Component Of Electric Field Gradient Tensor Research Articles

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.

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.

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.

Hyperfine Interactions in Copper Lattice Sites of Antiferromagnetic Compounds Representing the Analogues of Superconducting Copper Metal-Oxide Compounds

Emission 61Cu(61Ni) Mossbauer spectra of dielectric metal-oxide compounds of divalent copper with molecular formulas Ca1 – xSrxCuO2, Ca2CuO2Cl2, SrCuO2, Sr2CuO2Cl2, YBa2Cu3O7 – x, La2 – xSrxCuO4, and Nd2 – xCexCuO4 correspond to the quadrupole and Zeeman interactions of the 61Ni nuclei with local fields at the copper lattice sites, whereas the spectra of superconducting metal-oxide complexes correspond to the interaction of the quadrupole moment of the 61Ni nuclei with the tensor of the electric field gradient (EFG). For both groups of metal oxides, linear dependences of the quadrupole interaction constants on the calculated values of the principal component of the lattice EFG tensor in the copper lattice sites are observed both on the 61Ni nuclei (data of the emission Mossbauer spectroscopy on the 61Cu(61Ni) isotopes) and on the 63Cu nuclei (data of the nuclear magnetic resonance on the 63Cu isotope). This fact is explained by the constant values of the valence component of the EFG for both the 61Ni2+ and 63Cu2+ probes in all metal-oxide complexes of divalent copper.

33S nuclear quadrupole resonance study of dibenzyl disulfide toward understanding of cross-linked structures in rubber

Experimental and theoretical investigations of a sulfur-33 electric-field-gradient (EFG) tensor of disulfide bonds in 33S-labled dibenzyl disulfide have been presented. Temperature dependence of quadrupolar frequencies, νQ, is observed in the temperature range between 80 and 280 K, in which single peaks appear in all the 33S nuclear quadrupole resonance (NQR) spectra. Analysis of nutation echo 33S NQR spectra at 200 K yields the quadrupolar coupling constant, CQ value, of 46.8(6) MHz and the asymmetry parameter, ηQ, of 0.48(7). The orientation of the 33S EFG tensor of the disulfide is obtained by quantum chemical calculations: the largest EFG tensor component, VZZ, is approximately perpendicular to the molecular plane (C-S-S), and the smallest component, VXX, is approximately 41° off the C-S bond. Extensive quantum chemical calculations are systematically performed to investigate dependences of 33S EFG tensors on changes of torsion angles in disulfide and trisulfide bonds, indicating that analysis of νQ and CQ values potentially makes it possible to assign the secondary structures of cross-linking in a rubber.

Temperature Dependence of NMR Parameters Calculated from Path Integral Molecular Dynamics Simulations

The influence of temperature on NMR chemical shifts and quadrupolar couplings in model molecular organic solids is explored using path integral molecular dynamics (PIMD) and density functional theory (DFT) calculations of shielding and electric field gradient (EFG) tensors. An approach based on convoluting calculated shielding or EFG tensor components with probability distributions of selected bond distances and valence angles obtained from DFT-PIMD simulations at several temperatures is used to calculate the temperature effects. The probability distributions obtained from the quantum PIMD simulations, which includes nuclear quantum effects, are significantly broader and less temperature dependent than those obtained with conventional DFT molecular dynamics or with 1D scans through the potential energy surface. Predicted NMR observables for the model systems were in excellent agreement with experimental data.

NMR study of the electric field gradient in the paramagnetic phase of M3V2O8 (M = Co, Ni) compounds

The NMR spectra and the decay of a spin echo signal from 51V nuclei in Kagome-staircase Co3V2O8 (CVO) and Ni3V2O8 (NVO) single crystals are measured in the temperature range 30–300 K and a magnetic field H0 = 20 kOe. The orientation dependences of the 51V NMR line shape are used to determine the electric field gradient (EFG) parameters, namely, quadrupole frequency νQ and asymmetry parameter η. These parameters for NVO and CVO are νQ = 180(10) kHz, η = 0.5(1) and νQ = 130(10) kHz, η = 0.6(1), respectively. A comparison of the results of calculating EFG tensors with a point charge model and the NMR data indicates that the crystallographically equivalent vanadium atoms in the Ni3V2O8 and Co3V2O8 compounds differ in the EFG axis orientation. M3V2O8 crystals are found to have vanadium positions (V1, V2) with different orientations of the z axis, which specifies the direction of the principal value of EFG (Vzz): these orientations lie in the bc plane and make an angle of either +51(5)° (V1) or −51(5)° (V2) with axis c. In the temperature range 30–300 K, the EFG tensor components and the local symmetry of the charge surrounding of the vanadium positions in NVO and CVO oxides are found to change insignificantly.

