Quadrupole Interaction Term Research Articles

Thermal expansion of α-nitrogen ice in terahertz spectroscopy

The volumetric thermal expansion coefficient of α-nitrogen (N2) ice is calculated for temperatures between 10 and 25 K using its terahertz transmission data and a phonon model. The observed dip in terahertz transmission around 1.45 THz is modeled as phonon absorption based on an intermolecular potential which is sum of the Lennard-Jones potential and quadrupole–quadrupole interaction term. Using this model and our experimental data, the lattice parameters of α-N2 ice were obtained.

Entanglement, magnetic and quadrupole moments properties of the mixed spin Ising–Heisenberg diamond chain

Thermal entanglement, magnetic and quadrupole moments properties of the mixed spin-12 and spin-1 Ising–Heisenberg model on a diamond chain are considered. Magnetization and quadrupole moment plateaus are observed for the antiferromagnetic couplings. Thermal negativity as a measure of quantum entanglement of the mixed spin system is calculated. Different behavior for the negativity is obtained for the various values of Heisenberg dipolar and quadrupole couplings. The intermediate plateau of the negativity has been observed at the absence of the single-ion anisotropy and quadrupole interaction term. When dipolar and quadrupole couplings are equal there is a similar behavior of negativity and quadrupole moment.

Adsorption and Diffusion of Light Gases in ZIF-68 and ZIF-70: A Simulation Study

We have computed the adsorption and diffusion of CO2, N2, CH4, and H2 in zeolitic imidazolate framework (ZIF) materials ZIF-68 and ZIF-70 from atomistic simulations. These simulations were performed using geometries obtained from density functional theory (DFT) optimization of the experimental crystal structure of ZIF-68 and on four structures of ZIF-70, one based on the experimental crystal structure and three having different imidazole/nitroimidazole substitution ratios. The framework charges for charge−quadrupole interaction (CQI) terms in our simulations were parametrized with charges obtained from Bader charge decomposition (periodic DFT calculations) and ChelpG charges (cluster DFT calculations). The adsorption and diffusion of the quadrupolar fluids can be dramatically different when using the Bader and ChelpG charges. Agreement between simulations and experiments for the N2 adsorption isotherms in ZIF-68 and 70 is very good when CQI terms are included. In contrast, simulations overpredict the amou...

Extensions to the HELIUM code to handle intense X-ray light

The X-ray free electron lasers currently being built promise light of sufficient intensity to cause direct double photoionization of the inner K-shells of Ne and Ar atoms. The Ne and Ar K-shell electrons experience a binding energy that is almost the same in the neutral atom as in the corresponding two-electron ion, Ne8+ or Ar16+. We report on new numerical methods we have implemented for calculating double ionization rates for these two-electron positive ions interacting with an intense X-ray free electron laser pulse. The numerical method builds upon an existing code (HELIUM) for solving the full-dimensional time-dependent Schrödinger equation that, operating within the electric dipole approximation, has found successful application in the optical to XUV wavelength range. The primary extensions to HELIUM are the inclusion of magnetic dipole and electric quadrupole interaction terms appropriate to extreme laser intensities and wavelengths approaching atomic dimensions.

Dynamics of precessing binary black holes using the post-Newtonian approximation

We investigate the (conservative) dynamics of binary black holes using the Hamiltonian formulation of the post-Newtonian (PN) equations of motion. The Hamiltonian we use includes spin-orbit coupling, spin-spin coupling, and mass monopole/spin-induced quadrupole interaction terms. In the case of both quasi-circular and eccentric orbits, we search for the presence of chaos (using the method of Lyapunov exponents) for a large variety of initial conditions. For quasi-circular orbits, we find no chaotic behavior for black holes with total mass 10 - 40 solar masses when initially at a separation corresponding to a Newtonian gravitational-wave frequency less than 150 Hz. Only for rather small initial radial distances, for which spin-spin induced oscillations in the radial separation are rather important, do we find chaotic solutions, and even then they are rare. Moreover, these chaotic quasi-circular orbits are of questionable astrophysical significance, since they originate from direct parametrization of the equations of motion rather than from widely separated binaries evolving to small separations under gravitational radiation reaction. In the case of highly eccentric orbits, which for ground-based interferometers are not astrophysically favored, we again find chaotic solutions, but only at pericenters so small that higher order PN corrections, especially higher spin PN corrections, should also be taken into account.

