Showing papers on "Quadrupole published in 2013"

Atomic Data and Nuclear Data Tables

Abstract: a b s t r a c t The ab initio quasirelativistic Hartree–Fock method developed specifically for the calculation of spectral parameters of heavy atoms and highly charged ions is used to derive transition data for a multicharged tungsten ion. The configuration interaction method is applied to include electron correlation effects. The relativistic effects are taken into account in the Breit–Pauli approximation for quasirelativistic Hartree–Fock radial orbitals. The energy level spectra, radiative lifetimes and Lande gfactors are calculated for the 4p 6 4d 2 , 4p 6 4d4f, and 4p 5 4d 3 configurations of the ion W 36+ . The transition wavelengths, spontaneous transition probabilities, oscillator strengths, and line strengths for the electric dipole, electric quadrupole, electric octupole, and magnetic dipole transitions among the levels of these configurations are tabulated.

Polarizable Atomic Multipole-Based AMOEBA Force Field for Proteins

Abstract: Development of the AMOEBA (atomic multipole optimized energetics for biomolecular simulation) force field for proteins is presented. The current version (AMOEBA-2013) utilizes permanent electrostatic multipole moments through the quadrupole at each atom, and explicitly treats polarization effects in various chemical and physical environments. The atomic multipole electrostatic parameters for each amino acid residue type are derived from high-level gas phase quantum mechanical calculations via a consistent and extensible protocol. Molecular polarizability is modeled via a Thole-style damped interactive induction model based upon distributed atomic polarizabilities. Inter- and intramolecular polarization is treated in a consistent fashion via the Thole model. The intramolecular polarization model ensures transferability of electrostatic parameters among different conformations, as demonstrated by the agreement between QM and AMOEBA electrostatic potentials, and dipole moments of dipeptides. The backbone and...

Large-scale structures in dipole and quadrupole wakes of a wall-mounted finite rectangular cylinder

Abstract: Large-scale quasi-periodic vortex structures shed behind a wall-mounted rectangular cylinder were reconstructed from conditional averaging of several planar particle image velocimetry measurements based on the phase of the pressure at the cylinder surface. The measurements were taken for a square cross-section cylinder with height-to-width ratio of h/d = 8 partially immersed in two nominally thin turbulent boundary layers of thickness-to-height ratios of δ/h = 0.09 and 0.32. The Reynolds number based on the diameter was 12,000. For the thinner boundary layer in the time-averaged wake, one stream wise vortex pair was present at the free end (dipole wake) while for the thicker boundary layer, another pair was also observed at the wall junction (quadrupole wake). The detailed description of the shed structures giving rise to these time-averaged vortex pairs indicates more complex connections than previously proposed arch-type structures, which implies different vortex dynamic processes in the wake. The structures obtained for the dipole and quadrupole wakes were similar at the free end but significantly different at the junction resulting in distinct imprint on the mean and turbulent fields.

An Improved Multipole Approximation for Self-gravity and Its Importance for Core-collapse Supernova Simulations

Abstract: Self-gravity computation by multipole expansion is a common approach in problems such as core-collapse and Type Ia supernovae, where single large condensations of mass must be treated. The standard formulation of multipole self-gravity in arbitrary coordinate systems suffers from two significant sources of error, which we correct in the formulation presented in this article. The first source of error is due to the numerical approximation that effectively places grid cell mass at the central point of the cell, then computes the gravitational potential at that point, resulting in a convergence failure of the multipole expansion. We describe a new scheme that avoids this problem by computing gravitational potential at cell faces. The second source of error is due to sub-optimal choice of location for the expansion center, which results in angular power at high multipole l values in the gravitational field, requiring a high—and expensive—value of multipole cutoff l max. By introducing a global measure of angular power in the gravitational field, we show that the optimal coordinate for the expansion is the square-density-weighted mean location. We subject our new multipole self-gravity algorithm, implemented in the FLASH simulation framework, to two rigorous test problems: MacLaurin spheroids for which exact analytic solutions are known, and core-collapse supernovae. We show that key observables of the core-collapse simulations, particularly shock expansion, proto-neutron star motion, and momentum conservation, are extremely sensitive to the accuracy of the multipole gravity, and the accuracy of their computation is greatly improved by our reformulated solver.

