Atomic Quadrupole Research Articles

Quadrupole moments and hyperfine constants of metastable states ofCa+,Sr+,Ba+,Yb+,Hg+, and Au

Atomic quadrupole moments and hyperfine constants of the metastable states of , , , , and are calculated by the multiconfiguration Dirac-Hartree-Fock and relativistic configuration-interaction methods. For , the configuration is . For the other ions, the configuration consists of a single -electron outside a set of closed shells. Current interest in the quadrupole moments of these states is due to the fact that optical transitions of these ions may be useful as references for frequency standards. Energy shifts of the metastable states due to the interactions of the quadrupole moments with external electric field gradients are among the largest sources of error in these frequency standards. For the quadrupole moments, agreement is obtained to within about 10% with the available measurements. For the hyperfine constants, good agreement is obtained with measurements and with other calculations, except for the factors of the states of , , and , where the correlation effects are so large that they reverse the sign of the constant relative to the Dirac-Hartree-Fock value. As a test of the calculational methods, quadrupole moments and hyperfine constants are calculated for the states in isoelectronic neutral Au. This yields a value of the nuclear quadrupole moment .

Dynamic electrostriction of a Bose condensate and of a system of neutral atoms

It is shown that the condensate of a Bose gas of neutral atoms has electrical properties that are reflected in the dynamics of the condensate and do not reduce to a trivial polarization of the atomic gases in an external electric field. The concept of an isotropic atomic quadrupole moment whose distribution creates a distribution of the macroscopic electric potential 〈φ〉 in a system of neutral atoms is used. The nonuniform distribution of atoms that arises in a sound wave, for example, will produce an electric field whose behavior is determined by the dynamics of 〈φ〉.

Experimental X-ray Charge Density Studies on the Binary Carbonyls Cr(CO)6, Fe(CO)5, and Ni(CO)4

The experimental charge densities in the binary carbonyls Cr(CO)(6) (1), Fe(CO)(5) (2), and Ni(CO)(4) (3) have been investigated on the basis of high-resolution X-ray diffraction data collected at 100 K. The nature of the metal-ligand interactions has been studied by means of deformation densities and by topological analyses using the Atoms in Molecules (AIM) approach of Bader. A detailed comparison between the experimental results and theoretical results from previous work and from gas-phase and periodic DFT/B3LYP calculations shows excellent agreement, both on a qualitative and quantitative level. An examination of the kappa-restricted multipole model (KRMM) for Cr(CO)(6), using theoretically derived structure factors, showed it to provide a somewhat worse fit than a model with freely refined kappa' values. The experimental atomic graphs for the metal atoms in 2 and 3 were found to be dependent on the multipole model used for that atom. In the case of compound 2, restriction of the multipole populations according to idealized site symmetry of D(3h) gave an atomic graph in essential agreement with the theoretical gas-phase study. For compound 3, all multipole models fail to reproduce the atomic graph obtained from the theoretical gas-phase study. The atomic quadrupole moments for the C atoms in all compounds were consistent with significant pi back-donation from the metal atoms.

On the Representation of Molecular Quadrupole Moments in Terms of Atomic Moments

The magnitude and algebraic sign of the molecular quadrupole moments of the homonuclear diatomic molecules N2, O2, F2, P2, S2 and Cl2 are analyzed by expressing them as a sum of the quadrupole moments of the free atoms and an induced molecular quadrupole due to bond formation. This induced molecular quadrupole is further analyzed in terms of in situ atomic dipole and quadrupole moments constructed following the electron partitioning method suggested by Hirshfeld. These in situ moments are interpreted in terms of the sigma and pi character of the chemical bonds and are compared with those predicted by the DMA method of Stone (The Theory of Intermolecular Forces; Clarendon: Oxford, 1996).

