetic resonance (NMR) local spectroscopic study of the NMR lineshape and Knight shift of a six-component ${\mathrm{Al}}_{0.5}\mathrm{TiZrPdCuNi}$ metallic alloy that can be prepared either as a crystalline high-entropy alloy (HEA) or as an amorphous metallic glass (MG) at the same chemical composition. For both structural modifications of the material (HEA and MG), we have determined the distribution of electric-field-gradient (EFG) tensors and the local electronic density of states (DOS) $g({\ensuremath{\varepsilon}}_{\mathrm{F}})$ at the Fermi level at the position of $^{27}\mathrm{Al}$ nuclei. A theoretical $I=\frac{5}{2}$ quadrupole-perturbed NMR spectrum, pertinent to both cubic HEAs and amorphous MGs, has been derived using the Gaussian isotropic model of the EFG tensor distribution, and excellent fits of the experimental spectra were obtained. The EFG distribution function of the MG state is about twice broader than that of the HEA state, reflecting the existence of a (distorted) crystal lattice in the latter and its absence in the former. The ${T}^{2}$ dependence of the Knight shift indicates that the DOS is changing rapidly with energy within the Fermi level region for both structural modifications. The local DOS at the $^{27}\mathrm{Al}$ sites of the HEA sample is $\ensuremath{\sim}10%$ larger than that of the MG state, indicating comparable degrees of disorder.

Insights into the aftereffects phenomenon in solids based on DFT and time-differential perturbed γ−γ angular correlation studies in 111In (→ 111Cd) -doped tin oxides

Recently, a model based on a combined ab initio/time-differential perturbed $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ angular correlation (TDPAC) study in the $^{111}\mathrm{In}(\ensuremath{\rightarrow}^{111}\mathrm{Cd})$-doped ${\mathrm{SnO}}_{2}$ semiconductor was proposed to enlighten the origin of the dynamic hyperfine interactions (HFIs) observed in oxides after the electron-capture (EC) decay of the probe nucleus of the $^{111}\mathrm{In}$ parent. It was demonstrated that both the EC as well as the acceptor level introduced by the Cd impurity can contribute to the variation of the electric-field gradient (EFG) at the Cd site (responsible for this phenomenon) due to charge fluctuations of the electronic holes created [Darriba et al., J. Phys. Chem. C 122, 17423 (2018)]. To disentangle both effects, we performed here TDPAC reversible experiments in $^{111}\mathrm{In}(\ensuremath{\rightarrow}^{111}\mathrm{Cd})$-doped SnO in the temperature range 20--900 K and a complete electronic structure density functional theory study of the Cd-doped SnO system as a function of the charge state $(q)$ of the impurity. The isovalent $^{111}\mathrm{Cd}$ probe impurity in this isocationic oxide was selected to demonstrate that the acceptor character of the probe is not a necessary condition to observe this electronic phenomenon when the EC is already present. A majority fraction of probes sensed a time-dependent HFI (HFI1) for all temperatures, and the unexpected minority always sensed a static interaction (HFI2). Comparing results from these experiments, the ab initio calculations of the EFG tensor and defect formation energies, HFI1 and HFI2, were assigned to $^{111}\mathrm{Cd}$ probes localized at substitutional Sn sites free of defects [with the valence band (VB) completely filled, $q=0$] and with an electronic hole trapped $(q=1+)$, respectively. In addition, we show that the systems with charge state between these values have very similar formation energies at the top of the VB and different predicted EFGs, giving support from first principles to the existence of random fluctuations between different EFGs, necessary in the construction of the on-off perturbation factor used. We demonstrate that all the probes fill their electronic holes before the TDPAC time window except the outermost one, giving a quantification of the number of electronic holes involved in the production of the dynamic effect, only one in SnO. The probes related to HFI2 reach their stable electronic configuration $(q=1+)$ before the emission of the first \ensuremath{\gamma} ray $({\ensuremath{\gamma}}_{1})$ of the \ensuremath{\gamma}-\ensuremath{\gamma} cascade, while those related to HFI1 fill the last hole after the emission of ${\ensuremath{\gamma}}_{1}$, producing the dynamic interaction. Enlighted by these results and reviewing TDPAC experiments from the literature using probes with different nuclear decay characteristics, we concluded that, in the absence of EC decay of the probe nucleus of the parent, any probe impurity introducing acceptor or donor states (in semiconductors and insulators) whose ionization changes the EFG should observe a time-dependent HFI provided the lifetime of the nuclear levels that feed the ${\ensuremath{\gamma}}_{1}$ level and this level itself is shorter than the lifetime of the recovery process (i.e., the lifetime of the electronic holes or the ionized donor electrons).