How to analyse powder nuclear quadrupole interaction data with non-axial symmetry for interdependent electric field gradient tensor components

The measurement of nuclear quadrupole interactions from powder (random) samples yields two parameters, namely Vzz and the asymmetry parameter η. Usually, these two parameters are plotted separately versus an external variable. This parametrization is perfectly suited to hide correlations between electric field gradient tensor components, even linear dependences. A new parametrization is proposed that, in the case of linear dependences, consists of a constant scale factor, the ‘asymptotic’ asymmetry parameter, also a constant, and a control parameter that is the only function of an external variable. This parametrization reduces the number of freely adjustable parameters in data fitting by nearly a factor of two. All solid-state effects are contained in a single control parameter. In the case of linear dependences, a two-tiered data analysis is proposed that is compulsory. An extension of the analysis to nonlinear dependences is given as well. The proposed two-tier analysis in the Czjzek plot reveals the structure of the electric field gradient (EFG) tensor. Several examples will be given.

The concept of trajectories in the data analysis of non-axially symmetric nuclear quadrupole interactions

The conventional analysis of non-axially symmetric nuclear quadrupole interaction data requires two adjustable parameters, namely Vzz and the asymmetry parameter η, and these two parameters are plotted separately versus an external parameter, e.g. temperature. Thus 2N parameters are fitted for N temperature points. In this way, possible interdependencies of electric field gradient tensor components are ignored. The correct strategy for the data analysis would be to analyze the data conventionally, plot the data in the Czjzek-plot, and for a linear trajectory perform a simultaneous fit of all data with N + 2 adjustable parameters (N values of a control parameter plus a scale factor plus the slope) in a second tier. The concept of trajectories can be extended to non-linear trajectories.

Powder perturbation functions in angular correlations for distributions of electric field gradient tensor components: analytical expressions for I=1

Analytical expressions for powder perturbation functions in angular correlations for the following distributions of electric field gradient tensor components are derived for I=1: (i) straight line distributions (one-dimensional (1D) trajectories) applicable for cases where tensor components depend linearly on each other and (ii) 2D distributions (areas) in the Czjzek-plot, a variant of a Cartesian Vxx versus Vzz-plot. For the sake of simplicity, a weight of unity was used for the trajectories and areas, respectively. The results contain the 1D or 2D Fourier transform (eventually in a rotated coordinate system) of the distribution function and can easily be extended for other weights and/or shapes. A new set of parameters to describe the distributions is given. These results have implications for the analysis of 2H-NMR data.

Determination of the orientations for the 17O NMR tensors in a polycrystalline l-alanine hydrochloride

We report a solid-state 17O NMR study of the 17O electric-field-gradient (EFG) and chemical shielding (CS) tensors for the carboxyl oxygen in an l-alanine hydrochloride. Using [ 17O]– and [ 13C, 17O]– l-alanine hydrochlorides, both the magnitudes and the orientations in the molecular frame of the 17O EFG and CS tensors could be determined by the analysis of the 17O magic-angle spinning (MAS) and stationary NMR spectra. For the carbonyl oxygen, the smallest EFG tensor component, V XX , and the largest EFG component, V ZZ , roughly lies in the carboxyl molecular plane and the direction of V XX is parallel to the dipolar vector between 13C and 17O, that is, the direction of C O bond. The angles between the intermediate EFG component, V YY , and δ 33 component, and between δ 22 component and V ZZ are found to be approximately 10° and 35°, respectively. We also present the results of the quantum chemical calculations for a theoretical hydrogen-bonding model, indicating that hydrogen-bonding strengths make it possible to vary both magnitudes and orientations of the carbonyl 17O EFG tensors in amino acid hydrochlorides.

