Calculated Field Gradient Research Articles

Electric field gradient calculations forLixTiS2and comparison withLi7NMR results

The elements of the electric field gradient tensor at Li position in the intercalation compound ${\mathrm{Li}}_{x}\mathrm{Ti}{\mathrm{S}}_{2}$ (with $x=0.25$, 0.33, 0.67, and 1.0) were calculated with first-principles methods and periodic supercell models. The theoretical results obtained with density functional and Hartree-Fock hybrid methods were compared with experimental field gradients extracted from $^{7}\mathrm{Li}$ NMR spectra from the literature and from our measurements presented here. The dependence of calculated field gradients on the basis set and the explicit form of the exchange-correlation density functional was investigated. In agreement with earlier studies a pronounced effect of polarization functions at the Li site was observed. After optimization of internal degrees of freedom in $\mathrm{Li}\mathrm{Ti}{\mathrm{S}}_{2}$ all methods under consideration give quadrupole coupling constants in close agreement with experiment. For $xl1$ the calculated quadrupole coupling constants were found to depend more sensitively on the method which was attributed to differences in the description of spin localization. The calculations allow one to distinguish between Li atoms placed at octahedral and tetrahedral interstitial sites of the host lattice $\mathrm{Ti}{\mathrm{S}}_{2}$.

The active-site metal coordination geometry of cadmium-substituted alcohol dehydrogenase

The structure of eleven complexes of cadmium-substituted alcohol dehydrogenase with or without coenzyme and with different non-protein cadmium ligands has been estimated by combined quantum chemical and molecular mechanical geometry optimisations. The geometry of the optimised complexes is similar to the crystal structure of cadmium-substituted alcohol dehydrogenase, indicating that the method behaves well. The optimised structures do not differ significantly (except for the metal bond lengths) from those of the corresponding zinc complexes, which shows that cadmium is a good probe of zinc coordination geometries. The electric field gradients at the cadmium nucleus have been calculated quantum chemically at the MP2 level with a large cadmium basis set, and they have been used to interpret experimental data obtained by perturbed angular correlation of γ-rays. The experimental and calculated field gradients (all three eigenvalues) differ by less than 0.35 a.u. (3.4·1021 Vm–2), the average error is 0.11 a.u., and the average relative error in the two largest eigenvalues of the field gradients is 9%. Calculated field gradients of four-coordinate structures agree better with the experimental results than do those of any five-coordinate model. Thus, the results indicate that the catalytic metal ion remains four-coordinate in all examined complexes. Two measurements are best explained by a four-coordinate cadmium ion with Glu-68 as the fourth ligand, indicating that Glu-68 probably coordinates intermittently to the catalytic metal ion in horse liver alcohol dehydrogenase under physiological conditions.

The electric field gradient at the nearest-neighbour host site due to a monovacancy in copper metal

The electric field gradient at the nearest-neighbour site due to a monovacancy in copper metal has been evaluated more accurately than before. The screening charge distribution has been determined in an appropriate muffin-tin scattering potential that was previously used in the energy band calculations of the host metal. The strain field has been evaluated by using host atom displacements determined for a discrete lattice in a lattice statics procedure. Unlike other calculations, no adjustable parameter has been used. The agreement between the calculated field gradient and experiment is very good and is much better than in previous work.

Cluster calculation of electronic structure and hyperfine interactions for α-Fe 2O 3

The MSX α cluster technique has been used to study the electronic structure of hematite α-Fe 2O 3, where iron is formally in a 3 d 5 6 S state. The calculated energy levels are compared with X-ray emission and photoelectron spectra. The wave functions have been used to compute the charge distribution, as well as hyperfine parameters such as quadrupole coupling constant, isomer shift and magnetic hyperfine field. The results indicate a considerable influence of chemical bonding on these parameters due to charge transfer and covalency. From the calculated field gradient and the measured quadrupole coupling constant a nuclear quadrupole moment for 57 m Te of about 0.11 b is deduced. This value is smaller than the most recent estimates of 0.15 b based on the ionic model but not as small as the value of 0.082 b obtained from first principles calculations on iron dihalides.