Muon-Nitrogen Quadrupolar Level Crossing Resonance in a Charge Transfer Salt.

Although muons are primarily regarded as a local spin probe, they can also access the charge state of an atom or molecule via quadrupolar level crossing resonance (QLCR) spectroscopy. We use Li+TCNQ– (TCNQ = 7,7,8,8-tetracyanoquinodimethane), a simple charge transfer salt, to test the potential of this technique in molecular systems by studying the interaction of a positive muon with the TCNQ nitrogen atoms. We show that both a positive muon and muonium are able to add to the nitrogen, leading to a singlet spin state for the addition molecule. This produces a characteristic three line QLCR spectrum, with the observed line positions and intensities determined by the principal values and orientation of the electric field gradient tensor at the nitrogen. Ab initio calculation of this field gradient and the resulting QLCR spectrum give good agreement with the experiment. A nonresonant background contribution to the relaxation rate also provides evidence for spin excitations rapidly diffusing along the TCNQ chains. These reflect mobile unpaired electrons introduced by muonium addition. It is thus shown that a single set of muon measurements can be sensitive to both spin and charge degrees of freedom in the same molecular material.

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.

On spin-lattice relaxation of nuclear quadrupole resonance in polycrystalline solids

The analysis of spin–lattice relaxation in nuclear quadrupole resonance (NQR) of spin-52 reported by Okubo and Igarashi (Z. Naturforsch. A. 56 (2001) 777) is extended to take account of the distribution of the initial non-equilibrium populations created by a resonant radio-frequency pulse in powder. The proposed theory is applicable to axially symmetric electric field gradient tensor and is examined for spin–lattice relaxation of 127I NQR in polycrystalline pyridine iodine monochloride measured at 469 MHz at 77 K.

Computation of Phonon Density of States, Atomic Electrostatic Potential and Electric Field Gradient Tensor Using Single Crystal Data of Six Benzene Sulfonamide Based Compounds

Molecular dynamic study of benzene sulfonamide based compounds was carried out to compute several properties like phonon density of states, atomic electric potential and electric field gradient tensor components and then compared. This work establishes the correlation between physical properties and the quantity of carbon atoms in a molecule. The GULP program was used to do all the calculations and reported single crystal data.

The antiferromagnetic phase transition in the layered Cu0.15Fe0.85PS3 semiconductor: experiment and DFT modelling

The experimental studies of the paramagnetic-antiferromagnetic phase transition through Mössbauer spectroscopy and measurements of temperature and field dependencies of magnetic susceptibility in the layered Cu0.15Fe0.85PS3 crystal are presented. The peculiar behavior of the magnetization - field dependence at low-temperature region gives evidence of a weak ferromagnetism in the studied alloy. By the ab initio simulation of electronic and spin subsystems, in the framework of electron density functional theory, the peculiarities of spin ordering at low temperature as well as changes in interatomic interactions in the vicinity of the Cu substitutional atoms are analyzed. The calculated components of the electric field gradient tensor and asymmetry parameter for Fe ions are close to the ones found from Mössbauer spectra values. The Mulliken populations show that the main contribution to the ferromagnetic spin density is originated from 3d-copper and 3p-sulfur orbitals. The estimated total magnetic moment of the unit cell (8.543 emu/mol) is in reasonable agreement with the measured experimental value of ∼9 emu/mol.

