Reconciliation of the forward scattering and wave theories of electric-field-gradient-induced birefringence

We consider propagation of a linearly polarized, harmonic, plane electromagnetic wave incident on a dilute gas subject to a non-uniform electrostatic field. We work to electric quadrupole–magnetic dipole order. In general, the wave is distorted to include a perpendicular component induced by the electrostatic field gradient, and the resultant is not a plane wave. Although the induced component is small, its contribution to the polarization-dependent refractive index of the gas in Buckingham's quadrupole experiment is significant. We show that distortion of the incident wave accounts exactly for the present discrepancy between wave theory and forward scattering theory of electric-field-gradient-induced birefringence in a gas: both theories yield the result obtained originally by Buckingham and Longuet-Higgins.     

Paramagnetic magnetochiral effect in the H h and V h components of Rayleigh light scattering by molecular systems

A static magnetic field, acting on an isotropic medium composed of paramagnetic chiral molecules perpendicular to the propagation direction of the optical beam, is shown to induce an axial differential effect—magnetochiral Rayleigh light scattering. Diamagnetic and paramagnetic contributions to the effect are given in terms of the linear and nonlinear electric dipole, magnetic dipole and electric quadrupole polarizabilities responsible also for natural optical activity, the Faraday effect as well as magnetochiral birefringence. Specific cases are discussed.     

Density functional theory calculations of nuclear quadrupole coupling constants with calibrated 14N quadrupole moments

Density functional calculations of the electric field gradient tensor at the nitrogen nucleus in 13 test molecules, containing 14 nitrogen sites, have been performed using the linear combination of Gaussian-type orbital Kohn-Sham density functional theory (LCGTO-KSDFT) approach. Local and gradient corrected functionals were used for all-electron calculations. All the molecular structures were optimized at their respective levels of theory with extended basis sets. Calibrated ¹⁴N nuclear quadrupole moments were obtained through a fitting procedure between calculated electric field gradients and experimental nuclear quadrupole coupling constants of the test set of molecules for each basis set and functional considered. With these calibrated ¹⁴N nuclear quadrupole moments, the nuclear quadrupole coupling constants of the following selected systems were determined: fluoromethylisonitrile, pyridine, pyrrole, imadazole, pyrazole, 1,8-bis(dimethyl-amino)naphthalene, cyclotetramethylenetetranitramine, cocaine and heroin.     

Magnetic multipole moments

Literature definitions of magnetic multipole moment operators are shown to be at variance, and new definitions are formulated which are consistent with a general multipole interaction hamiltonian and with the radiation field of a dynamic charge distribution. The applicability of traceless multipole moments is examined.

The multipole hamiltonian is used to derive expressions for some magnetic quadrupole distortion tensors. For those describing the quadrupole moment induced by a magnetic field and by a field gradient the number of independent components for various molecular symmetries is evaluated.     

Molecular relativistic electric field gradient calculations suggest revision of the value of the nuclear electric quadrupole moment of 127I

Relativistic ab initio methods are used to compute the electric field gradient at the iodine nucleus in nine different closed-shell diatomic molecules. Combining these theoretical electric field gradients with experimental nuclear quadrupole coupling constants gives a consistent value of the nuclear quadrupole moment of ¹²⁷I of—696(12)millibarn. We argue that this value is more precise than the current standard value of the nuclear quadrupole moment of ¹²⁷I and recommend adjusting the reference value accordingly. The precision of this determination is still determined by technical limitations in the theoretical work, in particular the neglect of the two-electron Gaunt interaction in the Hamiltonian and correlation contributions beyond those described at the CCSD(T) level of theory, but the errors are reduced relative to the theoretical work that underlies the current standard value of this nuclear quadrupole moment. As a secondary study we also considered the calculation of the small electric field gradient at the gold nucleus in the AuI molecule and conclude that this computation remains a challenge for theoreticians.     