A dipole–quadrupole interaction term in E1 photon transitions

Evidence is presented for a dipole–quadrupole interaction term in the primary E1 transitions of average resonance capture data. This evidence is obtained by testing a proposed generalized Landau Fermi liquid model for spherical and deformed nuclei, which includes the effect of the dipole–quadrupole interaction. The present formulation succeeded in unifying the description of the E1 photon strength functions for spherical and deformed nuclei. The Landau–Migdal interaction constants, as well as the effective nucleon mass, are determined as F 0′=1.49±0.08, F 1=0.12±0.21, and m ∗/m=1.04±0.07 . The temperature dependence of the damping width of the giant dipole resonance is investigated within a generalized Fermi liquid model and its predictions are compared with experimental data, as well as microscopic calculations.

Adventures of a Rydberg electron in an anisotropic world

The study of subtle interactions in atomic and molecular systems has stirred scientific curiosity since the dawn of quantum mechanics. Even today, research into perturbative long-range interactions continues to push into new territory, driven largely by the experimental capabilities of Rydberg state spectroscopy to detect effects of extremely weak interactions. While static long-range multipole interactions have been studied for years, the presence of dynamic terms that involve both position and momentum operators has been demonstrated only surprisingly recently. In this paper we document the existence of an effective vector interaction term in the long-range potential experienced by a moving charged particle in the presence of an anisotropic ionic core. In contrast to ordinary static quadrupole or dipole interaction terms, the existence of this vector interaction hinges on the motion of the distant charge as it roams beyond the confines of the core.

Intramolecular Hydrogen Bonding, Gauche Interactions, and Thermodynamic Functions of 1,2-Ethanediamine, 1,2-Ethanediol, and 2-Aminoethanol: A Global Conformational Analysis

The global conformational potentials of 1,2-ethanediol, 1,2-ethanediamine, and 2-aminoethanol (X−CH2−CH2−Y; X, Y = OH or NH2) were obtained at the MP2/6-311+G(2d,p) level by scanning through the dihedral angles of the two functional groups and the carbon−carbon bond with the remaining nuclear coordinates being energy-minimized. It was found that the potentials could be represented by the direct-bond potentials between the adjacent molecular fragments and by the through-space electrostatic potentials between the vicinal and geminal fragments. Here, the through-direct-bond potentials are represented by the conventional three Fourier terms of the internal rotation angles, and the through-space potentials, which include the intramolecular hydrogen bonding between X and Y, are represented by the general functional forms of the electric dipole−dipole, dipole−quadrupole, and quadrupole−quadrupole interaction terms. The fitted electrostatic interaction strengths between the X and Y fragments are in good agreement with the predictions of the theoretical molecular fragment dipole and quadrupole moments calculated by the Hirshfeld charge population analysis. Under the present energy decomposition scheme, the intrinsic gauche interactions, which are free of the contribution of the intramolecular H-bonding, could be obtained and correlated with the group electronegativities of X and Y. The potentials were also calculated by the MM3 molecular mechanics method and compared with the present results. With the global conformation potentials, the thermodynamic functions of the molecules and also their individual conformers are calculated and compared with the gas-phase experimental thermodynamic data in the literature.

High angular momentum 6pnl and 6dnl doubly excited Rydberg states of barium

6p32/nl (n=11 to 15, l=5 to n-1) and 6d52/nl (n=11 to 14, l=6 to n-1) doubly excited Rydberg states of barium have been studied using a multistep laser excitation technique. The excitation is via the bound 6s12/nl states which are populated using an electric-field switching method which allows the selective population of high-l angular momentum states. The resulting spectra clearly demonstrate the presence of dielectronic correlation. The authors show that this correlation is well described in terms of the (j-l)K coupling scheme, taking into account in a perturbative way the dipole and quadrupole interaction terms.

Electron paramagnetic resonance of nickel in silicon — II. hyperfine and quadrupole interactions

An electron paramagnetic resonance (EPR) study on n-type silicon doped with nickel enriched to 88.1% 61Ni is presented. The structure due to the 61Ni isotope with nuclear spin I = 3 2 was investigated. The EPR spectrum with the appearance of “forbidden” lines can be described by a spin Hamiltonian including the nuclear Zeeman, hyperfine and quadrupole interaction terms. A computer calculation of energy levels and transition probabilities of all EPR transitions was made explaining the angular dependence of the magnetic field positions of the resonances and their intensities. The hyperfine tensor A, with principal values A [100] = 1.01 MHz, A [011] = -39.98 MHz and A [01̄1] = -37.60 MHz, is nearly axial around [1 0 0]. An analysis of hyperfine and quadrupole interactions was carried out revealing the specific effect of the nickel impurity on the electronic structure of the centre. Based on the information about spin and charge density as derived in the analysis, a dihedral bonding model for the Si:Ni - s centre is supported.

