Electric Quadrupole Tensor Research Articles

Communication: Multiple-property-based diabatization for open-shell van der Waals molecules.

We derive a new multiple-property-based diabatization algorithm. The transformation between adiabatic and diabatic representations is determined by requiring a set of properties in both representations to be related by a similarity transformation. This set of properties is determined in the adiabatic representation by rigorous electronic structure calculations. In the diabatic representation, the same properties are determined using model diabatic states defined as products of undistorted monomer wave functions. This diabatic model is generally applicable to van der Waals molecules in arbitrary electronic states. Application to locating seams of conical intersections and collisional transfer of electronic excitation energy is demonstrated for O2 - O2 in low-lying excited states. Property-based diabatization for this test system included all components of the electric quadrupole tensor, orbital angular momentum, and spin-orbit coupling.

Extended bodies in a Kerr spacetime: exploring the role of a general quadrupole tensor

The equatorial motion of extended bodies in a Kerr spacetime is investigated in the framework of the Mathisson–Papapetrou–Dixon model, including the full set of effective components of the quadrupole tensor. The numerical integration of the associated equations shows the specific role of the mass and current quadrupole moment components. While most of the literature on this topic is limited to spin-induced (purely electric) quadrupole tensor, the present analysis highlights the effect of a completely general quadrupole tensor on the dynamics. The contribution of the magnetic-type components is indeed related to a number of interesting features, e.g., enhanced inward/outward spiraling behavior of the orbit and spin-flip-like effects, which may have observational counterparts. Finally, the validity limit of the Mathisson–Papapetrou–Dixon model is also discussed through explicit examples.

On the interaction between an electric quadrupole moment and electric fields

AbstractIn this work, quantum effects are discussed which arise from the interaction between an electric quadrupole moment and electric fields. It is shown that, by choosing a diagonal electric quadrupole tensor whose components are constants, the interaction between an electric quadrupole moment and electric fields gives rise to the scalar Aharonov‐Bohm effect and to bound states analogous to the confinement of a quantum particle to a quantum dot. Moreover, the influence of a constant force field on the confinement analogous to a quantum dot, and the influence of an antidot‐like potential on the Landau levels of an electric quadrupole moment are discussed.

Destructive interference ofE2matrix elements in a triaxial rotor model

A triaxial rotor model with independent inertia and electric quadrupole tensors is applied to nuclei that have certain $E2$ matrix elements equal to zero. It is shown that such vanishing $E2$ matrix elements are explained by the model as a destructive interference effect. The example of $^{196}\mathrm{Pt}$ is considered.

The role of electric field gradient in modeling elastic ferroelectrics

In this article a continuum model for simulating the microscopic behavior of ferroelectrics is proposed. The model is based on an alternative phase field formulation, where spontaneous polarization, mechanical strain, electric field and electric field gradient are used as constitutive variables. The electric field gradient is energetically conjugated to the quadrupole polarization, thus it is about a theory with electric quadrupoles. A variational principle has been used for the derivation of the field equations and the appropriate boundary conditions. Like polarization vector, it is assumed that electric quadrupole tensor is separated into a reversible and a spontaneous part, too. It is proved that spontaneous quadrupole tensor is responsible for the domain wall thickness. Computational examples concerning ferroelectric materials with charge and dipole defects are carried out with the proposed model. The additional boundary conditions provided by the variational principle seem to be useful especially to handle dipole defects.

7Li and 51V NMR studies on local symmetry and charge disproportionation in quasi-one-dimensional conductor β-Li0.33V2O5

We have made 7Li and 51V NMR measurements on a single crystal to investigate the local symmetry and the charge disproportionation in the metallic phase of the quasi-one-dimensional conductor β-Li0.33V2O5. The electric quadrupole tensors at the Li sites are determined and the Li ordering is discussed on the basis of the recent X-ray diffraction results. We also report the temperature dependence of the 51V Knight shift and the 51V nuclear spin-lattice relaxation rate, indicating the presence of the charge disproportionation even in the metallic phase.

Triaxial rotor model description ofE2properties inOs186,188,190,192

The triaxial rotor model with independent inertia and electric quadrupole tensors is applied to the description of the extensive set of $E2$ matrix elements available for $^{186,188,190,192}\mathrm{Os}$. Most large and medium transition $E2$ matrix elements can be reproduced to within $~10%,$ and most diagonal elements to within $~30%$. Most small transition matrix elements can be reproduced to within $~30%,$ and they support the interference effect exhibited by the model between the inertia and $E2$ tensors: this is a new feature of quantum rotor models. The diagonal $E2$ matrix elements at higher spins in the $K=2$ band are extremely sensitive to admixtures of higher $K$ values: the low experimental values in $^{190,192}\mathrm{Os}$ indicate significant admixtures of $K=4$ components. Attention is given to the ${K}^{\ensuremath{\pi}}={4}^{+}$ bands in these nuclei and the controversial issue of whether they are of quadrupole or hexadecapole nature.