Non-coincidence effect in methyl ethyl ketone: a solvent-dependent Raman study

The wavenumber shift of the isotropic and anisotropic profiles of the CO stretching mode of methyl ethyl ketone (MEK) was measured in several polar and non-polar solvents at different concentrations. The anisotropy shift function F = δν(2ε + n2)2ε−1 was plotted as a function of solute concentration (ϕ). A discontinuity around 50% appears to be present in many solvent systems. The variation of shift with concentration may arise as a result of several interactions such as dipole–dipole, dipole–quadrupole, quadrupole–quadrupole and higher multipole interactions in the solute–solvent systems. The plot of lnF against ϕ is linear over the entire range. It may be inferred from the data that repulsive-type intermolecular forces play a significant role in these molecular systems. The steric effects may be responsible for the discontinuity in the F vs ϕ plot apart from the atomic quadrupole effects and other intermolecular forces. Copyright © 2004 John Wiley & Sons, Ltd.

Atomic quadrupolar effect in intermolecular electrostatic interactions of chloroalkanes: the cases of chloroform and dichloromethane

The atomic quadrupolar effect in intermolecular electrostatic interactions is studied for chloroform and dichloromethane. From the fitting to the electrostatic potentials around these molecules obtained by ab initio molecular orbital (MO) calculations, atomic quadrupoles of the magnitude as large as Θ≅1.5 ea 0 2 are obtained for the chlorine atoms in these molecules. It is shown that a reasonably good fit to the electric field around the molecules can be obtained only by including those atomic quadrupoles, indicating that atomic quadrupoles are essential for correct representation of the intermolecular electrostatic interactions of these molecules. From the calculations of the radial distribution functions (rdfs) of liquid chloroform and dichloromethane by the Monte Carlo and molecular dynamics methods, it is shown that a significant atomic quadrupolar effect is seen in the rdfs of the C…C, C…H and H…H pairs. The intermolecular distances in the optimized structures of the dimers of chloroform and dichloromethane calculated by the ab initio MO method support the new features in the rdfs of the liquids that are seen upon including the effect of atomic quadrupoles. It is suggested that an atomic quadrupole has a significant effect on the angular (rather than radial) component of the location of the atoms of neighboring molecules.

Atomic dipole moments calculated using analytical molecular second-moment gradients.

We have implemented analytical second-moment gradients for Hartree-Fock and multiconfigurational self-consistent-field wave functions. The code is used to calculate atomic dipole moments based on the generalized atomic polar tensor (GAPT) formalism [Phys. Rev. Lett. 62, 1469 (1989)], and the proposal of Dinur and Hagler (DH) for the calculation of atomic multipoles [J. Chem. Phys. 91, 2949 (1989)]. Both approaches display smooth basis-set convergence toward a well-defined basis-set limit and give reasonable electron correlation effects on the calculated atomic properties. However, the atomic charges and atomic dipole moments obtained from the GAPT partitioning scheme are unable to provide even qualitatively meaningful molecular quadrupole moments for some molecules, and thus the atomic multipole moments calculated in this scheme cannot be considered well suited for analyzing the electron density in molecules and for calculating intermolecular interaction energies. In contrast, the DH approach gives atomic charges and dipole moments that by definition exactly reproduce the molecular quadrupole moments. The approach of DH is, however, restricted to planar molecules and thus suffers from not being applicable to molecules of arbitrary shape. Both the GAPT and DH approaches give rather poor results for octupole and hexadecapole moments, indicating that at least atomic quadrupole moments are required for an accurate representation of the molecular charge distribution in terms of atomic electric moments.

Donor–Acceptor Bond in Nontransition and Transition Element Complexes: Studies with Natural Bonding Orbital Approach

Electronic structures of tin, antimony, titanium, and niobium chloride complexes were analyzed using density functional theory. Parameters of nuclear quadrupole resonance spectra calculated using pseudopotential and all-electron basis states were compared with the experimental values. It was shown that the use of the central atom pseudopotential leads to a significant deviation of the atomic quadrupole coupling constants from their experimental values. The bonding in complexes was analyzed by making use of the natural orbitals of metal–chlorine and metal–ligand bonds. Donor–aceptor interactions in complexes of main group elements are described within the framework of sp-hybridization, while those in the transition element complexes, within the sd-hybridization framework.