First-post-Newtonian quadrupole tidal interactions in binary systems

Abstract: We consider tidal coupling in a binary stellar system to first-post-Newtonian order. We derive the orbital equations of motion for bodies with spins and mass quadrupole moments and show that they conserve the total linear momentum of the binary. We note that spin-orbit coupling must be included in a 1PN treatment of tidal interactions in order to maintain consistency (except in the special case of adiabatically induced quadrupoles); inclusion of 1PN quadrupolar tidal effects while omitting spin effects would lead to a failure of momentum conservation for generic evolution of the quadrupoles. We use momentum conservation to specialize our analysis to the system's center-of-mass-energy frame; we find the binary's relative equation of motion in this frame and also present a generalized Lagrangian from which it can be derived. We then specialize to the case in which the quadrupole moment is adiabatically induced by the tidal field (in which case it is consistent to ignore spin effects). We show how the adiabatic dynamics for the quadrupole can be incorporated into our action principle and present the simplified orbital equations of motion and conserved energy for the adiabatic case. These results are relevant to gravitational wave signals from inspiralling binary neutron stars.

A continuum solvent model of the multipolar dispersion solvation energy

Abstract: The dispersion energy is an important contribution to the total solvation energies of ions and neutral molecules. Here, we present a new continuum model calculation of these energies, based on macroscopic quantum electrodynamics. The model uses the frequency dependent multipole polarizabilities of molecules in order to accurately calculate the dispersion interaction of a solute particle with surrounding water molecules. It includes the dipole, quadrupole, and octupole moment contributions. The water is modeled via a bulk dielectric susceptibility with a spherical cavity occupied by the solute. The model invokes damping functions to account for solute–solvent wave function overlap. The assumptions made are very similar to those used in the Born model. This provides consistency and additivity of electrostatic and dispersion (quantum mechanical) interactions. The energy increases in magnitude with cation size, but decreases slightly with size for the highly polarizable anions. The higher order multipole mome...

Enhanced quadrupole effects for atoms in optical vortices.

Abstract: We show that the normally weak optical quadrupole interaction in atoms is enhanced significantly when the atom interacts at near resonance with an optical vortex. In particular, the forces and torque acting on the atom are shown here to scale up with the square of the winding number l of the vortex. Because the integer l can be arranged to be large, this property allows for processes involving dipole-forbidden, but quadrupole-allowed, transitions in atoms, such as cesium and oxygen, to come into play. We show that the mechanical effects of vortex light on atoms involving translational and rotational motion as well as trapping should be significantly enhanced for quadrupole transitions and present novel features with useful implications for the emerging field of atomtronics.

Electric field gradient quadrupole Raman modes observed in plasmon-driven catalytic reactions revealed by HV-TERS.

Abstract: Electric field gradient quadrupole Raman modes are observed in plasmon-driven chemical reactions investigated with high vacuum tip-enhanced Raman spectroscopy (HV-TERS). TER spectra reveal that 4-nitrobenzenethiol (4NBT) catalytically dimerizes to dimercaptoazobenzene (DMAB) under an HV-TERS setup. More importantly, we find that the electric field gradient leads to strong enhancement of the infrared (IR)-active modes of DMAB. The observation of both the Raman-active and IR-active modes of DMAB provides spectral evidence for ultrasensitive chemical analysis.

A Continuum Solvent Model of the Multipolar Dispersion Solvation Energy B

Abstract: The dispersion energy is an important contribution to the total solvation energies of ions and neutral molecules. Here, we present a new continuum model calculation of these energies, based on macroscopic quantum electrodynamics. The model uses the frequency dependent multipole polarizabilities of molecules in order to accurately calculate the dispersion interaction of a solute particle with surrounding water molecules. It includes the dipole, quadrupole, and octupole moment contributions. The water is modeled via a bulk dielectric susceptibility with a spherical cavity occupied by the solute. The model invokes damping functions to account for solute–solvent wave function overlap. The assumptions made are very similar to those used in the Born model. This provides consistency and additivity of electrostatic and dispersion (quantum mechanical) interactions. The energy increases in magnitude with cation size, but decreases slightly with size for the highly polarizable anions. The higher order multipole moments are essential, making up more than 50% of the dispersion solvation energy of the fluoride ion. This method provides an accurate and simple way of calculating the notoriously problematic dispersion contribution to the solvation energy. The result establishes the importance of using accurate calculations of the dispersion energy for the modeling of solvation.

