Showing papers on "Quadrupole published in 1971"

The molecular Zeeman effect in diamagnetic molecules and the determination of molecular magnetic moments (g values), magnetic susceptibilities, and molecular quadrupole moments

Abstract: The experimental and theoretical literature on the molecular Zeeman effect is surveyed. The observation of the linear (H) and quadratic (H 2) Zeeman effect leads to a direct determination of the molecular g values, magnetic susceptibility anisotropies and molecular quadrupole moments. The recent results are discussed and the available molecular g values, magnetic susceptibility anisotropies, and molecular quadrupole moments are tabulated.

Operating Parameters of a Quadrupole in a Grounded Cylindrical Housing

Abstract: Quadrupole theory and design are based on the solution of Mathieu’s equations, which assume that zero potential, except for the symmetry axes between the electrodes, is infinitely far away. In practice, the quadrupole rods are mounted within a grounded housing not much larger than the electrode structure itself. This study determines the operating parameters and optimum electrode size for a quadrupole with electrodes of circular cross section located within a zero-potential cylindrical surface. It is found that the rod size is only weakly dependent on the location of the external, zero-potential surface and the optimum rod size is r=1.1468r0 for a cylinder radius of 3.54r0. Although the optimum rod size is only 1.15% smaller than the commonly used value of r=1.16r0, it is found that 43% higher sensitivity at a resolution of 400 (ΔM measured at half-height) results from using the optimum radius electrodes.

Zero‐Point Vibrational Corrections to One‐Electron Properties of the Water Molecule in the Near‐Hartree—Fock Limit

Abstract: The zero‐point vibrational motion of the water molecule in its ground electronic state is analyzed with a near‐Hartree—Fock potential energy surface constructed from a (9s5p2d/4s1p) /[4s3p2d/2s1p] basis set of contracted Gaussian orbitals. The harmonic and cubic force constants relative to the computed minimum are obtained, and a normal coordinate analysis is carried out for several isotopic variants. A set of one‐electron properties including molecular moments, field gradients, forces, and densities is computed at each point on the potential surface, and then averaged over the zero‐point motion with a vibrational wavefunction which contains anharmonicity terms through the cubic constants. The vibrational corrections are typically about 1% of the equilibrium values, but are as large as 20% in cases such as the 17O quadrupole coupling constant along the C2 axis. The theoretical isotope shifts for the quadrupole moments of H2O and D2O are in good agreement with experiment. Predictions are made for isotope s...

Quadrupole Phase Transitions in Magnetic Solids

Abstract: We have studied the phase transitions of magnetic systems with large biquadratic interactions in the molecular-field approximation. Quadrupole and dipole phase transitions occur at different temperatures whenever the biquadratic interactions are greater than the bilinear terms for effective spin interactions with $\mathcal{S}g~\frac{3}{2}$. For isotropic or Ising-like interactions with $\mathcal{S}=1$ there is only a quadrupole phase transition when the biquadratic interactions are larger.

Electric Field Gradients at 57Fe in ZnFe2O4 and CdFe2O4

Abstract: The nuclear quadrupole coupling constants and isomer shifts of 57Fe in the spinels ZnFe2O4 and CdFe2O4 were measured using the Mossbauer effect. The signs of the quadrupole coupling constants were determined from spectra which were taken in an applied magnetic field. The sign is negative in both spinels. The isomer shifts and Fe–O distances indicate that Fe3+ in ZnFe2O4 is somewhat more covalently bonded than in CdFe2O4. The external field gradients at the Fe3+ positions can be interpreted in terms of the ionic point‐multipole model modified by some charge transfer between oxygen and the cations. The point charge contribution to the field gradient is positive in case of ZnFe2O4 and nearly zero in case of CdFe2O4; the predominant contribution is due to the electric dipole moments of the oxygen ions and is negative. The dipole polarizability of the oxygen ion which gave the best fit is αD = 0.8 A3. The effect of charge transfer on the ionic field gradient is small.