Linear Dichroism in X-Ray Absorption and Orbital Orderings

Linear Dichroism in X-Ray Absorption and Orbital Orderings

Electron Delocalization in Acyclic andN-Heterocyclic Carbenes and Their Complexes: A Combined Experimental and Theoretical Charge-Density Study

Combined experimental and theoretical charge-density studies on free and metal-coordinated N-heterocyclic carbenes have been performed to investigate the extent of electron delocalization in these remarkable species. Tracing the orientation of the major axis of the bond ellipticity (the least negative curvature in the electron density distribution) along the complete bond paths distinguishes unambiguously between fully delocalized systems and those with interrupted cyclic electron delocalization. Evaluation of charge-density-based properties such as atomic quadrupole moments serves as a direct and quantitative measure of the extent of pi-electron delocalization and reveals consistency between theory and experiment. A detailed topological analysis of theoretical charge densities for two benchmark carbene systems, viz., 1,2-dimethylpyrazol-3-ylidene 1a and 1,3-dimethylimidazol-2-ylidene 2a, and their corresponding stable chromium pentacarbonyl complexes 1 and 2, highlights the advantages of charge-density-based criteria to analyze such complex electronic situations. Thus, 1a and 2a display a different extent of electron delocalization; yet nearly identical p(pi) occupations at the carbene center are computed for 1a and 2a. However, atomic quadrupoles Q(zz) - the charge-density analogues of p(pi) occupation - reveal faithfully the electronic differences in 1a and 2a and demonstrate the sensitivity of charge-density-based properties to the bonding situation. The acyclic aminocarbene (iPr(2)N)(2)CCr(CO)(4) has also been studied, and the high barrier to rotation about the C-N bond is shown not to arise solely from p(pi)-p(pi) bonding.

Production of a new certified reference material for trace elements in Antarctic krill

Under the coordination of the Istituto Superiore di Sanità (ISS), Rome, Italy, and of the Institute for Reference Materials and Measurements of the Joint Research Centre, European Commission (EC-JRC-IRMM), Geel, Belgium, a new certified reference material (CRM) for trace elements based on Antarctic krill was produced. The instrumental techniques resorted to in the certification project included flame, hydride generation, cold vapour and electrothermal atomization atomic absorption spectrometry (with and without Zeeman background correction), inductively coupled plasma atomic emission spectrometry, quadrupole and magnetic sector high resolution inductively coupled plasma mass spectrometry and neutron activation analysis. The certified values established for selected trace elements are as follows (in µg g−1 ± the 95% confidence interval): As, 5.02 ± 0.40; Cd, 0.73 ± 0.06; Co, 0.110 ± 0.010; Cu, 65.2 ± 2.3; Fe, 56.6 ± 2.3; Mn, 4.12 ± 0.10; Ni, 1.28 ± 0.12; Pb, 1.11 ± 0.09; Se, 7.37 ± 1.13; and Zn, 66.0 ± 2.0. Each value was obtained by combining data of several laboratories provided that four or more independent methods of analysis were used. For several other elements (Ag, Al, Br, Ca, Cl, Cr, Hg, I, K, Mg, Na, Rb, Sc, Sn, Sr and V) informative concentrations were given whenever the above criteria could not be respected.

External-Field Shifts of the (199)Hg(+) Optical Frequency Standard.

Frequency shifts of the 199Hg+ 5d106s 2S1/2 (F = 0, MF = 0) to 5d96s2 2D5/2 (F = 2, MF = 0) electric-quadrupole transition at 282 nm due to external fields are calculated, based on a combination of measured atomic parameters and ab initio calculations. This transition is under investigation as an optical frequency standard. The perturbations calculated are the quadratic Zeeman shift, the scalar and tensor quadratic Stark shifts, and the interaction between an external electric field gradient and the atomic quadrupole moment. The quadrupole shift is likely to be the most difficult to evaluate in a frequency standard and may have a magnitude of about 1 Hz for a single ion in a Paul trap.

Periodic density functional theory study of Pt(111): surface features of slabs of different thicknesses

Bulk platinum and platinum slabs one to four (111) layers thick have been studied using the HF and DFT CO-LCAO (Hartree-Fock and density functional theory crystalline-orbital and linear-combination-of-atomic-orbitals) CRYSTAL program. The objective of this paper is to test the suitability of slabs of different thicknesses for modelling the (111) surface of platinum. The cohesive properties of the bulk (lattice constant, bulk modulus, cohesive energy) are reported and the electronic structure of the platinum bulk is discussed. The surface and relaxation energies as well as the relaxation distances of the slabs were evaluated. The electronic structure of the slabs is discussed in terms of Mulliken population analysis, the density of states, the band structure and electron-density difference maps. `Initial-state' surface-atom core-level shifts are reported, as well as atomic dipole and quadrupole moments perpendicular to the surface.