Neutron star deformation due to multipolar magnetic fields

Abstract: Certain multi-wavelength observations of neutron stars, such as intermittent radio emissions from rotation-powered pulsars beyond the pair-cascade death line, the pulse profile of the magnetar SGR 1900+14 after its 1998 August 27 giant flare, and X-ray spectral features of PSR J0821 4300 and SGR 0418+5729, suggest that the magnetic fields of non-accreting neutron stars are not purely dipolar and may contain higherorder multipoles. Here, we calculate the ellipticity of a non-barotropic neutron star with (i) a quadrupole poloidal-toroidal field, and (ii) a purely poloidal field containing arbitrary multipoles, deriving the relation between the ellipticity and the multipole amplitudes. We present, as a worked example, a purely poloidal field comprising dipole, quadrupole, and octupole components. We show the correlation between field energy and ellipticity for each multipole, that the l = 4 multipole has the lowest energy, and that l = 5 has the lowest ellipticity. We show how a mixed multipolar field creates an observationally testable mismatch between the principal axes of inertia (to be inferred from gravitational wave data) and the magnetic inclination angle. Strong quadrupole and octupole components (with amplitudes � 10 2 times higher than the dipole) in SGR 0418+5729 still yield ellipticity � 10 8 , consistent with current gravitational wave upper limits. The existence of higher multipoles in fast-rotating objects (e.g., newborn magnetars) has interesting implications for the braking law and hence phase tracking during coherent gravitational wave searches.

Thermal lattice expansion effect on reactive scattering of H2 from Cu(111) at T(s) = 925 K.

Abstract: Surface phonons and surface temperature may have important effects on reactions of molecules at surfaces, and at present much remains unknown about these effects. A question addressed here, which has received little attention so far, is how reaction at elevated temperature is affected by thermal lattice expansion. To answer this question for the benchmark reaction of H2 and D2 with Cu(111), we have performed quantum and quasi-classical dynamics calculations. The specific reaction parameter (SRP) approach to density functional theory (DFT) has been used to compute the required six-dimensional potential energy surfaces (PES). Computed reaction probabilities and rotational quadrupole alignment parameters have been compared for surface temperatures Ts = 0 and 925 K. Surface thermal expansion of the lattice leads to a considerable decrease of reaction barrier heights and thereby to increased reaction probabilities as well as decreased rotational quadrupole alignment parameter values in associative desorption.

Quadrupole-octupole coupling in the light actinides

Abstract: The relevance of coupling of quadrupole and octupole collective degrees of freedom in physical observables is explored in calculations with the Gogny force for the light radon, radium, and thorium isotopes. The results of the generator coordinate method calculations for the properties of negative parity states show an improvement over the traditional ones that consider just the octupole moment.

Ultrafast Third-Order Optical Nonlinearity in Au Triangular Nanoprism with Strong Dipole and Quadrupole Plasmon Resonance

Abstract: Au triangular nanoprisms have been prepared by the wet chemical method. By using absorption measurements and finite difference time domain (FDTD) calculations, the dipole and quadrupole plasmon resonances of Au triangular nanoprisms are investigated experimentally and theoretically. Calculations show that large electric fields are confined at the tips of the Au prisms, leading to large third-order optical nonlinearities. The Z-scan measurements show a third-order optical susceptibility of about 1.25 × 10–11 esu at 1240 nm, which is 19 times larger than that at 800 nm. The ultrafast light response time is about 482 fs measured by optical Kerr effect technique at 800 nm. The distinct third-order optical nonlinearities and the ultrafast response time enable the Au triangular prisms to be a good candidate for future all-optical switches and ultrafast optical information manipulators.

