Electric Multipole Polarizabilities Research Articles

Accurate calculation of multipole polarizabilities for one-electron atom in Debye plasmas

The electric multipole polarizabilities of one-electron atoms embedded in weakly coupled Debye plasmas are calculated in the non-relativistic framework. The static dipole, quadrupole, octopole, and hexadecapole polarizabilities for hydrogen atoms in both ground and excited states at a variety of Debye screening parameters are calculated in high precision based on the sum-over-states method, where the system bound and continuum states are produced by employing the generalized pseudospectral method. It is shown that the contribution of bound states to the polarizability decreases with increasing the plasma screening strength, whereas the contribution of continuum states is enhanced. At very small screening parameters where the plasma environment starts to take effect, it is found that the 2l-pole polarizability for s-wave states with principle quantum number n≥l+1 has an abrupt change from its non-screening value to infinity. We attribute such a phenomenon to the sudden non-degeneracy of different angular momentum states in the n shell. With continuously increasing the screening strength, the polarizabilities for n≥l+1 states decrease to certain values and, eventually, they approach to infinity at the critical screening parameter. For states with n≤l, the 2l-pole polarizabilities show regular enhancement from the non-screening value to infinity. The present results are compared with other theoretical calculations available in the literature and it is shown that our work has established by now the most accurate predictions of multipole oscillator strengths and polarizabilities for one-electron atoms in Debye plasmas.

Ab initio calculations of electric multipole moments, (higher) polarizabilities and first hyperpolarizabilitiy of (H2S)n, n = 1 – 4

In this work, the electric multipole moments μα,Θαβ,Ωαβγ,Φαβγδ and the polarizabilities ααβ,Aα,βγ,Eα,βγδ,Cαβ,γδ and the first hyperpolarizability βαβγ for H2S have been calculated at the MP2, CCSD and CCSD(T)/aug-cc-pVXZ (X = T, Q, 5) levels of theory. The multipole moments were extrapolated to the CBS limit. In addition, the electric properties of H2S and H2S dimer were computed using density functional theory. Some new stable configurations of complexes (H2S)n = 2–4 have been found. New insight has been obtained on the features of the vibrational spectra of considered complexes, and anisotropic and isotropic properties of Raman scattering of H2S dimer.

Analytical transition-matrix treatment of electric multipole polarizabilities of hydrogen-like atoms

The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the case of the bound system formed by the Coulomb interaction the corresponding inhomogeneous integral equation determining an off-shell scattering function, which consistently describes virtual multiple scattering, can be solved exactly analytically for all electric multipole polarizabilities. Our method allows to reproduce the known Dalgarno–Lewis formula for electric multipole polarizabilities of the hydrogen atom in the ground state and can also be applied to determine the polarizability of the atom in excited bound states.

Properties of alkali-metal atoms and alkaline-earth-metal ions for an accurate estimate of their long-range interactions

Accurate knowledge of interaction potentials among the alkali-metal atoms and alkaline-earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali-metal atoms with the ${\mathrm{Ca}}^{+}$, ${\mathrm{Ba}}^{+}$, ${\mathrm{Sr}}^{+}$, and ${\mathrm{Ra}}^{+}$ alkaline-earth ions systematically, which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation $R$. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above-mentioned systems, which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random-phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representations of the dispersion coefficients versus $R$ are given among all the alkaline ions with Rb.

Dispersion potential between three-bodies with arbitrary electric multipole polarizabilities: molecular QED theory.

Molecular quantum electrodynamics is used to obtain an expression for the retarded dispersion energy shift between three arbitrarily electrically polarizable atoms or molecules. A generalized Craig-Power Hamiltonian that depends quadratically on the electric displacement field is employed together with third-order diagrammatic perturbation theory. This approach simplifies the calculation relative to the use of the usual multipolar coupling Hamiltonian that is linear in the displacement field. Specific higher multipole non-additive contributions are then extracted. These include dipole-dipole-quadrupole, dipole-quadrupole-quadrupole, and dipole-dipole-octupole potentials valid for oriented and isotropic species with arbitrary separation distances between particles, extending recent work in which these energy shifts were given for equilateral triangle and collinear geometries. Near-zone limiting forms are found to agree with earlier works in which static inter-particle couplings were used.

