Electric Multipole Moments Research Articles

Cluster interpretation of properties of alternating parity bands in heavy nuclei

The properties of the states of the alternating parity bands in actinides, Ba, Ce and Nd isotopes are analyzed within a cluster model. The model is based on the assumption that cluster type shapes are produced by the collective motion of the nuclear system in the mass asymmetry coordinate. The calculated spin dependences of the parity splitting and of the electric multipole transition moments are in agreement with the experimental data.

Calculation of molecular electric and magnetic multipole moment integrals of integer and noninteger n Slater orbitals using overlap integrals

AbstractClosed formulas are established for the magnetic multipole moment integrals of integer and noninteger n Slater‐type orbitals (ISTOs and NISTOs) in terms of electric multipole moment integrals for which the analytic expressions through the overlap integrals with ISTOs and NISTOs are derived. The overlap integrals are evaluated by the use of auxiliary functions. Using the derived expressions the multipole moment integrals, and therefore the electric and magnetic properties of molecules, can be evaluated most efficiently and accurately. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Matching conditions in metric-affine gravity

By using an isotropic field configuration for the triplet ansatz sector of the metric-affine theories of gravity (MAG), we find a class of harmonic solutions which represents the interior and exterior field of a distribution endowed with electric and strong gravitoelectric multipole moments. Moreover, the general matching and junction conditions in MAG and their reduction to the triplet ansatz sector are presented.

Higher Electric Multipole Moments for Some Polyatomic Molecules from Accurate SCF Calculations

Higher electric multipole moments for the ground-state electronic configuration of some polyatomic molecules, i.e. CH4, NH3, H2O, were calculated from SCF-HFR wavefunctions using Slater-type orbital basis sets. The calculated results for electric multipole moments of these molecules are in good agreement with the theoretical and experimental ones.

Exact calculation of the angular momentum loss, recoil force, and radiation intensity for an arbitrary source in terms of electric, magnetic, and toroid multipoles.

An exact calculation of the radiation intensity, angular momentum loss, and the recoil force for the most general type of source, characterized by electric, magnetic, and toroid multipole moments and radii of any multipolarity and an arbitrary time dependence, is presented. The results are expressed in terms of time derivatives of the multipole moments and mean radii of the corresponding distributions. Although quite cumbersome, the formulas found by us represent exact results in the correct multipole analysis of configurations of charges and currents that contain toroidal sources. So the longstanding problem in classical electrodynamics of relating the radiation properties of a system to quantities completely describing its internal electromagnetic structure is thereby exactly solved. By particularizations to the first multipole contributions, corrections to the familiar formulas from books are found, mostly on account of the toroid moments and their interference with the usual electric and magnetic ones.

Electric quadrupole and hexadecapole moments for X2CCX2, X = H, F, Cl, Br, and I*

AbstractWe have calculated electric quadrupole and hexadecapole moments for ethene, tetrafluoroethene, tetrachloroethene, tetrabromoethene, and tetraiodoethene. A large basis set of [9s6p5d2f/5s4p2d] size is thought to provide reference near‐Hartree–Fock results for the electric multipole moments of ethene: Θxx=1.34 and \documentclass{article}\pagestyle{empty}\begin{document}$\Theta_{zz}=1.53\ ea_{0}^{2}$\end{document} for the quadrupole Φxxxx=−17.38, Φyyyy=20.29, and \documentclass{article}\pagestyle{empty}\begin{document}$\Phi_{zzzz}=-17.04\ ea_{0}^{4}$\end{document} for the hexadecapole moment (with z as the CC axis and the molecule on the xz plane). The electron correlation correction to the above values is estimated from coupled cluster calculations as Θxx=−0.12 and \documentclass{article}\pagestyle{empty}\begin{document}$\Theta_{zz}=-0.34\ ea_{0}^{2}$\end{document} for the quadrupole and Φxxxx=1.26, Φyyyy=−1.30, and \documentclass{article}\pagestyle{empty}\begin{document}$\Phi_{zzzz}=1.80\ ea_{0}^{4}$\end{document} for the hexadecapole moment. For the halogenated ethenes we have obtained the following quadrupole moment values from second‐order Mø ller–Plesset perturbation theory calculations: Θxx=−1.14 (C2F4), 1.94 (C2Cl4), 3.61 (C2Br4), 6.84 (C2I4) and Θzz=−1.04 (C2F4), −0.41 (C2Cl4), −0.15 (C2Br4), −0.87 (C2I4) \documentclass{article}\pagestyle{empty}\begin{document}$ea_{0}^{2}$\end{document}. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Finite-field Møller–Plesset perturbation theory and coupled cluster calculations of the electric multipole moments and the dipole polarizability of As 2