Characterization of the negatively charged NV defect through the spin density distribution and the hyperfine coupling constants

The spin density function and hyperfine coupling constants of the NV− defect (a vacancy with one nitrogen atom as a first neighbor) in its triplet ground state, are computed by using hybrid functionals, a Gaussian type all electron basis set, the supercell scheme (216 atoms before the defect formation), and the CRYSTAL code. The charged defect has been simulated by using the charge compensated (CC) scheme, in which a background of positive charge is added to restore the neutrality of the unit cell. The local geometry, charge and spin distribution are also reported and discussed. The EPR constants (Fermi contact, the hyperfine coupling and electric field gradient tensors) of the N (both 14N and 15N) and of two C (for the 13C isotope) atoms around the vacancy are in excellent agreement with the recent experimental results by Felton et al. (Phys. Rev. B, 79,075 203, 2009). The comparison is extended to the many other experimental data collected in the last 30 years, to simpler functionals (LDA and PBE), larger supercells (512 atoms), and to recent simulations. It is shown that the present results are much closer to experiment than previous theoretical studies, with a quantitative, rather than qualitative, agreement.

Warm-up spectroscopy of quadrupole-split nuclear spins in n -GaAs epitaxial layers

The efficiency of the adiabatic demagnetization of the nuclear spin system (NSS) of a solid is limited, if quadrupole effects are present. Nevertheless, despite a considerable quadrupole interaction, recent experiments validated the thermodynamic description of the NSS in GaAs. This suggests that nuclear spin temperature can be used as a probe of nuclear magnetic resonances. We implement this idea by analyzing the modification of the NSS temperature in response to an oscillating magnetic field at various frequencies, an approach termed as the warm-up spectroscopy. It is tested in a $n$-GaAs sample where both mechanical strain and built-in electric field may contribute to the quadrupole splitting, yielding the parameters of electric field gradient tensors for $^{75}\mathrm{As}$ and both Ga isotopes, $^{69}\mathrm{Ga}$ and $^{71}\mathrm{Ga}$.

Equatorial Electronic Structure in the Uranyl Ion: Cs2UO2Cl4 and Cs2UO2Br4.

Electric field gradient (EFG) tensors in the equatorial plane of the linear UO22+ ion have been measured by nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) experiments and computed by relativistic Kohn-Sham methods with and without environment embedding for Cs2UO2Cl4 and Cs2UO2Br4. This approach expands the possibilities for probing the electronic structure in uranyl complexes beyond the strongly covalent U-O bonds. The combined analyses find that one of the two largest principal EFG tensor components at the halogen sites points along the U-X bond (X = Cl, Br), and the second is parallel to the UO22+ ion; in Cs2UO2Cl4, the components are nearly equal in magnitude, whereas in Cs2UO2Br4, due to short-range bromide-cesium interactions, the equatorial component is dominant for one pair of Br sites and the axial component is larger for the second pair. The directions and relative magnitudes of the field gradient principal axes are found to be sensitive to the σ and π electron donation by the ligands and the model of the environment. Chlorine-35 NQR spectra of 235U-depleted and 235U-enriched Cs2UO2Cl4 exhibited no uranium-isotope-dependent shift, but the resonance of the depleted sample displayed a 58% broader line width.

Fast and Accurate Electric Field Gradient Calculations in Molecular Solids With Density Functional Theory.

Modern approaches for calculating electric field gradient (EFF) tensors in molecular solids rely upon plane-wave calculations employing periodic boundary conditions (PBC). In practice, models employing PBCs are limited to generalized gradient approximation (GGA) density functionals. Hybrid density functionals applied in the context of gauge-including atomic orbital (GIAO) calculations have been shown to substantially improve the accuracy of predicted NMR parameters. Here we propose an efficient method that effectively combines the benefits of both periodic calculations and single-molecule techniques for predicting electric field gradient tensors in molecular solids. Periodic calculations using plane-wave basis sets were used to model the crystalline environment. We then introduce a molecular correction to the periodic result obtained from a single-molecule calculation performed with a hybrid density functional. Single-molecule calculations performed using hybrid density functionals were found to significantly improve the agreement of predicted 17O quadrupolar coupling constants (C q ) with experiment. We demonstrate a 31% reduction in the RMS error for the predicted 17O C q values relative to standard plane-wave methods using a carefully constructed test set comprised of 22 oxygen-containing molecular crystals. We show comparable improvements in accuracy using five different hybrid density functionals and find predicted C q values to be relatively insensitive to the choice of basis set used in the single molecule calculation. Finally, the utility of high-accuracy 17O C q predictions is demonstrated by examining the disordered 4-Nitrobenzaldehyde crystal structure.