DEUTERON ELECTRIC QUADRUPOLE AND OCTUPOLE POLARIZABILITIES

The direct transition-matrix approach to determination of the electric polarizabilities of quantum bound systems developed in my preceding work is applied to study the electric multipole polarizabilities of a two-particle bound complex with a central interaction between the particles. Expressions for the electric quadrupole and octupole polarizabilities of the deuteron are derived and their values in the case of the S-wave separable interaction potential are calculated.

Electric Multipole Polarizabilities of Quantum Bound Systems in the Transition Matrix Formalism

A new general formalism for determining the electric multipole polarizabilities of quantum (atomic and nuclear) bound systems based on the use of the transition matrix in momentum space has been developed. As distinct from the conventional approach with the application of the spectral expansion of the total Green’s function, our approach does not require preliminary determination of the entire unperturbated spectrum; instead, it makes possible to calculate the polarizability of a few-body bound complex directly based on solving integral equations for the wave function of the ground bound state and the transition matrix at negative energy, both of them being real functions of momenta. A formula for the multipole polarizabilities of a two-body bound complex formed by a central interaction potential has been derived and studied. To test, the developed t-matrix formalism has been applied to the calculation of the dipole, quadrupole and octupole polarizabilities of the hydrogen atom.

Casimir potential of a compact object enclosed by a spherical cavity

We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects' scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the enclosing object is an otherwise empty metallic spherical shell, much larger than the internal object, and the two are sufficiently separated, the Casimir force can be expressed in terms of the static electric and magnetic multipole polarizabilities of the internal object, which is analogous to the Casimir-Polder result. Although it is not a simple power law, the dependence of the force on the separation of the object from the containing sphere is a universal function of its displacement from the center of the sphere, independent of other details of the object's electromagnetic response. Furthermore, we compute the exact Casimir force between two metallic spheres contained one inside the other at arbitrary separations. Finally, we combine our results with earlier work on the Casimir force between two spheres to obtain data on the leading order correction to the Proximity Force Approximation for two metallic spheres both outside and within one another.

Multipolar Ordering in Electro‐ and Magnetostatic Coupled Nanosystems

Electric and magnetic multipole moments and polarizabilities are important quantities in studies of intermolecular forces, non-linear optical phenomena, electrostatic, magnetostatic or gravitational potentials and electron scattering. The experimental determination of multipole moments is difficult and therefore the theoretical prediction of these quantities is important. Depending on purposes of the investigation several different definitions of multipole moments and multipole-multipole interactions are used in the literature. Because of this variety of methods it is often difficult to use published results and, therefore, even more new definitions appear. The first goal of this review is to give an overview of mathematical definitions of multipole expansion and relations between different formulations. The second aim is to present a general theoretical description of multipolar ordering on periodic two-dimensional lattices. After a historical introduction in the first part of this manuscript the static multipole expansion in cartesian and spherical coordinates as well as existing coordinate transformations are reviewed. On the basis of the presented mathematical description multipole moments of several symmetric charge distributions are summarized. Next, the established numerical approach for the calculation of multipolar ground states, namely Monte Carlo simulations, are reviewed. Special emphasis is put on the review of ground states in multipolar systems consisting of moments of odd or even order. The last section is devoted to the magnetization reversal in dense packed nanomagnetic arrays, where the magnetic multipole-multipole interactions play an important role. Comparison between the theory and recent experimental results is given.