Molecular dynamic simulation of quadrupole relaxation of atomic ions in aqueous solution

Molecular dynamics (MD) simulations were performed in order to investigate the molecular origin of the nuclear quadrupole relaxation mechanism for Li+, Na+, and Cl− ions in dilute aqueous solution. Different boundary conditions were investigated in the simulations, but neither the boundary conditions nor the system size have any significant effect on the different time correlation functions (tcf:s) calculated. It is found that the field gradient tcf, determining the NMR relaxation rate for these ions, is almost completely due to the water molecules in the first shell. The calculated field gradient tcf:s show a complex time-dependence not describable with a mono-exponential decay. The very rapid decay shown by the field gradient tcf for all three ions can partly be attributed to a correlated water motion in the first hydration shell. The relaxation rates obtained from the simulations are in excellent agreement with experimental data for Na+ and Cl−, while the Li+ relaxation rate is less well produced.

Electronic structure and Mössbauer quadrupole splittings in iron (II) pentacyanides

Multiple-scattering calculations have been performed for the isoelectronic series of the iron (II) pentacyanides Fe${(\mathrm{CN})}_{5}$${\mathrm{NO}}^{2\ensuremath{-}}$, Fe${(\mathrm{CN})}_{5}$${\mathrm{CO}}^{3\ensuremath{-}}$, and Fe${(\mathrm{CN})}_{5}$${\mathrm{N}}_{2}^{3\ensuremath{-}}$. Fe $3d$ and $4p$ populations and total electron densities at the iron nucleus derived from these calculations are used to interpret experimental M\"ossbauer quadrupole splittings and electric field gradients at the iron nucleus. Covalency effects involving the Fe $3d$ and $4p$ orbitals ($\ensuremath{\pi}$ back donation and $\ensuremath{\sigma}$ donation, respectively) are found to play a major role in the calculated field gradients. The calculated quadrupole splittings are found to be in good agreement with the experimental values.

NMR spectra of Li and N in single crystals of Li3N: discussion of ionic nature

Quadrupole splittings of 7Li and 14N were measured in single crystals of Li3N as a function of the orientation to the magnetic field. The experimentally determined field gradients are compared with numerically calculated values. Assuming ionic bonding in Li3N, the calculated field gradients have a correct interpretation of NMR spectra, in contradiction to conclusions of other authors on their experimental NMR results of polycrystalline Li3N. From the orientation dependence of the chemical shift the deformation of the electron cloud of N3- can be estimated.

Theory of quadrupole interaction in the ground state ofZn67nucleus in zinc metal

The calculated field gradient in zinc metal with antishielding effects included by an ab initio procedure is shown, in conjunction with observed quadrupole-coupling data from M\ossbauer and nuclear-quadrupole-resonance measurements, to give a quadrupole moment of 0.13 barns for zinc nuclear ground state, $^{67}\mathrm{Zn}$ $\frac{5}{{2}^{+}}$, in satisfactory agreement with the atomic beam value of 0.15\ifmmode\pm\else\textpm\fi{}0.015 barns.

Theory of nuclear quadrupole interaction in cadmium using a first-principles pseudopotential

The field gradient in cadmium metal is calculated using a first-principles pseudopotential and including antishielding effects for the conduction electrons in an ab initio manner. The calculated field gradient in combination with the quadrupole coupling constant from perturbed-angular-correlation measurements leads to a quadrupole moment of 0.71 barns in good agreement with an earlier value obtained using an adaptation to other energies of an empirical pseudopotential derived from Fermi-surface data and in reasonable agreement with 0.77 barns from ionic crystal data. These results testify to both the importance of antishielding effects for conduction electrons and the reasonableness of the pseudopotential procedure used earlier.

The effect of p, d, and f Gaussian polarization functions on the computed one-electron properties of AHn oxygen and sulfur hydrides

A series of LCAO-MO-SCF calculations, using various basis sets of Gaussian-type functions, has been made in order to study the effects of p, d, and f polarization functions on calculated one-electron properties for a 10-electron isoelectronic series of oxygen hydrides and for an 18-electron series of sulfur hydrides. Conclusions from these results suggest that several one-electron properties have a predictable, although not monotonic convergence pattern. Except for calculated field gradients, f GPF's have only a small effect on the calculated values.