We have calculated the quadrupole ( Θ) and hexadecapole ( Φ) moment and the static dipole polarizability ( α αβ ) of As 2. The electric properties have been extracted from finite-field Møller–Plesset and coupled cluster calculations with large, carefully optimized basis sets of Gaussian-type functions. A very large (21s16p10d4f) basis set is thought to provide near-Hartree–Fock values for the electric moments, the mean and the anisotropy of the dipole polarizability: Θ=1.46 ea 0 2, Φ=−52.4 ea 0 4, α=64.95 and Δα=40.37 e 2 a 0 2 E h −1. At the SDQ-MP4 level of theory the R-dependence of the electric properties has been calculated with a [7s6p5d2f] basis set as [ Θ(R)− Θ(R e )]/ea 0 2 =2.84(R−R e )−0.87(R−R e ) 2−0.32(R−R e ) 3−0.21(R−R e ) 4 [ Φ(R)− Φ(R e )]/ea 0 4 =21.0(R−R e )+8.7(R−R e ) 2−1.6(R−R e ) 3−2.0(R−R e ) 4 [ α(R)− α(R e )]/e 2a 0 2E h −1 =17.42(R−R e )−0.048(R−R e ) 2−0.33(R−R e ) 3+1.71(R−R e ) 4 [Δα(R)−Δα(R e )]/e 2a 0 2E h −1 =22.62(R−R e )+6.68(R−R e ) 2+2.79(R−R e ) 3+1.04(R−R e ) 4 around the experimental bond length of R e=2.1026 Å. Basis set effects have been studied at all levels of theory. Comparing the electric properties of the sequence N 2, P 2, As 2 it is seen that the quadrupole moment is negative for N 2 but positive for P 2 and As 2 while the hexadecapole is negative for all three diatomics. The mean dipole polarizability increases with size, α( N 2)< α( P 2)< α( As 2) and the same trend is observed for the anisotropy as well, Δα(N 2)< Δα(P 2)< Δα(As 2).

Electric Multipole Moments for Some First-Row Diatomic Hydride Molecules

As an example of the use of the analytical formulas derived for electric multipole moment integrals over STOs in our previous work (I.I. Guseinov, et al., J. Mol. Struct. (Theochem) 465 (1999) 5), the -pole electric moments have been calculated for the ground electronic states of LiH, BH and FH of the first-row diatomic hydride molecules. Calculated electric multipole moment values are in agreement with literatures. By the use of these analytical formulas the -pole moments for multiatomic molecules can be evaluated most efficiently and accurately by employing STOs as basis sets.

A variety of properties of the [formula omitted] excited state of PF computed by configuration interaction calculations

Extended basis set configuration interaction calculations on the first known excited state (a 1Δ) of PF have been performed and are presented for the first time. A variety of properties are reported including: (i) spectroscopic constants; (ii) vibrational energies and anharmonicity parameters ( ΔG v+1/2 ); (iii) rotational excitations; (iv) selected one-electron properties such as the electric multipole moments, the 17F electric nuclear quadrupole coupling, the second moments of the charge distribution, etc.; (v) vibrational electric dipole moments; (vi) cascade vibrational lifetimes. Good agreement is obtained with the restricted number of experimental data available. The accuracy of the present results is discussed and compared with that obtained for the X 3Σ − ground state and related homologous diatomics.

Accurate higher electric multipole moments for carbon monoxide

We have obtained accurate values for the higher electric multipole moments of CO. We rely on finite-field coupled cluster calculations with large gaussian-type basis sets. At the CCSD(T) level of theory the quadrupole moment varies as [ Θ( R)− Θ( R e)]/ ea 0 2=1.03( R− R e)+0.40( R− R e) 2 around the experimental bond length of R e =2.132221 a 0 . For the octopole and hexadecapole moment we find [Ω(R)−Ω(R e )]/ea 0 3=1.49(R−R e )−1.81(R−R e ) 2−0.45(R−R e ) 3−0.17(R−R e ) 4, [ Φ( R)− Φ( R e)]/ ea 0 4=−4.61( R− R e)+0.67( R− R e) 2+2.29( R− R e) 3+1.04( R− R e) 4. Our best values Ω=3.46 ea 0 3 and Φ=−9.07 ea 0 4 are in reasonable agreement with recent experimental estimates deduced from far-infrared absorption in the high-density gas spectrum of CO–Ar. Agreement is less satisfactory with values obtained from the liquid spectrum.

Miscellaneous property computations on the [formula omitted]-state of phosphorus monofluoride by configuration interaction calculations

Extended basis set configuration interaction calculations on the ground state of phosphorus monofluoride PF( X 3Σ − ) have been achieved. Several properties are reported, classified as follows: (i) spectroscopic constants; (ii) vibrational energies and related anharmonicity parameters; (iii) pure rotational excitations; (iv) selected one-electron properties such as electric multipole moments, anisotropic hyperfine parameters, 17F nuclear quadrupole coupling and others; (v) vibrational dipole moments; (vi) cascade vibrational lifetimes. Good agreement is obtained with the restricted number of experimental data available. A comparison is made between the accuracy of the present results and that of analogous diatomics for which supplementary experimental data have been reported.