Relevance of the Electric-Dipole−Electric-Quadrupole Contribution to Raman Optical Activity Spectra

We examine the importance of the electric-dipole--electric-quadrupole polarizability tensor in the intensity theory of Raman optical activity (ROA) spectra. Using density functional theory, ROA spectra of organic cyclic compounds, alanine, oligoalanines, and examples from the literature are analyzed in detail, and a statistical investigation is performed. It is found that the contribution of the electric-dipole--electric-quadrupole tensor is often small, except for some special cases that involve C-H stretching vibrations.

Triaxial rotor model for nuclei with independent inertia and electric quadrupole tensors

The triaxial rotor model for nuclei is investigated by relaxing the use of irrotational moments of inertia. The dependence of observables of the model on the electric quadrupole tensor, through a triaxiality angle $(\ensuremath{\gamma})$, and on the inertia tensor, through a mixing angle, is illustrated. This formalism provides insights into the physics of triaxial rotations in nuclei.

Measuring oxygen–phosphorus distances and the orientation of electric field gradient tensors using 17O–{ 31P} REDOR in phosphate glasses

Rotational echo double resonance (REDOR) of spin- 1 2 nuclei is an extremely useful tool for the determination of distances in solids as well as of relative orientations of chemical shift and dipole tensors. We present the corresponding version for measuring the relative orientation of electric quadrupole and dipole tensors and demonstrate its applicability for non-bridging oxygens in phosphate glasses using 17O–{ 31P} REDOR NMR. The orientational information is found in the changes of the second-order quadrupole patterns as a function of the echo delay. Results and numeric simulations are presented for 17O–{ 31P} REDOR NMR of 17O-enriched sodium phosphate glasses. For non-bridging oxygens, the symmetric quadrupole tensor is found to be aligned along the phosphorus–oxygen bond. The distance between P and the non-bridging oxygen is calculated for two glasses of different compositions.

Experimental investigation of the6s21S0→5d6s3D1,2forbidden transitions in atomic ytterbium

We have observed the Stark-induced ${6s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}5d6s{}^{3}{D}_{1}$ transition in Yb, and measured properties relevant to the study of atomic parity nonconservation in this transition. An atomic beam of Yb is excited by 408-nm light in the presence of an external dc electric field, resulting in cascade fluorescence at 556 nm as the excitation decays through the $6s6p{}^{3}{P}_{1}$ state. The density of the atomic beam and the fluorescence detection efficiency are calibrated by directly exciting the $6s6p{}^{3}{P}_{1}$ state with 556-nm light. Using an estimate of the ${}^{3}{D}_{1}{\ensuremath{-}}^{3}{P}_{1}$ branching fraction, we obtain a measurement of the vector transition polarizability, $|\ensuremath{\beta}|=2.18(33)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8} {\mathrm{ea}}_{0}/(\mathrm{V}/\mathrm{cm}).$ In addition, we have observed the ${6s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}5d6s{}^{3}{D}_{2}$ transition at 404 nm. The electric quadrupole transition amplitude and tensor transition polarizability have been measured. We have also measured the dc Stark shifts, hyperfine structure, and isotope shifts for both transitions.

The molecular electric quadrupole tensor of ethene from the rotational Zeeman effect of CH2=CD2

The Zeeman effect of several rotational transitions of [1,1-2H2]ethene has been observed in the millimetre wave range using field strengths close to 2·65 T and cell temperatures near - 170 °C. The rotational g values and susceptibility anisotropies fitted to the field splittings were transferred to those of CH2=CH2 leading to gaa = - 0·3954(9), gbb = - 0·1159(3), gcc = 0·0453(2), 2ζ aa - ζ bb - ζ cc = 0·759(21) × 10- 29 erg G- 2, and 2ζ bb - ζ cc - ζ aa = 1·926(45) 10- 29 erg G- 2. These data are combined to yield Qaa = 1·48(10), Qbb = 1·67(19), Qcc = - 3·16(19) for the principal axis electric quadrupole tensor components (all in 10- 26 esu) of ethene. The errors are standard deviations, and do not include contributions possibly arising from zero-point vibrational effects.

Theory of a reflection experiment for determining magnetoelectric properties of cubic antiferromagnets at optical frequencies

Abstract Certain classes of magnetic cubic crystals may exhibit optical effects described by time-odd tensors of electric quadrupole and magnetic dipole origin. The latter is the magnetoelectric tensor at the optical frequency, Refraction phenomena in cubic antiferromagnets can be related to the electric quadrupole tensor, but not to the magnetoelectric tensor. However, this property, as well as the electric quadrupole tensor, can be determined using reflection techniques. A theory is presented of a suitable experiment in which the reflected intensity is measured for different incident and analyzed polarization states.