Systematics of low-lying states of even-even nuclei in the neutron-deficient lead region from a beyond-mean-field calculation

Abstract: Background: Nuclei located in the neutron-deficient Pb region have a complex structure, rapidly evolving as a function of neutron and proton numbers. The most famous example is ${}^{186}$Pb where the three lowest levels are ${0}^{+}$ states, the two excited ${0}^{+}$ states being located at low excitation energy around 600 keV. Coexisting structures with different properties are found in the neighboring nuclei. Many experiments have been performed over the last few years in which in-band and out-of-band $\ensuremath{\gamma}$-ray transition probabilities have been measured.Purpose: A detailed interpretation of experimental data requires the use of a method going beyond a mean-field approach that permits to determine spectra and transition probabilities. Such methods have already been applied to selected isotopes in this mass region. Our aim is to provide a systematic investigation of this mass region in order to determine how well experimental data can be understood using a state-of-the-art method for nuclear structure.Method: The starting point of our method is a set of mean-field wave functions generated with a constraint on the axial quadrupole moment and using a Skyrme energy density functional. Correlations beyond the mean field are introduced by projecting mean-field wave functions on angular-momentum and particle number and by mixing the symmetry-restored wave functions as a function of the axial quadrupole moment.Results: A detailed comparison with the available data is performed for energies, charge radii, spectroscopic quadrupole moments, and $E0$ and $E2$ transition probabilities for the isotopic chains of neutron deficient Hg, Pb, Po, and Rn. The connection between our results and the underlying mean field is also analyzed.Conclusions: Qualitative agreement with the data is obtained although our results indicate that the actual energy density functionals have to be improved further to achieve a quantitative agreement.

Coulomb stable structures of charged dust particles in a dynamical trap at atmospheric pressure in air

Abstract: A mathematical simulation of a dust particle's behavior in the electrodynamic linear quadrupole trap with closing end electrodes allowed us to reveal several features of the phenomena Regions of stable confinement of a single particle, in dependence of frequency and charge-to-mass ratio, were determined With an increase of the medium's dynamical viscosity, the region for confining charged particles by the trap becomes wider We obtained values of the maximum quantities of charged particles confined by the trap at atmospheric pressure in air Firstly, we presented observations of ordered Coulomb structures of charged dust particles obtained in the quadrupole trap in air at atmospheric pressure The structures consisted of positively charged oxide aluminum particles 10?15??m in size and hollow glass microspheres 30?50??m in diameter The ordered structure could contain particles of different sizes and charges The trap could confine a limited number of charged particles The ordered structures of charged micro-particles obtained in the experiments can be used to study Coulomb systems without neutralizing the plasma background and action of ion and electron flows, which are always present in non-homogeneous plasma

A viable explanation of the CMB dipolar statistical anisotropy

Abstract: The presence of a dipolar statistical anisotropy in the spectrum of cosmic microwave background (CMB) fluctuations was reported by the Wilkinson Microwave Anisotropy Probe (WMAP), and has recently been confirmed in the Planck 2013 analysis of the temperature anisotropies. At the same time, the Planck 2013 results report a stringent bound on the amplitude of the local-type non-Gaussianity. We show that the non-linear effect of the dipolar anisotropy generates not only a quadrupole moment in the CMB but also a local-type non-Gaussianity. Consequently, it is not easy to build models having a large dipolar modulation and at the same time a sufficiently small quadrupole and level of local bispectral anisotropy to agree with the present data. In particular, most models proposed so far are almost excluded, or are at best marginally consistent with observational data. We present a simple alternative scenario that may explain the dipolar statistical anisotropy while satisfying the observational bounds on both the quadrupole moment and local-type non-Gaussianity.

Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions

Abstract: We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance the extent of the charge distribution–the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 A from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 A ) is half that of the point multipole expansion up to the octupole order.

A transferable H2O interaction potential based on a single center multipole expansion: SCME.