An Introduction to Mössbauer Spectroscopy

Abstract: 1 Introduction to the Mossbauer Effect.- 1. Pictorial Description.- 2. Background Concepts.- 2. 1. Natural Line Width.- 2. 2. Recoil Energy Loss.- 2. 3. Resonance and Resonance Fluorescence.- 2. 4. Doppler Broadening.- 2. 5. Einstein Solids.- 2. 6. Recoil-Free Emission of Gamma Rays.- 3. The Mossbauer Effect.- 3. 1. Pictorial Approach.- 3. 2. Observation of the Mossbauer Effect.- 4. Theory.- 2 Instrumentation.- 1. Instrumentation.- 1. 1. Gamma-Ray Detection.- 1. 2. Doppler Velocity Drive.- 2. Accuracy and Precision.- 2. 1. Calibration Methods.- 2. 2. Time of Counting.- 3. Experimental Techniques.- 3. 1. Sources.- 3. 2. Mossbauer Absorbers.- 3. 3. f-Factor Measurements.- 3. 4. Variable Temperature.- 3. 5. Scattering Methods.- 4. Applications of Computers to Mossbauer Spectra.- 4. 1. Computation of Mossbauer Spectra from a Theoretical Model.- 4. 2. Curve Fitting of Mossbauer Data by Least-Square Analysis.- 4. 3. Curve Fitting of Mossbauer Data by Constrained Least-Square Analysis.- 3 Nuclear Properties Determined from Mossbauer Measurements.- 1. A Phenomenological View of the Hyperfine Interactions.- 2. Differences in the Nuclear Charge Radius?R/R.- 2. 1. ?|?(0)|2 from "Pure Ionic" Valence States.- 2. 2. ?|?(0)|2 from Band Theory.- 2. 3. ?|?(0)|2 Caused by Overlap.- 2. 4. ?|?(0)|2 from the Shielding of p Holes.- 2. 5. ?R Ratios Method.- 2. 6. Nuclear Information from?R.- 3. Nuclear Quadrupole Moments Q and Spins I.- 3. 1. Quadrupole Moment Ratios Q*/Q.- 3. 2. Direct Determination of Quadrupole Moment Values.- 3. 3. Direct Determination of Nuclear Spins.- 4. Nuclear Magnetic Dipole Moments.- 5. Nuclear Lifetimes.- 6. Internal Conversion.- 7. Parity, Multipole Mixing, and Time Reversal.- 7. 1. Mossbauer Observation of Parity Nonconservation.- 7. 2. Multipole Mixing and Time Reversal.- 8. Nuclear Reactions and Devices.- 4 The Electric Field Gradient Tensor.- 1. The "Standard Form" EFG Tensor Due to a Single-Point Charge.- 2. The Ligand Contribution.- 3. The Valence Electron Contribution.- 4. Quadrupole Splittings.- 4. 1. The Nuclear Quadrupole Interaction.- 4. 2. Ligand-Only Splittings.- 4. 3. Valence-Only Splittings.- 4. 4. Ligand-Valence Combined Splittings.- 5. Potpourri.- 5. 1. Compounds with Internal Magnetic Fields.- 5. 2. Applied Magnetic Fields.- 5. 3. The Gol'danskii-Karyagin Effect.- 5. 4. Single Crystal Samples.- 6. The Utility of EFG Information.- Appendix I.- Appendix II.- 5 Application to Solid-State Physics.- 1. Isomer Shift.- 2. Magnetic Hyperfine Structure.- 3. Electric Quadrupole Interaction.- 4. Lattice Dynamics.- 6 Application to Coordination Chemistry.- 1. Crystalline Structure.- 2. Complex Isomerism.- 2. 1. Cis-Trans Isomerism.- 2. 2. Ligand Linkage Isomerism.- 2. 3. Spin-State Equilibria.- 3. Structure of Complicated Complex Compounds.- 4. Electronic Structure of Molecules.- 4. 1. Using Ligand Field Theory.- 4. 2. Using Molecular Orbital Theory.- 4. 3. Using the Spin Hamiltonian.- 7 Application to Organometallic Compounds.- 1. Isomer Shifts.- 1. 1. Organoiron Compounds.- 1. 2. Organotin Compounds.- 2. Quadrupole Splitting.- 2. 1. Organoiron Compounds.- 2. 2. Organotin Compounds.- 3. Conformational Studies.- 3. 1. Cyclooctatetraene Iron Tricarbonyl [COTFe(CO)3].- 3. 2. [?-C5H5Fe(CO)2]2 SnCl2 and Related Molecules.- 4. Conclusion.- 8 Mossbauer Spectroscopy and Physical Metallurgy.- 1. Mossbauer Application to Physical Metallurgy.- 1. 1. Precipitation in the Cu-Fe System.- 1. 2. Phase Transition in Stainless Steel.- 1. 3. Internal Oxidation Studies.- 1. 4. Magnetic Properties in Au-Fe Alloys.- 1. 5. Near-Neighbor Interaction in ?-Fe-Mo Alloys.- 1. 6. Near-Neighbor Interaction in Fe-C Alloys.- 1. 7. Order-Disorder in FeAl and Fc3Al.- 1. 8. Thin Films and Superparamagnetism.- 1. 9. Mossbauer Effect as a Nondestructive Analytical Tool.- 2. Physical Metallurgy Considerations Concerning the Mossbauer Effect.- 3. Summary.- 9 Application to Biochemical Systems.- 1. Hemoproteins.- 2. Experimental Conditions.- 2. 1. Enrichment.- 2. 2. Effect of Thickness.- 2. 3. State of the Absorber.- 3. Effect of Experimental Variables.- 3. 1. Effect of Temperature.- 3. 2. Effect of Magnetic Field.- 4. Spin-Spin Equilibrium.- Appendix A Nomenclature of Mossbauer Spectroscopy.- Appendix B Bibliographic Sources.- Appendix C Selected References on Mossbauer Spectroscopy.