ICP-AES and ICP-MS Quantification of Trace Elements in the Marine Macroalga Fucussample, a New Candidate Certified Reference Material

To develop a Certified Reference Material (CRM) suitable for monitoring the ongoing pollution affecting the marine and coastal environment, the International Atomic Energy Agency (IAEA), in collaboration with the United Nations Environmental Programme (UNEP) and the Intergovernmental Oceanographic Commission (IOC), launched a project for the preparation of a new CRM based on the marine macroalga Fucussample The authors' laboratory participated in the project as regards the analysis of As, Cd, Co, Cr, Cu, Fe, Ni, Pb, and Zn. Both inductively coupled plasma atomic emission spectrometry (ICP-AES) and quadrupole inductively coupled plasma mass spectrometry (ICP-MS) were used to this end. Complete digestion of the organic matrix and full mastering of both emission and mass spectra interferences were crucial to the obtainment of reliable data eligible for inclusion in the set of results chosen for the actual certification.

Finite-element multiconfiguration Hartree-Fock calculations of the atomic quadrupole moment ofAr+(2P3/2)

The atomic quadrupole moment, ${Q}_{\mathrm{zz}},$ and the electric field gradient at the nucleus, ${q}_{\mathrm{zz}},$ of the ${}^{2}{P}_{3/2}$ ground state of ${\mathrm{Ar}}^{+}$ have been calculated using a finite-element multiconfiguration Hartree-Fock method. The Hartree-Fock value for ${Q}_{\mathrm{zz}}({\mathrm{Ar}}^{+})$ is $\ensuremath{-}0.57213 \mathrm{a}.\mathrm{u}.$ The valence-correlation contribution obtained by correlating the valence $3s$ and $3p$ shells is calculated to be 0.048 44 a.u. The core-correlation and relativistic corrections are $\ensuremath{-}0.00299 \mathrm{a}.\mathrm{u}.$ and $\ensuremath{-}0.00035 \mathrm{a}.\mathrm{u}.,$ respectively, yielding a final atomic quadrupole moment of $\ensuremath{-}0.5271(11) \mathrm{a}.\mathrm{u}.,$ which in absolute value is 1.2% larger than the recently measured value of $\ensuremath{-}0.5208(2) \mathrm{a}.\mathrm{u}.$ The corresponding values for ${q}_{\mathrm{zz}}({\mathrm{Ar}}^{+})$ are 4.1129 a.u, $\ensuremath{-}0.2295 \mathrm{a}.\mathrm{u}.,$ 0.4211 a.u., and 0.0187 a.u., respectively, yielding a final value of 4.323(10) a.u. for ${q}_{\mathrm{zz}}.$

Halogen Nuclear Quadrupole Coupling Constants: Comparison of ab initio Calculations which include Correlation, with Experiment

Abstract Ab initio determination of the electric field gradient (EFG) tensors at halogen and other centres ena-bled determination of the nuclear quadrupole coupling constants (NQCC) for a diverse set of axially symmetric (C3v , C∞v, D∞h and other symmetries) inorganic and organic molecules, where the heavy ele-ments are Cl, Br, and I with C, Si, Ge, and Sn hydrides. The latter elements are in an approximately tetrahedral environment. The study presents results at a standardised level of calculation, triple-zeta in the valence space (TZV) plus polarisation functions (TZVP) for the equilibrium geometry stage; all-electron MP2 correlation is included in all these studies. f-Orbital exponents were optimised for both Br and I centres in the methanes; the atomic populations of the f-orbital components are very small for the Br-and I-atoms, confirming their role as polarisation functions rather than having any bonding character. The EFG are determined at equilibrium with the TZVP basis set, except Sn and I centres where the basis set is TZV + MP2. For the bromo and iodo compounds, especially the latter, it is essential to allow for core polarisation, by decontraction of the p,d-functions. This is conveniently done by initial optimization of the structure with a partly contracted basis, followed by reestablishment of the equilibrium structure with the decontracted basis. A close correlation of the observed (microwave spectral) data with the calculations was observed, using the 'best' values for the atomic quadrupole moments for Cl, Br, and I; thus there seems no need to postulate that the value of QBr for 79Br and 81Br are in error. The SCF and MP2 wave-functions were converted into localised molecular orbitals by the Boys Method. This allowed a study of the differing s/p/d-hybridisation ratios, and the centroid positions, to be compared with the quadrupole coupling constants. The charge distributions for the atoms were converted into local bond dipoles, which in turn are correlated with the electronegativity differences of the bonded atoms.