Configuration interaction calculations of miscellaneous properties of the [formula omitted] excited state and related [formula omitted] transition bands of phosphorus monoxide

Extended basis set configuration interaction calculations on the excited state ( C ′ 2Δ ) and several C ′ 2Δ– X 2Π r transition bands of phosphorus monoxide have been performed. A variety of molecular properties are reported including: (i) spectroscopic constants; (ii) vibrational energies of the C ′ 2Δ -state, transition band energies of several C ′ 2Δ– X 2Π r bands and related Franck–Condon parameters; (iii) selected one-electron properties such as the electric multipole moments, 17 O nuclear quadrupole coupling, anisotropic hyperfine parameters, etc; (iv) vibrational electric dipole moments; (v) C ′ 2Δ vibrational lifetimes through cascade and via electric dipolar decays C ′ 2Δ→ X 2Π r . Good agreement is obtained with the available limited amount of experimental data. The accuracy of the present results is discussed and compared to that obtained for the X 2Π r -state and for excited states of homologous diatomics.

Calculation of three-center electric and magnetic multipole moment integrals using translation formulas for Slater-type orbitals

By the use of translation formulas for the expansion of Slater-type orbitals (STOs) in terms of STOs at a new origin, three-center electric and magnetic multipole moment integrals are expressed in terms of two-center multipole moment integrals for the evaluation of which closed analytical formulas are used. The convergence of the series is tested by calculating concrete cases. Computer results with an accuracy of 10−7 are obtained for 2ν– pole electric and magnetic multipole moment integrals for 1≤ν≤5 and for arbitrary values of screening constants of atomic orbitals and internuclear distances.

Calculation of Electric Multipole Moment Integrals Using Translation Formulas for Slater-Type Orbitals

Using translation formulas for Slater-type orbitals the infinite series through the overlap integrals are derived for the electric multipole moment integrals. By the use of the derived expressions the electric multipole moment integrals, and therefore, the electric properties of molecules can be evaluated most efficiently and accurately. The convergence of the series is tested by calculating concrete cases. An accuracy of for the computer results is obtained for , and for the arbitrary values of internuclear distances and screening constants of atomic orbitals.

Computation of molecular integrals over Slater type orbitals. II. Calculation of electric multipole moment integrals using translation formulas

Analytical expressions through the overlap integrals are derived for the electric multipole moment integrals over Slater type orbitals. These formulas can be used for the calculation of the 2 ν-pole electric moments of a molecule in the Hartree–Fock–Roothaan approximation.

Electric Current Multipole Moments in Classical Electrodynamics

The general theory for electric current multipoles appearing at the motion of magnetic dipoles and change in these values or orientation has been suggested. Static multipoles, including an anapole, have been studied in detail.

COULOMB EXCITATION AT INTERMEDIATE ENERGIES

▪ Abstract The experimental technique of intermediate-energy Coulomb excitation allows for in-beam γ-ray spectroscopy of β-unstable nuclei far from stability with low beam intensities. Measurements of excitation energies and electric multipole moments in neutron-rich nuclei in the π(sd) shell have provided experimental data that can be compared to shell-model and microscopic calculations, extending our knowledge of the evolution of nuclear shells as the nuclear driplines are approached.

Molecular dynamics simulation of polarizable ice adlayers on MgO(100)

We have performed molecular dynamics simulations at 150 and 200 K to study the structure of ice adlayers on MgO(100). An improved interaction potential based on a distribution of electric multipole moments and polarizabilities on the water molecules was used which accounted for the non-local nature of H 2O and for the self-consistent polarization of water in the presence of the substrate electric field. The monolayer geometry and the structure of the first steps of multilayering are determined, and are shown to be in good agreement with previous calculations which used the simplest potentials and electron diffraction, and with helium scattering and infrared spectroscopy experiments. The present calculations corroborate the existence of a stable, nearly planar water monolayer. The centers of mass of the H 2O molecules adopt a square arrangement commensurate with the substrate network, leading to weak hydrogen bonds between adjacent molecules. Although the layers above the monolayer appear less ordered, they display at these temperatures a geometry which looks like a distorted hexagonal ice-like ordering with strong hydrogen bonding.

Evaluation of molecular electric multipole moments using Slater-type orbitals

A general formula in terms of overlap integrals has been established for the 2 ν-pole electric moments of a molecule by the Hartree–Fock–Roothaan method involving the use of real or complex Slater-type orbitals (STOs). Using this formula we have calculated the monopole, dipole, quadrupole, and octupole moments of the ground states for a series of diatomic molecules. By the use of the derived expressions the electric multipole moment integrals, therefore, the electric properties of molecules can be evaluated most efficiently and accurately.

Supersymmetric sum rules for electromagnetic multipoles

We derive model independent, non-perturbative supersymmetric sum rules for the magnetic and electric multipole moments of any theory with N=1 supersymmetry. We find that in any irreducible N=1 supermultiplet the diagonal matrix elements of the l-multipole moments are completely fixed in terms of their off-diagonal matrix elements and the diagonal (l-1)-multipole moments.