Far‐Infrared Collision‐Induced Absorption in CO2. I. Temperature Dependence

Abstract: Accurate measurements of collision‐induced absorption in CO2 are made at a number of temperatures in the range from − 40 to 60°C in the wavelength region 7–250 cm−1. Direct evidence for the separation of the pure translational band from the rotational–translational band is obtained at all temperatures. This and other aspects of the band shape are discussed. Over the entire temperature range, the experimentally determined Kramers–Kronig integral is found to be in good agreement with the theoretical value, i.e., the static dielectric constant. This agreement is achieved only when the contribution of the quadrupole–quadrupole energy in the radial distribution function, of particular importance for CO2 because of its large quadrupole moment, is calculated accurately. A value of the quadrupole moment is obtained, (4.5 ± 0.2)10−26 esu, which is in satisfactory agreement with that obtained by the method of Buckingham and Disch, which does not depend on a knowledge of intermolecular force constants. Induction due to higher multipole moments and the overlap interaction is considered.

Application of the Theory of Irreducible Tensor Operators to Molecular Hyperfine Structure

Abstract: The theory of irreducible tensor operators is employed to evaluate the matrix elements of the electric quadrupole and magnetic dipole interactions for molecules with several coupling nuclei Two different coupling schemes are considered, namely the unequal coupling and nearly equal coupling representations The relative intensities of the hyperfine transitions are also derived Application of the theory is stressed in an expository manner

The scattering of thermal electrons by carbon monoxide

Abstract: Close-coupling calculations are carried out for the scattering of electrons with energies up to 0.1 eV by a rigid rotator with dipole and quadrupole moments equal to those of carbon monoxide. By appropriate choice of the short range potential, the experimental data on CO momentum transfer cross sections can be closely reproduced. For the scattering of thermal electrons, CO is similar to N2 with the addition of a permanent dipole moment. The observed cross section minimum occurs through the addition of the decreasing electron-dipole contribution and an increasing spherically symmetric short range contribution.

35Cl and 19F NMR Spin–Lattice Relaxation Time Measurements and Rotational Diffusion in Liquid ClO3F

Abstract: The NMR spin–lattice relaxation times of 35Cl and been 19F have measured by pulse techniques over the entire liquid range of ClO3F (130–368°K). The chlorine relaxation which is due solely to the nuclear quadrupole interaction can be used together with the known quadrupole coupling constant to determine the correlation time for molecular orientation, τθ,2. The fluorine relaxation is dominated by the spin–rotation interaction with only a small intermolecular dipole contribution at the lowest temperatures. In order to obtain the angular momentum correlation time, τJ, an independent estimate of the spin–rotation tensor was made by combining gas‐phase measurements of T1(19F) with previous data on the chemical shift and gas‐phase dielectric relaxation. The results for this quasispherical molecule are in accord with rotational diffusion theory and Hubbard's relation, τθ,2τJ = I / 6kT, at the lowest temperatures and agree over the entire range with the extended treatment of McClung.

Electron resonance studies of the renner effect

Abstract: The gas phase electron resonance spectra of NCO in its ground 2Π3/2 vibronic state and in two excited vibronic states are described. Theoretical analysis of the spectra yields effective g values for the three states. In additon the 14N magnetic hyperfine and electric quadrupole coupling constants and the electric dipole moment are determined. The theory of the Renner coupling of electronic and vibrational motion is extended, and shown to account for anomalous contributions to the g values. The theory also shows that these contributions are closely related to the Renner coupling constant.

Self-consistent-field wave functions, energies, multipole moments, diamagnetic susceptibility and shielding tensors, and electric field gradient tensors for nitrogen dioxide and ozone

Abstract: Using basis sets of ‘ double zeta plus polarization ’ quality, non-empirical self-consistent-field calculations have been carried out on the ground states of NO2 and O3. The computed total energies, -204·0679 and -224·3093 hartree, are the lowest reported to date for these molecules and are estimated to lie about 0·06 hartree above the respective Hartree-Fock limits. Calculations were also carried out without d (or polarization) functions and it was determined that (a) d functions are about three times more important on the central atom than on the terminal oxygens in both molecules and (b) d functions are 2·5 to 3 times less important in O3 than in SO2. Calculated second moments of the electronic charge distribution and diamagnetic susceptibilities are in good to excellent agreement with experiment for ozone. Dipole moments for both molecules and quadrupole coupling constants for NO2 are only in qualitative agreement with experiment. The calculated molecular quadrupole moments of O3, for reasons not unde...