Improved density functional theory results for frequency-dependent polarizabilities, by the use of an exchange-correlation potential with correct asymptotic behavior

The exchange-correlation potentials vxc which are currently fashionable in density functional theory (DFT), such as those obtained from the local density approximation (LDA) or generalized gradient approximations (GGAs), all suffer from incorrect asymptotic behavior. In atomic calculations, this leads to substantial overestimations of both the static polarizability and the frequency dependence of this property. In the present paper, it is shown that the errors in atomic static dipole and quadrupole polarizabilities are reduced by almost an order of magnitude, if a recently proposed model potential with correct Coulombic long-range behavior is used. The frequency dependence is improved similarly. The model potential also removes the overestimation in molecular polarizabilities, leading to slight improvements for average molecular polarizabilities and their frequency dependence. For the polarizability anisotropy we find that the model potential results do not improve over the LDA and GGA results. Our method for calculating frequency-dependent molecular response properties within time-dependent DFT, which we described in more detail elsewhere, is summarized.

High-order multipolar hyperpolarizabilities with imaginary frequency for H and He

Calculations are reported of X{sub zz,zz,z,z}{sup 3}({minus}i{omega}; i{omega}, 0,0), X{sub zz,zz,x,x}{sup 3} ({minus}i{omega}; i{omega}; 0,0), X{sub zzz,z,z,z}{sup 3}({minus}i{omega}; i{omega},0,0), X{sub zz,z,z,z,z}{sup 4}({minus}i{omega}; i{omega}, 0,0,0), and X{sub zz,x,x,z,z}{sup 4}({minus}i{omega}; i{omega}, 0,0,0) for H and He. These are the independent components of the atomic (quadrupole){sup 2}-(dipole){sup 2}, (octupole)-(dipole){sup 3}, and (quadrupole)-(dipole){sup 4} hyperpolarizability tensors for an imaginary frequency i{omega}. The first three quantities have been used for the determination of the R{sup {minus}8} dispersion contribution to the H-H, H-He, and He-He collision-induced pair polarizability functions. The last two quantities will be needed in future calculations of the leading order (R{sup {minus}7}) dispersion contributions to the collision-induced first hyperpolarizability ({beta}) for the H-He pair. The calculations were based on sum-over-states formulations with near-exact wave functions for H and highly accurate explicitly electron-correlated wave functions for He. For this reason the authors believe them to be of benchmark quality. 8 refs., 3 tabs.

Finite-element multiconfiguration Hartree-Fock calculations of the atomic quadrupole moments of C+(2P) and Ne+(2P).

Finite-element multiconfiguration Hartree-Fock calculations of the atomic quadrupole moments of C+(2P) and Ne+(2P).

Finite-element multiconfiguration Hartree-Fock calculations of the atomic quadrupole moments of excited states of Be, Al, In, Ne, Ar, Kr, and Xe.

The atomic quadrupole moments Q zz of Be(2s2p; 3 P 2 ), Al(3p; 2 P 3/2 ), In(5p; 2 P 3/2 ), Ne(2p 5 3s 3 P 2 ), Ar(3p 5 4s; 3 P 2 ), Kr(4p 5 5s; 3 P 2 ), and Xe(5p 5 6s; 3 P 2 ) have been calculated using a finite-element multiconfiguration Hartree-Fock method. The obtained Q zz (Be) of 2.265 a.u. agrees with previously calculated values