Calculations of the geometry and binding energy of aromatic dimers: Benzene, toluene, and toluene–benzene

Calculations of the geometries and energies of the benzene, toluene, and toluene–benzene dimers using a combination of atom–atom and multipolar potentials are presented and discussed. An exponential-six atom–atom potential plus a molecular quadrupole–quadrupole interaction term gives the reported parallel displaced C2h benzene dimer geometry. The excited state behavior of the benzene dimer can be qualitatively understood based on this calculation. The toluene–benzene dimer is well modeled by these terms in addition to a dipole–quadrupole interaction term. Both parallel displaced and perpendicular configurations are obtained in agreement with the experimental data. Using exponential-six dipole–dipole, quadrupole–quadrupole, and dipole–quadrupole interactions the toluene dimer can be satisfactorily modeled. The calculations generally suggest that excitation of parallel displaced dimers can lead to rearrangement (and possible excimer formation) in the excited state.

EPR of the vanadyl ion in Tutton salts at zero magnetic field

EPR measurements at zero magnetic field have provided accurate measurements of hyperfine principal values for the vanadyl ion doped in a series of Tutton salts. Unlike in previous EPR determinations, the in-plane anisotropy of the hyperfine tensor was found to vary only slightly from one environment to another. The nuclear quadrupole interaction term has also been determined from the zero-field spectrum and yields a value for the nuclear quadrupole moment of 51V in agreement with that determined from atomic-beam measurements.

Magnetically induced quadrupole interactions and anisotropic hyperfine fields at Fe-sites in RFe2-compounds

57Fe Mossbauer studies of HoFe2 and DyFe2 at various temperatures exhibit a small but definite asymmetry in the peak positions as well as in the peak widths. The symmetry in the line widths suggests that the magnetization deviates from [100] direction, whereas the asymmetry in the peak positions can arise either due to the existence of magnetically induced quadrupole interactions or due to the presence of an appreciable component of hyperfine field at right angle to the magnetization direction. The observed spectra have, therefore, been analysed in terms of two different approaches. In the first approach the total quadrupole interaction is assumed to consist of an axially symmetric magnetically induced part in addition to the usual term, whereas in the second approach the hyperfine coupling tensor has been assumed to be anisotropic. The sign and magnitude of quadrupole interaction terms as well as the magnitudes of the components of hyperfine coupling tensor have been estimated. Various approaches used earlier to analyse the magnitudes of anisotropic hyperfine fields have been shown to be functionally similar to our second approach of fitting. For 57Fe nuclear excited state an explicit analytical expression has been derived for an axially symmetric quadrupole splitting in terms of the observed peak positions of the nuclear Zeeman pattern.

The structure of liquid bromine

The atom-atom correlation function for liquid bromine, derived from the X-ray diffraction studies reported in the preceding paper, is compared with the results of Monte Carlo computer simulations and reference site interaction model (RISM) calculations for various bromine-like model molecules. The models used included the two-centre Lennard-Jones interaction model, both by itself and with idealized point quadrupole and quadrupole-induced dipole interaction terms in the computer simulations, and two and three-centre hard-sphere models in RISM. None of these models lead to atom-atom correlation functions which are in good agreement with that obtained from experiment. This suggests that additional information about the interactions between bromine molecules will be needed before the structure of liquid bromine can be completely understood. Finally, by comparing the results of our computer simulations with RISM results for analogous models, we obtain some insight into the accuracy of the reference site interaction model.

Thermal conductivities of ortho and para hydrogen

The thermal conductivity of molecular hydrogen has been calculated using a Lennard—Jones potential added to a quadrupole—quadrupole interaction term. Large differences between ortho and para hydrogen were obtained particularly in the range about 200 K. Results for “normal” hydrogen, here taken as a simple sum of results for the two components, were found to agree very well with recommended values for experiments on normal hydrogen.