Quadrupole Effects in NMR Spectra on Short-Lived β-Radioactive Nuclei, 12B and 12N

Abstract: Quadrupole effects in NMR on 12 B( T 1/2 =20 ms) and 12 N( T 1/2 =11 ms) have been investigated by using the polarized nuclei produced and implanted through nuclear reactions and the resultant asymmetric β decay. The implantation media were polycrystalline bcc metals (Nb, Mo, Ta and W), TiB 2 and ZrB 2 . To increase the observable effects in NMR, a frequency-modu-lated r.f. field was employed. The spectra in bcc metals show the characteristics of quadrupole interaction for nuclear spin \(I{=}1\hslash\), and the determined coupling constants depend largely on the periodic groups of the related elements. The spectra in the bcc metals together with those in the fcc metals (Al, Cu, Pt and Au) indicate that the major implanted sites are interstitial. From the results on TiB 2 and ZrB 2 and the known values on 11 B, the ratio of quadrupole moments is determined as | Q ( 12 B)/ Q ( 11 B)|=0.42±0.04, and the moment of 12 B is deduced to be | Q ( 12 B)|=0.017 1 ±0.001 6 b.

E2 CORE POLARIZATION BY NEUTRONS IN THE (i/sub 13/2/)$sup -2$ CONFIGURATION IN $sup 206$Pb.

Abstract: Using the 204Hg(α,2n) reaction and the pulsed beam of our 225 cm cyclotron, we have been able to localize the 12+ and 10+ states of the (i13/2)-2 configuration in 206Pb at the energies 4 027.2 and 3 957.6 keV, respectively. It has been possible to determine the partial E2 transition probability for the 12+ → 10+ transition and to derive an effective charge for the i13/2 neutron, which is 0.94±0.04. It is concluded that the quadrupole polarization charge for the i13/2 neutron is about 50% larger than for the h9/2 proton.

Electric quadrupole contributions to the optical activity of crystalline transition metal complexes

Abstract: It is shown that the circular dichroism data from crystalline transition metal complexes of D 3 symmetry provides evidence for electric dipole-electric quadrupole contributions to the optical activity, as distinct from the usual electric dipole-magnetic dipole mechanism. Specifically, in the 1 A 1→1 E(T 2g ) transition, which is electric quadrupole allowed and magnetic dipole forbidden in the parent Oh complex, and the high frequency charge-transfer transitions of E symmetry, could provide significant electric quadrupole contributions to the circular dichroism. The electric quadrupole rotational strength obeys the Condon sum rule.

Dissociation Energy, Ionization Potential, Electron Affinity, Dipole and Quadrupole Moments of Chlorine Monoxide (ClO, 2Π) from Ab Initio Molecular Orbital Calculations

Abstract: Molecular self‐consistent‐field wavefunctions near the Hartree–Fock limit have been computed by the Roothaan expansion method for ClO(2Π), ClO+(3Σ), and ClO−(1Σ) at an internuclear separation of 1.570 A. Combination of the computed total energies with estimates for the molecular extra correlation energies yielded values of < 2.9, 2.2 ± 0.5, and 11.2 ± 0.4 eV for the binding energy, vertical electron affinity, and vertical ionization potential, respectively, of ClO. The above results, and the computed dipole moment, 0.81 ± 0.16 D, are in satisfactory agreement with experimental data. In addition to the above properties, the dipole and quadrupole moments have been calculated for ClO+ and ClO−.

Studies in Mössbauer spectroscopy. Part IV. Signs of the quadrupole coupling constants for some organotin(IV) compounds

Abstract: Mossbauer spectra of some four-, five-, and six-co-ordinate organotin(IV) compounds, covering seven different structural types, have been measured in an applied magnetic field. From the signs of the quadrupole coupling constants, it is shown that the electric field gradient at the tin nucleus arises primarily from differences in the electron densities of the tin–ligand bonds (i.e.|qval| > |qlat|). The relative signs of the coupling constants agree with those predicted for regular structures by the point-charge model, except for the cis-R2SnX4 complexes. The apparently anomalous sign for the latter is probably due to deviations from strict octahedral geometry. It is deduced that the field gradient is largely determined by the disposition of the tin–carbon bonds.