Abstract: A transferable potential energy function for describing the interaction between water molecules is presented. The electrostatic interaction is described rigorously using a multipole expansion. Only one expansion center is used per molecule to avoid the introduction of monopoles. This single center approach turns out to converge and give close agreement with ab initio calculations when carried out up to and including the hexadecapole. Both dipole and quadrupole polarizability are included. All parameters in the electrostatic interaction as well as the dispersion interaction are taken from ab initio calculations or experimental measurements of a single water molecule. The repulsive part of the interaction is parametrized to fit ab initio calculations of small water clusters and experimental measurements of ice Ih. The parametrized potential function was then used to simulate liquid water and the results agree well with experiment, even better than simulations using some of the point charge potentials fitted to liquid water. The evaluation of the new interaction potential for condensed phases is fast because point charges are not present and the interaction can, to a good approximation, be truncated at a finite range.

Magnetic dipole and electric quadrupole moments of the 229 Th nucleus

Abstract: We determine the magnetic dipole $\ensuremath{\mu}=0.360(7){\ensuremath{\mu}}_{N}$ and the electric quadrupole $Q=3.11(6)$$e$b moments of the ${}^{229}$Th nucleus by combining our high-precision calculations of the hyperfine constants with measurements reported in Campbell et al. [Phys. Rev. Lett. 106, 223001 (2011)]. We find that the previous value $\ensuremath{\mu}=0.46(4){\ensuremath{\mu}}_{N}$ [Gerstenkorn et al., J. Phys. (Paris) 35, 483 (1974)] is incorrect by 25%. We report a method for determining the accuracy of theoretical hyperfine constants $B/Q$ and demonstrate that it can be used to extract the electric quadrupole moment $Q$ with a 1%--2% uncertainty for a large number of nuclei. This approach allowed us to identify 40% inconsistencies in measurements of Ra${}^{+}$ hyperfine constants $B$.

CMB dipole asymmetry from a fast roll phase

Abstract: The observed CMB (cosmic microwave background) dipole asymmetry cannot be explained by a single field model of inflation - it inevitably requires more than one field where one of the fields is responsible for amplifying the super-Hubble fluctuations beyond the pivot scale. Furthermore the current constraints on $f_NL$ and $tau_NL$ require that such an amplification cannot produce large non-Gaussianity. In this paper we propose a model to explain this dipole asymmetry from a spectator field, which is responsible for generating all the curvature perturbations, but has a temporary fast roll phase before the Hubble exit of the pivot scale. The current data prefers spectator scenario because it leaves no isocurvature perturbations. The spectator model will also satisfy the well-known constraints arising from quasars, and the quadrupole and octupole of the CMB.

Deformation and breakup of a leaky dielectric drop in a quadrupole electric field

Abstract: The deformation and breakup of a leaky dielectric drop suspended in a leaky dielectric medium subjected to a quadrupole electric field are studied. Analytical (linear and nonlinear asymptotic expansions in the electric capillary number, , a ratio of electric to capillary stress) and numerical (boundary element) methods are used. A complete phase diagram for the drop deformation in the – plane is presented, where and are the non-dimensional ratios of the resistivities and dielectric constants, respectively, of the drop and the medium phase. The prolate and oblate deformations are mapped in the phase diagram, and the flow contours are also shown. The large deformation and breakup of a drop at higher are analysed using the boundary element method. Several non-trivial shapes are observed at the onset of breakup of a drop. A prolate drop always breaks above a certain critical value of . In the oblate deformation cases, breakup as well as steady shapes are observed at a higher value of . A detailed study of prolate and oblate deformation tendencies due to the normal and tangential electric stresses and the countervailing role of viscous stresses is presented. The circulation inside a drop is found to be more intense for a quadrupole field as compared with a uniform electric field. More intense internal circulations can lead to enhanced mixing characteristics and will have implications in microfluidic devices.