ENDOR of Gd3+in CaO. An investigation of the quadrupole hyperfine interaction

ENDOR measurements were done on 155Gd3+ and 157Ge3+ in CaO, using the natural distribution of Gd isotopes. For H//(100) the following parameters were measured. Some ENDOR complications related to the presence of more than one isotope are discussed. The main objective of the experiments is to investigate the isotropic electric quadrupole interaction term. Comparison with earlier experiments show that B is not very sensitive to the host crystals. This result permits the test of a recent theoretical value of B obtained for free Gd3+ with aid of relativistic linked cluster many-body perturbation theory. Satisfactory agreement between theory and experiment is found.

Zero-field paramagnetic resonance of trivalent gadolinium in several lanthanide tris(ethylsulfate) nonahydrates and nonadeuterates: Determination of crystal-field and hyperfine-structure parameters

Abstract : Employing isotopically pure trivalent 155Gd, 157Gd, and 160Gd as guests in dilute mixed crystals of lanthanum tris(ethylsulfate) nonahydrate (La3(C2H5SO4)3.9H2O), it has been possible to determine both accurate zero-field splitting parameters of crystal field origin and hyperfine structure constants due to magnetic dipole and electric quadrupole interaction terms. The zero-field paramagnetic resonance spectroscopic method is used. It is reasoned that the quadrupole hyperfine constant is due, almost entirely, to lattice contributions; moreover, it is shown to be of the expected order of magnitude and sign. The hyperfine anomaly is discussed. A set of crystal field parameters are reported for the first time for 160Gd in crystals of La(C2H5SC4)3.9D2O which differ significantly from those of the hydrate. Variations of crystal field parameters with various lanthanon host ions are also observed. Finally, a few comments concerning zero-field line widths and their measurement are made. (Modified author abstract)

The ν1 Band of Carbon Dioxide in Pressure-Induced Absorption. II. Density and Temperature Dependence of the Intensity; Critical Phenomena

The ν1 band of gaseous carbon dioxide has been studied in pressure-induced absorption at temperatures of ~ 190, ~ 300, and ~ 470 K, over a density range from 0.5 to 300 amagat, and with path lengths from 0.007 to 56 m. The observed temperature variation of the binary absorption coefficient can be satisfactorily accounted for only by adding a quadrupole–quadrupole interaction term to the usual Lennard–Jones model for the inter-molecular potential. The band profile is in agreement with the theory of quadrupole-induced absorption. There is some increase in the intensity of the band near the critical point due to the divergence of the correlation length. A very marked increase in the intensity is possibly prevented by the "cancellation effect".

Calculations on the force constants of triatomic group II metal halides

A comparison between various polarizable ion models for calculating bending force constants of linear MX2 molecules is presented. A convergence test is applied to the models. Further, the contribution of an induced dipole-induced quadrupole interaction term to the force constant, is examined. The criteria for a useful comparison between calculated and experimental values of force constants are discussed.

Thermal diffusion as a probe of binary diffusion coefficients at elevated temperatures I. Techniques, and results for carbon dioxide + nitrogen

Thermal diffusion measurements made by the two-bulb method are reported for the system CO2+ N2; these cover the composition range 10 to 90 % CO2and the approximate temperature range 300 to 800 K. By using the results in conjunction with an extension upwards in temperature of a previously described technique, values of the binary (concentration) diffusion coefficientD12are determined for the temperature range 300 to 1800 K. The present work is not only novel in using the technique to probe concentration diffusion at elevated temperatures, but also in testing the technique’s viability for use with relatively complex gas mixtures. The upper temperature limit of this extended technique is determined by the onset of invalidity of assumptions implicit in classical kinetic theory, but is thought not to be reached in this work. Comparison of the values obtained for D12with the direct measurements of Walker & Westenberg, which cover the range 300 to 1150 K, shows a mean absolute deviation of 1.3 % and a mean algebraic deviation of + 0.5 %; a similar comparison for the range 1100 to 1800 K with the data of Pakurar & Ferron, individual values of which scatter considerably and have uncertainties of about 10 %, shows a mean absolute deviation of 3.7 % and a mean algebraic deviation of -2.7 %. The overall concordance of the present calculations with the experimental data seems good enough to establish both the utility of the calculational technique and the freedom from systematic error of the point-source method of measuring high-temperature diffusion coefficients. The experimental thermal diffusion data are also compared with the predictions of the commoner intermolecular potential models; of these, given a reasonable value of the well-depth parameter, the exp:6(α = 13) and Lennard-Jones (9:6) perform well, especially at the higher temperatures, and the addition of a quadrupole interaction term to the L.-J. (12:6) model effects a marked improvement in the latter’s performance.