Role of spin state on the geometry and nuclear quadrupole resonance parameters in hemin complex

Theoretical calculations of structural parameters, 57Fe, 14N and 17O electric field gradient (EFG) tensors for full size-hemin group have been carried out using density functional theory. These calculations are intended to shed light on the difference between the geometry parameters, nuclear quadrupole coupling constants (QCC), and asymmetry parameters ( η Q) found in three spin states of hemin; doublet, quartet and sextet. The optimization results reveal a significant change for propionic groups and porphyrin plane in different spin states. It is found that all principal components of EFG tensor at the iron site are sensitive to electronic and geometry structures. A relationship between the EFG tensor at the 14N and 17O sites and the spin state of hemin complex is also detected.

A Theoretical Study of 51V Electric Field Gradient Tensors in Pyrovanadates and Metavanadates

A computational study of the 51V electric field gradient (EFG) tensors in pyrovanadates, α-Zn2V2O7, Cd2V2O7, β-Mg2V2O7 and BaCaV2O7, and the metavanadates, LiVO3, α-NaVO3, KVO3, ZnV2O6 and MgV2O6, is presented. Restricted Hartree–Fock and hybrid density functional theory calculations have been used to investigate the effects of the size of vanadium-oxygen clusters, basis set size, proton-termination and embedded cluster techniques on the accuracy of the calculated EFG tensors. Good agreement between theory and experiment is obtained for most of the vanadates. A sound methodology is suggested for calculating the EFG tensor in pyrovanadates which contain isolated V2O7 4− clusters. For metavanadates, the charges of the bridging oxygen atoms can be differentiated from those of terminal oxygen atoms by terminating the former with hydrogen atoms, and embedded cluster molecular orbital calculations are useful in accounting for the long-range electrostatic interactions which influence the EFG tensor components. EFG tensor orientations vary for different pyrovanadate structural types, and individual components are confined by symmetry elements in the metavanadates. A preliminary comparison is made between 51V EFG tensors calculated with ab initio and plane wave methods. Theoretical EFG tensor components and orientations, in combination with experimental 51V solid-state nuclear magnetic resonance data, are demonstrated to be useful tools for prediction of molecular structure.

Experimental determination of orientations for the 17O electric-field-gradient and chemical shielding tensors in l-alanine

We have presented a solid-state 17O NMR study of [ 13C, 17O]- l-alanine. Using the experimental results for the 13C– 17O dipolar vector and Euler angles, the absolute orientations of 17O chemical shielding (CS) and electric-field-gradient (EFG) tensors with respect to the molecular frame can be determined for l-alanine. The present results suggest that the intermediate EFG tensor components, V YY , lie in the carboxylate plane and parallel to the C–O bond directions, while the least shielded components, δ 11, and the intermediate CS tensor components, δ 22, roughly lie in the molecular plane and the direction of δ 22 components are approximately 38° and 25° off the C–O bonds for O1 and O2, respectively. These results are in reasonable agreement with those of our quantum chemical calculations reported previously.

Structural Preference versus Metal within the MB2C2 (M=Mg, Sc, Ca, Y, Ln) Phases: The Coloring Problem Revisited by DFT Calculations

The question of coloring: Calculations present a definite solution to the “coloring problem” in the MB2C2 phases (M=Mg, Sc, Ca, Y, Ln; see picture of the four structure types). Electric-field gradient tensor components from NMR spectroscopy readily allow differentiation between the different B/C topologies and give support to the theoretical results. Supporting information for this article is available on the WWW under http://www.wiley-vch.de/contents/jc_2002/2005/z503080_s.pdf or from the author. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

The tautomeric equilibria of cytosine studied by NQR spectroscopy and HF, MP2 and DFT calculations

A study was undertaken to check if such parameters as NQR frequencies, quadrupole coupling constants and the asymmetry parameters determined from the 14N NQR spectra can provide sufficient information to infer about the tautomeric form of a compound studied. The influence of the choice of functional on the 14N NQR parameters calculated by ab initio and DFT methods was analysed. Moreover, the influence of the neighbouring molecules on the NQR parameters was checked for the assumed symmetric planar environment of the cytosine molecule in which it is hydrogen-bonded to four other cytosine molecules. Since the use of a finite basis set is always a source of uncertainties in the electric field gradient tensor components, the final calculations for a layer were performed in two different basis sets: middle and extended.