Ab initiotheory of nuclear-quadrupole antishielding effects in metallic systems—application to zinc and cadmium

A first-principles investigation is carried out for the antishielding effects for the field gradients due to conduction electrons in zinc and cadmium. It is found that the field gradient due to conduction electrons external to the core electrons is antishielded in both metals very substantially, by a factor of about 60% of ${\ensuremath{\gamma}}_{\ensuremath{\infty}}$ in both cases, while the part of the field gradient due to conduction electrons in the region internal to the core electrons is subject to very little antishielding effect. Our calculated field gradients in the two metals, when combined with the experimental quadrupole coupling constants, lead to quadrupole moments of 0.46 and 0.67 b for $^{67}\mathrm{Zn}$${(9/2)}^{+}$ and $^{111}\mathrm{Cd}$${(5/2)}^{+}$, the latter agreeing well with a value from ionic crystal data.

Theory of nuclear quadrupole interaction in hexagonal close packed metals—cadmium and zinc

The conduction-electron contribution to the electric field gradient has been calculated for zinc and cadmium. From a study of the conduction and core electron distributions relative to each other, it is concluded that different components of the field gradient due to the conduction electrons, such as from the local and plane-wave components of the conduction-electron densities, should be shielded differently. A value of about ..gamma../sub infinity/is estimated for the field gradient due to the plane-wave component of the density. Using the calculated field gradients in the two metals, the quadrupole moments of /sup 67/Zn and /sup 111/Cd are obtained as 0.50 and 0.76 b, the latter being in good agreement with the value derived earlier from ionic crystal measurements. The effect of the larger antishielding factor on the earlier calculated field gradients in beryllium and magnesium is discussed and it is concluded that the earlier good agreement between theory and experiment for these metals is not significantly affected. Finally, the bearing of the results of the present work on the empirical correlation obtained recently between the conduction-electron and lattice contributions is discussed.

Electric Quadrupole Interaction of 20F in a KZnF3 Single Crystal

Abstract Nuclear magnetic resonance measurements were carried out on neutron activated 20F(T1/2=11s) nuclei in a single crystal of KZnF3. The quadrupolar splitted NMR spectrum, detected via the 20F β-radiation asymmetry, could be observed using a radio frequency modulation technique. The quadrupole coupling constant was determined to e2 q Q/h= + (12.0 ± 1.5) MHz at room temperature. The sign of e2 q Q was obtained from a simultaneous γ-ray anisotropy measurement on the succeeding 20Ne transition. Utilising a calculated field gradient of the fluorine atom, an fQ = 4.6% is determined. This value is compared with literature data of similar compounds.

A Large Volume Homogeneous Low Field Electromagnet

An electromagnet is described which generates low fields, typically 10 G, that are homogeneous over a large volume. The magnet is constructed of 12 coils lying on the surface of a sphere 1 m in diameter, and 18 coils lying on the surface of a concentric sphere 1.5 m in diameter. Both the measured and calculated field gradients show that (∂H/∂z)/H < 10−3 cm−1 for distances of 20 cm from the common center of the spheres along the common axis. Measured field gradients across the equator show that (∂H/∂x)/H and (∂H/∂y)/H < 2 × 10−4 cm−1 for distances of 30 cm from the common center. The currents in the coils on the outer sphere are in opposition to those in the coils on the inner sphere, in order to cancel the external magnetic field. This feature allows the magnet to be placed inside a close fitting magnetic shield, without interaction between the magnet and the shield. Design formulas, constructional details, and tests on the completed magnet are given.