Molecular multipoles and (hyper) polarizabilities from the Buckingham expansion:revisited

The Buckingham expansion is important for understanding molecular multipoles and (hyper) polarizabilities. In this study, we give a complete derivation of the Buckingham expansion in the traced form using successive Taylor series. Based on the derivation results, a general Buckingham expansion in the traced form is proposed, from which highly accurate numerical calculations using the finite field method can be achieved. The transformations from the traced multipoles and multipole-multipole polarizabilities to the corresponding traceless counterparts are realized with an auxiliary traced electric field gradient. The applications of thefinite field method in this study show good agreements with previous theoretical calculations and experimental measurements.     

Kerr effect caused by an electric current in a weakly ionized gas

The anisotropy of the velocity distribution caused by an electric current in a fluid leads to a molecular alignment via the non-spherical interaction. This alignment implies a birefringence proportional to the square of the applied electric field just as the ordinary Kerr effect. The kinetic theory of this phenomenon is presented for a lorentzian mixture, viz. a gas of few light charged linear molecules and of many heavy optically isotropic particles. The current-induced contribution to the Kerr effect turns out to be much larger than the contribution which stems from the usually considered orienting influence of the electric field on anisotropic molecules.     

The origin of non-planarity in ketyls

A series of one-electron properties, i.e. dipole, quadrupole, octupole moments, diamagnetic susceptibility, second moments and second moment anisotropies of charge distribution, electric field, electric field gradient, diamagnetic shielding, nuclear quadrupole coupling constant, have been obtained by ab initio S.C.F. calculations for the molecules COF₂, SO₂F₂ and SOF₂. The effect of the size of the gaussian basis sets, including d-type polarization functions, as well as the contraction schemes on the latter properties have been studied for the COF₂ molecule. This study enables us to determine the basis giving the best results as compared to experiment. With this basis the calculations have been extended to the properties of the molecules SO₂F₂ and SOF₂. Good overall agreement with experiment is obtained.     

Nuclear magnetic resonance in ferromagnetic terbium

The temperature dependence of the magnetic dipole and electric quadrupole hyperfine fields has been measured by NMR in ferromagnetic terbium metal. The results are in excellent agreement with a general theoretical relation connecting moments of the magnetization. This relation allows us to separate ionic and crystalline contributions to the nuclear electric field gradient.     

Electric quadrupole orientation in zinc. The variation of electric field gradient with atomic number through the 4sp series

Using the top-loading PrNi₅ nuclear demagnetisation stage /1/ to reach temperatures close to 1mK, electric quadrupole orientation of trace 4sp series impurities in zinc has been measured. Results establish the variation of the electric field gradient at impurity nuclei in this series and also yield the ratio of the electric quadrupole moments of⁷¹As and⁷²As.     

Ab initio study of the EFG at the N sites in imidazole

We study the nuclear quadrupole interaction at the nitrogen sites in the molecular and crystalline phases of the imidazole compound. We use PAW which is a state-of-the-art method to calculate the electronic structure and electric field gradient at the nucleus in the framework of the density functional theory. The quadrupole frequencies at both imino and amino N sites are in excellent agreement with measurements. This is the first time that the electric field gradient at crystalline imidazole is correctly treated by an ab initio theoretical approach.     

Chemisorption of Li and Na on iridium surfaces: An investigation with nuclear spin polarized atoms

The chemisorption of Li and Na on clean and oxygen covered polycrystalline iridium was investigated using nuclear spin polarized alkali atoms. During adsorption on the surface the moments of the nuclei act as microscopic probes. The nuclear quadrupole moments of the alkali atoms are interacting with the electric field gradient. The interaction reflects the charge distribution around the nucleus. The nuclear magnetic moments are interacting with magnetic fields generated by the magnetic moments of electrons.     

Finite-field calculation of electric quadrupole moments of ~2P_(3/2),~2D_(3/2,5/2),and ~2F_(5/2,7/2) states for Yb~+ ion

Electric quadrupole moments of low-lying excited states of Yb~+ are calculated by relativistic coupled-cluster theory with perturbations from external fields.The field-dependent energy differentiation provides accurate values of the electric quadrupole moments o f~2P_(3/2),~2D_(3/2,5/2),and~2F_(5/2,7/2) states which agree well with experimental values.The important role of the electronic correlation to the electric quadrupole moments is investigated.Our calculations indicate the early dispute of the electric quadrupole moment of the Yb~+(~2F_(7/2))state for which the measured and theoretical values have a large discrepancy.These electric quadrupole moment values can help us to determine the electric quadrupole shifts in start-of-the-art experiments of the Yb~+ ion.     