67Zn Mössbauer study of lattice-dynamical effects and hyperfine interactions in ZnF2

Using the high-resolution 93.3-keV transition in67Zn we studied the temperature dependence of the Lamb-Mossbauer factor (LMF), the center shift, and the quadrupole interaction in polycrystalline ZnF2 in the temperature range between 4.2 and 55.3 K. The LMF is anisotropic within the whole temperature range. The electric quadrupole tensor characterized byeV zz Q/h=+(8.2±0.1) MHz and η=(0.15±0.02) is independent of temperature. The results on the isomer shift (relative to ZnO) and on the electric quadrupole tensor are in very good agreement with recent theoretical cluster calculations.

67Zn Mössbauer investigation of lattice-dynamical effects and hyperfine interactions in ZnF2.

The temperature dependence of lattice-dynamical effects and of hyperfine interactions in $^{67}\mathrm{ZnF}_{2}$ has been investigated between 4.2 and 55.3 K with use of the 93.3-keV M\ossbauer resonance in $^{67}\mathrm{Zn}$. Within this temperature range the Lamb-M\ossbauer factor decreases from 1.23% to 0.46%. The electric quadrupole tensor characterized by ${\mathrm{eV}}_{\mathrm{zz}}$Q/h=+8.2\ifmmode\pm\else\textpm\fi{}0.1 MHz and \ensuremath{\eta}=0.15\ifmmode\pm\else\textpm\fi{}0.02 is independent of temperature. The data on the quadrupole tensor and on the Lamb-M\ossbauer factor exclude a beginning ferroelectric transition, which was proposed to occur at low temperatures. The results on the isomer shift (relative to ZnO) and on the electric quadrupole tensor are in very good agreement with recent theoretical cluster calculations.

Nuclear Quadrupole Resonance: The Present State and Further Development

The importance of nuclear electric quadrupole interactions in chemistry, both present and future, depends very much on their power to resolve problems in electronic structure and molecular dynamics. Fortunately, the subject, by its very nature, is “multinuclear”; even if the ground state of a given nucleus is non-quadrupolar, there often exist excited nuclear states which are, an example being 19F, for which quadrupole coupling constants are now being published from angular correlation measurements. Other new techniques are constantly extending the range of the experiments, recent examples being the use of SQUID magnetometers to detect acoustic 121Sb and 123Sb quadrupole resonance in antimony metal and Fourier transform quadrupole resonance spectroscopy based on fast field cycling to measure 2H quadrupole interactions in powders. Recently, much work on quadrupole interactions in solids of half-integral spin nuclei such as 17O or 27Al has been pursued in two different ways; by quadrupole double resonance in natural abundance, and nuclear magnetic resonance in very high magnetic fields, for which enrichment of low-abundance nuclei such as 170 is often required. In the liquid phase, measurements are now sufficiently reliable for comparisons of changes in the nuclear electric quadrupole tensor from gas to liquid and solid phases to be made. The new methods of partial alignment of polar molecules in the liquid phase in strong electric fields, or magnetically anisotropic molecules in high magnetic fields, seem certain to contribute to these developments.

Temperature Dependence of Second-Order Quadrupole Shift of Na23in NaD3(SeO3)2

The electric quadrupole tensors of Na 23 in NaD 3 (SeO 3 ) 2 are determined from the angular variation of the secornd-order quadrupole shifts above and below the ferroelectric transition temperature. The temperature variation of the shift below T c =-3^° C is proportional to the square of spontaneous polarization observed by pyroelectric measurement.

Nuclear magnetic resonance of 27Al in epidote, Ca2Al2(Fe,Al)Si3O12(OH)

Two types of nuclear electric quadrupole tensors have been observed for 27Al in epidote. The quadrupole coupling constant C and asymmetry parameter η are AlI |C|=11.9 MHz, η=0.3; AlII, |C|=4.6 MHz, η=0.34. They correspond to the Al1 and Al2 sites, respectively, of the epidote crystal structure. The electric field gradient tensors, with principal contributions from its nearest neighbors in the highly distorted AlO6 tetrahedra, are consistent with the epidote structure and with other aluminosilicate minerals.

ESR study of the CH 2Cl radical in a single crystal of CH 3Cl

Paramagnetic resonance spectra of the CH 2Cl radical produced by γ irradiation of a methyl chloride single crystal have been studied. From the coupling tensors of the hydrogen and chlorine, and the electric quadrupole tensor of chlorine, it has been shown that CH 2Cl has a nearly planar structure.