General models for the distributions of electric field gradients in disordered solids

Hyperfine studies of disordered materials often yield the distribution of the electric field gradient (EFG) or related quadrupole splitting (QS). The question of the structural information that may be extracted from such distributions has been considered for more than fifteen years. Experimentally most studies have been performed using Mössbauer spectroscopy, especially on . However, NMR, NQR, EPR and PAC methods have also received some attention. The EFG distribution for a random distribution of electric charges was for instance first investigated by Czjzek et al [1] and a general functional form was derived for the joint (bivariate) distribution of the principal EFG tensor component and the asymmetry parameter . The importance of the Gauss distribution for such rotationally invariant structural models was thus evidenced. Extensions of that model which are based on degenerate multivariate Gauss distributions for the elements of the EFG tensor were proposed by Czjzek. The latter extensions have been used since that time, more particularly in Mössbauer spectroscopy, under the name `shell models'. The mathematical foundations of all the previous models are presented and critically discussed as they are evidenced by simple calculations in the case of the EFG tensor. The present article only focuses on those aspects of the EFG distribution in disordered solids which can be discussed without explicitly looking at particular physical mechanisms. We present studies of three different model systems. A reference model directly related to the first model of Czjzek, called the Gaussian isotropic model (GIM), is shown to be the limiting case for many different models with a large number of independent contributions to the EFG tensor and not restricted to a point-charge model. The extended validity of the marginal distribution of in the GIM model is discussed. It is also shown that the second model based on degenerate multivariate normal distributions for the EFG components yields questionable results and has been exaggeratedly used in experimental studies. The latter models are further discussed in the light of new results. The problems raised by these extensions are due to the fact that the consequences of the statistical invariance by rotation of the EFG tensor have not been sufficiently taken into account. Further difficulties arise because the structural degrees of freedom of the disordered solid under consideration have been confused with the degrees of freedom of QS distributions. The relations which are derived and discussed are further illustrated by the case of the EFG tensor distribution created at the centre of a sphere by m charges randomly distributed on its surface. The third model, a simple extension of the GIM, considers the case of an EFG tensor which is the sum of a fixed part and of a random part with variable weights. The bivariate distribution is calculated exactly in the most symmetric case and the effect of the random part is investigated as a function of its weight. The various models are more particularly discussed in connection with short-range order in disordered solids. An ambiguity problem which arises in the evaluation of bivariate distributions of centre lineshift (isomer shift) and quadrupole splitting from Mössbauer spectra is finally quantitatively considered.

Nonempirical calculations of NQR spectrum parameters of azetidine

The components of the 14N electric field gradient (EFG) tensor, the corresponding nuclear quadrupole coupling constant (NQCC) X, and the asymmetry parameter q of azetidine were calculated using the restricted Hartree--Fock--Roothaan method. The geometry of azetidine was optimized with the 4-31G basis set, and the values of the ring puckering angle (0) and the angle between the N--H bond and the CNC plane ([3) were refined with the 6-31G* basis set. The effect of choice of geometry on calculated NQR parameters was studied. To clarify the origin of EFG at the nitrogen atom nucleus, the contributions from individual bond orbitals and lone electron pairs to the EFG tensor components eqi i were calculated in the framework of the LMO approach. It was demonstrated that the 4-31G + 6-31G*//6-31G* level calculations give NQCC and q values of azetidine that are in good agreement with the results of MW spectroscopy.

Lewis Acid Sites and Surface Aluminum in Aluminas and Zeolites: A High-Resolution NMR Study

It was the main purpose of this work to study the nature of Lewis acidity in various catalysts (aluminas and zeolites) pretreated under controlled atmosphere at different temperatures. Isotopically enriched ammonia [sup 15]NH[sub 3] chemisorption was employed to probe the surface active sites and to allow for magnetization transfer to surface and close-to-surface Al nuclei. A special deconvolution procedure was applied to obtain [sup 27]Al spectral parameters for different Al sites in partially resolved spectra. The procedure accounted for the normal distribution of electric field gradient tensor components at a particular site. It is shown that there are two kinds of Lewis sites on aluminas: namely, a tetrahedral site with isotropic shift of about 58 ppm and quadrupolar coupling constant QCC [approx equal] 6 MHz and a pentagonal site with a isotropic shift of about 40 ppm and a slightly smaller QCC. In zeolites the same kinds of sites exist in the nonframework aluminum debris, and in addition, the Broensted sites are associated with framework aluminum. 32 refs., 8 figs., 5 tabs.