Extraction of 3D field maps of magnetic multipoles from 2D surface measurements with applications to the optics calculations of the large-acceptance superconducting fragment separator BigRIPS

Abstract: The fringing fields of magnets with large apertures and short lengths greatly affect ion-optical calculations. In particular, for a high magnetic field where the iron core becomes saturated, the effective lengths and shapes of the field distribution must be considered because they change with the excitation current. Precise measurement of the three-dimensional magnetic fields and the correct application of parameters in the ion-optical calculations are necessary. First we present a practical numerical method of extracting full 3D magnetic field maps of magnetic multipoles from 2D field measurements of the surface of a cylinder. Using this novel method, we extracted the distributions along the beam axis for the coefficient of the first-order quadrupole component, which is the leading term of the quadrupole components in the multipole expansion of magnetic fields and proportional to the distance from the axis. Higher order components of the 3D magnetic field can be extracted from the leading term via recursion relations. The measurements were done for many excitation current values for the large-aperture superconducting triplet quadrupole magnets (STQs) in the BigRIPS fragment separator at the RIKEN Nishina Center RI Beam Factory. These distributions were parameterized using the Enge functions to fit the fringe field shapes at all excitation current values, so that unmeasured values are interpolated. The extracted distributions depend only on the position along the beam axis, and thus the measured three-dimensional field can easily be parameterized for ion-optical calculations. We implemented these parameters in the ion-optical calculation code COSY INFINITY and realized a first-order calculation that incorporates the effect of large and varying fringe fields more accurately. We applied the calculation to determine the excitation current settings of the STQs to realize various optics modes of BigRIPS and the effectiveness of this approach has been demonstrated.

The electric quadrupole moment of molecular hydrogen ions and their potential for a molecular ion clock

Abstract: The systematic shifts of the transition frequencies in the molecular hydrogen ions are of relevance to ultra-high-resolution radio-frequency, microwave and optical spectroscopy of these systems, performed in ion traps. We develop the ab-initio description of the interaction of the electric quadrupole moment of this class of molecules with the static electric field gradients present in ion traps. In good approximation, it is described in terms of an effective perturbation hamiltonian. An approximate treatment is then performed in the Born-Oppenheimer approximation. We give an expression of the electric quadrupole coupling parameter valid for all hydrogen molecular ion species and evaluate it for a large number of states of H2+, HD+, and D2+. The systematic shifts can be evaluated as simple expectation values of the perturbation hamiltonian. Results on radio-frequency (M1), one-photon electric dipole (E1) and two-photon E1 transitions between hyperfine states in HD+ are reported. For two-photon E1 transitions between rotationless states the shifts vanish. For a subset of rovibrational one-photon transitions the quadrupole shifts range from 0.2 to 10 Hz for an electric field gradient of 0.1 GV/m2. We point out an experimental procedure for determining the quadrupole shift which will allow reducing its contribution to the uncertainty of unperturbed rovibrational transition frequencies to the 1.10^(-15) relative level and, for selected transitions, even below it. The combined contributions of black-body radiation, Zeeman, Stark and quadrupole effects are considered for a large set of transitions and it is estimated that the transition frequency uncertainty of selected transitions can be reduced below the 1.10^(-15) level.

Unraveling the internal dynamics of the benzene dimer: a combined theoretical and microwave spectroscopy study

Abstract: We report a combined theoretical and microwave spectroscopy study of the internal dynamics of the benzene dimer, a benchmark system for dispersion forces. Although the extensive ab initio calculations and experimental work on the equilibrium geometry of this dimer have converged to a tilted T-shaped structure, the rich internal dynamics due to low barriers for internal rotation have remained largely unexplored. We present new microwave spectroscopy data for both the normal (C6H6)2 and partially deuterated (C6D6)(C6H6) dimers. The splitting patterns obtained for both species are unraveled and understood using a reduced-dimensionality theoretical approach. The hindered sixfold rotation of the stem can explain the observed characteristic 1 : 2 : 1 tunneling splitting pattern, but only the concerted stem rotation and tilt tunneling motion, accompanied by overall rotation of the dimer, yield the correct magnitude of the splittings and their strong dependence on the dimer angular momentum J that is essential to explain the experimental data. Also the surprising observation that the splittings are reduced by 30% for the mixed (C6D6)C(C6H6)S dimer in which only the cap (C) in the T-shaped structure is deuterated, while the rotating stem (S) monomer is the same as in the homodimer, is understood using this approach. Stark shift measurements allowed us to determine the dipole moment of the benzene dimer, μ = 0.58 ± 0.051 D. The assumption that this dipole moment is the vector sum of the dipole moments induced in the monomers by the electric field of the quadrupole on the other monomer yields a calculated value of μ = 0.63 D. Furthermore, the observed Stark behavior is typical for a symmetric top, another confirmation of our analysis.