Quadrupole Coupling in Dicobalt Octacarbonyl

The pure nuclear quadrupole resonance spectrum of 59Co in dicobaltoctacarbonyl was studied in the temperature range of − 196 to − 30°C. At liquid-nitrogen temperature, the quadrupole coupling parameters for the two independent crystallographic sites are (A)e2qQ / h = 90.18 ± 0.15 MHz, η = 0.3149 ± 0.001 and (B)e2qQ / h = 89.30 ± 0.15 MHz, η = 0.4837 ± 0.001. The asymmetry parameters for the two sites approach each other with increasing temperature. To understand the observed parameters, the environment of the cobalt atom in Co2(CO)8 is described in terms of an octahedron with distortions along its three and fourfold axes. Defining two corresponding axially symmetric field gradient tensors with z components qa and qb, a quadratic equation relating the ratio qa / qb to the observed asymmetry parameter η is derived. The calculated field gradient with the z axis along the Co–Co direction is in reasonable agreement with the observed quadrupole splitting in Fe2(CO)9. The difference in the η values for the two sites and the temperature dependence is explained assuming additional distortions of the molecule in the solid. The observed quadrupole coupling constant is shown to be almost equal to the contribution of the tetragonal distortion of the molecule. This part of the field gradient is attributed to a difference in occupation number between those bonding orbitals directed towards the position not occupied by a bridging carbonyl and other bonding orbitals. Values of 0.16–0.18 are obtained for the population difference for a single molecular orbital, depending on the degree of 4p participation in the bonding.

Characterization of Ground-State Wavefunctions by Measured Electronic Properties. III. A Gaussian Basis Self-Consistent-Field Calculation for Nitrogen Trifluoride

An LCAO MO SCF calculation has been carried out for nitrogen trifluoride using an uncontracted (73 / 73) Gaussian basis set. Energy parameters, dipole moment, field gradient, molecular quadrupole moment, second moments of charge, and population analysis are reported. The calculation is used to evaluate earlier wavefunctions obtained by more empirical methods. Combining experimental quadrupole-coupling-constant data with the calculated field gradient gives a nitrogen nuclear quadrupole moment of + 0.018 ± 0.003 × 10−24 cm2 which is in good agreement with earlier, less precise, estimates of this parameter.

Theoretical Analysis of the Electronic Structure and Molecular Properties of the Alkali Halides. III. Sodium Chloride

Results of a theoretical investigation of the electronic structure of NaCl within the SCF-LCAO-MO approximation are discussed. Special emphasis is given to the computation of molecular properties. Computed values (followed by experimental values in parentheses) for the total energy E, equilibrium separation Re, spectroscopic constants ωe, ωexe, and Be, and dipole moment μ, are: E = − 621.4574 a.u.; Re = 4.485 a.u. (4.4601); ωe = 378.3 cm−1 (364.6); ωexe = 2.589 cm−1 (2.05); Be = 0.2155 cm−1 (0.2181); μυ = 9.1540 + 0.0580 (υ + 12) + 0.0003 (υ 12)2; and μυ (exptl.) = 8.9734 + 0.0570 (υ + 12) + 0.0005 (υ + 12)2. The computed Hartree-Fock dissociation energy (DeHF = 0.117 a.u.) was coupled with estimated correlation and relativistic energy contributions (Decorr = 0.031 a.u., Derel = 0.002 a.u.), producing a lower limit value, Decalc = 0.146 a.u., a result somewhat smaller than the experimental value Deexptl. = 0.155 a.u. The discrepancy is due to neglect of small corrections discussed in this paper. The combination of calculated field gradients with experimental quadrupole coupling constants yielded the following electric quadrupole moments for sodium and chlorine: QNa = 0.0950 × 10−24cm2 and QCl35 = − 0.1171 × 10−24cm2.

Evaluation of the Nuclear Quadrupole Moment of N14

The nuclear quadrupole moment of Ni/sup 14/ was evaluated from molecular data using the calculated field gradient. The values obtained are Q(N/sup 14/) = 1.08 x 10/sup 26/ cm/sup 2/ for the vibrating nucleus and Q(N/sup 14/) = 1.06 x 10/sup 26/ cm/sup 2/ for the static nucleus. (L.T.W.)

On the Value of the Electric Quadrupole Moment of the Deuteron

The gradient of the electric field at the nucleus in the hydrogen molecule is calculated from a new electronic wave function which gives a simple but accurate formula for the electron density. The wave function is found by a generalization of the procedure first used by S. C. Wang. The calculated field gradient, together with the molecular beam measurements of Kellogg, Rabi, Ramsey and Zacharias, determines the value of the electric quadrupole moment of the deuteron. As stated by the latter authors, the quadrupole moment is 2.73 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}27}$ ${\mathrm{cm}}^{2}$. The writer estimates the limits of error of this value to be \ifmmode\pm\else\textpm\fi{}2 percent.