Quadrupole interactions in metals and alloys

The contributions of the perturbed charge density of conduction electrons due to quadrupole moments of impurity paramagnetic ions and nuclei to the electric field gradient at the nuclei in metals and alloys are analyzed. The indirect multipole interactions of nuclei in metals via the mediation of conduction electrons is investigated. The influence of these interactions on the NMR parameters is studied.     

Nuclear electric quadrupole interactions in liquids entrapped in cavities

Liquids entrapped in cavities and containing quadrupole nuclei are considered. The interaction of the quadrupole moment of a nucleus with the electric field gradient is studied. In such a system, molecules are in both rotational and translational Brownian motions which are described by the diffusion equation. Solving this equation, we show that the intra- and intermolecular nuclear quadrupole interactions are averaged to zero in cavities with the size larger than several angstroms.     

Sternheimer shielding in molecules

The effect of perturbing electric fields and electric-field gradients on the nuclear quadrupole coupling in molecules is investigated. The theory for the first-order effects is developed and it is shown that not only a perturbing field gradient but also a perturbing field, and higher terms, induce a finite field gradient at a nucleus in a molecule. The so-called Sternheimer (anti)shielding is thus considerably more complex in molecular than in atomic systems. The different shielding components have been calculated for HCl, HCN and NH₄ ⁺ using a finite perturbation ab initio molecular orbital method. The calculated values are then used to rationalize experimentally determined ¹⁴N quadrupole coupling constants in condensed media for HCN and NH₄ ⁺.     

Blood analysis for early cancer detection

The interaction between the nuclear quadrupole moments of ions and the electric field gradient in a biological membrane can explain the mechanism of active transport in cells. On the basis of a model, we discuss the NMR isotopic analyzer of blood for the detection of cancer without exposing the patient to any radiation. The method involves a low temperature technique.     

Electric quadrupole interaction of210Po(6+) in Bi single crystal

The electric quadrupole coupling constant of the²¹⁰Po(6⁺) isomer in a Bi single crystal was measured as a function of the temperature using the time-differential perturbed angular correlations technique. The electric field gradient (EFG) for Po in Bi is found to be temperature independent in the range 77–477 K. Using a calculated value of the nuclear quadrupole moment, the magnitude of the EFG is derived, and in turn serves to re-examine the systematics of quadrupole moments of λh ₉ ^2/2 configurations in the lead region.     

Selected aspects of the quantum dynamics and electronic structure of atoms in magnetic microtraps

We analyze the quantum properties of atoms in a magnetic quadrupole field. The quantum dynamics of ground state atoms in this field configuration is studied firstly. We formulate the Hamiltonian and perform a symmetry analysis. Due to the particular shape of the quadrupole field in general there exist no stable states. We provide resonance energies, lifetimes and calculate the density of states and investigate under what conditions quasi-bound states occur that possess long lifetimes. An effective scalar Schrödinger equation describing such states is derived. As a next step we explore the influence of a high gradient quadrupole field on the electronic structure of excited atoms. An effective one-body approach together with the fixed nucleus approximation is employed in order to derive the electronic Hamiltonian. We present the energy spectrum and discuss peculiar features such as non-trivial spin densities and magnetic field induced electric dipole moments.     

Electric quadrupole interaction of 212Rn isomers in Bi

The electric quadrupole interaction of the ²¹² Rn 8⁺ and 6⁺ isomers in a Bi single crystal was measured. The experimental results together with a shell-model calculation of the quadrupole moments provide a calibration of the electric field gradient for Rn impurities in Bi, to be used in future quadrupole-moment measurements of Rn isomers. A two-level analysis procedure was employed for the combined data of the 8⁺ and 6⁺ isomers.