Halogen bonding: a theoretical study based on atomic multipoles derived from quantum theory of atoms in molecules

Abstract: Atomic multipole moments derived from quantum theory of atoms in molecules are used to study halogen bonds in dihalogens (with general formula YX, in which X refers to the halogen directly interacted with the Lewis base) and some molecules containing C–X group. Multipole expansion is used to calculate the electrostatic potential in a vicinity of halogen atom (which is involved in halogen bonding) in terms of atomic monopole, dipole, and quadrupole moments. In all the cases, the zz component of atomic traceless quadrupole moments (where z axis taken along Y–X or C–X bonds) of the halogens plays a stabilizing role in halogen bond formation. The effects of atomic monopole and dipole moments on the formation of a halogen bond in YX molecules depend on Y and X atoms. In Br2 and Cl2, the monopole moment of halogens is zero and has no contribution in electrostatic potential and hence in halogen bonding, while in ClBr, FBr, and FCl it is positive and therefore stabilize the halogen bonds. On the other hand, the negative sign of dipole moment of X in all the YX molecules weakens the corresponding halogen bonds. In the C–X-containing molecules, monopole and dipole moments of X atom are negative and consequently destabilize the halogen bonds. So, in these molecules the quadrupole moment of X atom is the only electrostatic term which strengthens the halogen bonds. In addition, we found good linear correlations between halogen bonds strength and electrostatic potentials calculated from multipole expansion.

Multiconfigurational Dirac–Fock energy levels and radiative rates for Br-like tungsten

Abstract: Energies, lifetimes, and wavefunction compositions have been computed for all levels of odd parity 4s24p5 ground configuration and 3d94s24p6 excited configuration as well as 4s4p6 and 4s24p44d even parity excited configurations in highly charged Br-like tungsten ion (W XL) by using the multiconfigurational Dirac–Fock method. Also, we have reported the transition wavelengths, oscillator strengths, transition probabilities and line strengths for the electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transition from the 4s24p5 configuration. We have compared our calculated results with the other available experimental and theoretical results. The excellent agreement observed between our new results and those obtained using different approaches confirm the quality of our results.

Low-lying states of 184 W and 184 Os nuclei

Abstract: The energy levels, transition energy, B(E2) values, intrinsic quadrupole moment Q0 and potential energy surface for even-even 184W and 184Os nuclei were calculated using IBM-1. The predicted energy levels, transition energy, B(E2) values and intrinsic quadrupole moment Q0 results are reasonably consistent with the experimental data. A contour plot of the potential energy surfaces shows that two interesting nuclei are deformed and have rotational characters.

Fluid-solid equilibrium of carbon dioxide as obtained from computer simulations of several popular potential models: The role of the quadrupole

Abstract: In this work the solid-fluid equilibrium for carbon dioxide (CO2) has been evaluated using Monte Carlo simulations. In particular the melting curve of the solid phase denoted as I, or dry ice, was computed for pressures up to 1000 MPa. Four different models, widely used in computer simulations of CO2 were considered in the calculations. All of them are rigid non-polarizable models consisting of three Lennard-Jones interaction sites located on the positions of the atoms of the molecule, plus three partial charges. It will be shown that although these models predict similar vapor-liquid equilibria their predictions for the fluid-solid equilibria are quite different. Thus the prediction of the entire phase diagram is a severe test for any potential model. It has been found that the Transferable Potentials for Phase Equilibria (TraPPE) model yields the best description of the triple point properties and melting curve of carbon dioxide. It is shown that the ability of a certain model to predict the melting curve of carbon dioxide is related to the value of the quadrupole moment of the model. Models with low quadrupole moment tend to yield melting temperatures too low, whereas the model with the highest quadrupole moment yields the best predictions. That reinforces the idea that not only is the quadrupole needed to provide a reasonable description of the properties in the fluid phase, but also it is absolutely necessary to describe the properties of the solid phase.