A general formula obtained from induced moments for the retarded van der Waals dispersion energy shift between two molecules with arbitrary electric multipole polarizabilities: I. Ground state interactions

An expression for the dispersion energy shift arising from the interaction of two ground state polarizable molecules of arbitrary electric multipole moment order is obtained. The physical viewpoint adopted is one in which an electric polarizable body subject to vacuum fluctuations associated with an electric displacement field gives rise to an induced multipole moment. The moments induced at each centre couple to the retarded electric multipole–multipole resonant interaction tensor, resulting in a direct evaluation of the generalized formula for the dispersion potential between the pair. The present approach is compared and contrasted to a previous derivation of the interaction energy which required the Casimir–Polder potential as its starting point and employed fourth-order time-dependent perturbation theory. Although the functional forms obtained for the generalized energy shift differ in the two methods, identical expressions result for specific contributions to the dispersion potential. This is shown explicitly for the first few lowest order cases, comprising molecules possessing electric dipole, quadrupole and octupole polarizability characteristics. In this paper, the present approach is used to calculate energy shifts between an excited and an unexcited molecule.

A general formula obtained from induced moments for the retarded van der Waals dispersion energy shift between two molecules with arbitrary electric multipole polarizabilities: II. Excited state interactions

The method of induced multipole moments used in the preceding paper to calculate a generalized expression for the ground state dispersion energy between a pair of arbitrarily electrically polarizable molecules is extended to deal with the case in which one of the species is excited. As an application, the resonant contribution to the energy shift is computed explicitly for electric dipole, quadrupole and octupole polarizable systems and compared, where possible, with previous response theory calculations.

Ab initio determination of the electric multipole moments and static (hyper)polarizability of HCCX, X = F, Cl, Br, and I.

We report electric multipole moments and (hyper)polarizabilities for the haloethynes HCCX, X = F, Cl, Br, and I. The molecular properties have been obtained from finite-field self-consistent field, Møller-Plesset perturbation theory and coupled cluster calculations with large, carefully optimized basis sets of gaussian-type functions. The mean dipole (hyper)polarizability and the mean quadrupole polarizability near the Hartree-Fock limit are alpha/e(2)a(0) (2)E(h) (-1) = 23.74 (HCCF), 37.26 (HCCCl), 43.97 (HCCBr), 56.44 (HCCI), beta/e(3)a(0) (3)E(h) (-2) = -73.9 (HCCF), -67.0 (HCCCl), -39.5 (HCCBr), 42.7 (HCCI), gamma/e(4)a(0) (4)E(h) (-3) = 4,914 (HCCF), 6,554 (HCCCl), 9,328 (HCCBr), 14,949 (HCCI), and C/e(2)a(0) (4)E(h) (-1) = 160.3 (HCCF), 317.1 (HCCCl), 471.2 (HCCBr), 671.2 (HCCI). Electron correlation has a small effect on the dipole polarizability but affects strongly the hyperpolarizability. Agreement with the available experimental data is more or less fair for HCCF, HCCCl, and HCCBr but less satisfactory for HCCI.

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.

On the electric properties of Br2

Electric multipole moments and polarizabilities for Br2 are obtained from finite field self consistent field (SCF), many-body perturbation theory and coupled cluster calculations with large gaussian-type basis sets. At the MP2 level of theory the bond length dependence of the mean and the anisotropy of the dipole polarizability (ααβ/e 2 a 0 2 E h -1) around the equilibrium bond length of Re = 2·28105 A is adequately described by , . A very large \\[18s15p12d6f] basis set consisting of 330 basis functions yields SCF values α = 44·10 and Δ α = 28·31 e 2 a 0 2 E h -1. Adding electron correlation corrections obtained at the CCSD(T) level of theory and vibrational corrections obtained at the MP2 level, the mean dipole polarizability at the ground vibrational state is estimated at α = 44·74 (to be compared with the experimental value of 45·0) and the anisotropy at Δ α = 25·39 e 2 a 0 2 E h -1. At the MP2 level the mean second dipole hyperpolarizability γ/ e 4 a 0 4 E h -1 varies around R e as . SCF, MP2 and CCSD(T) results are combined to give as final theroeticalprediction the estimate of γ = (10·2 ± 1·0) x 103 e 4 a 0 4 E h -3.

A new generalization of the Casimir–Polder potential to higher electric multipole polarizabilities

An elementary method for calculating retarded interaction energies for a pair of molecules with electric multipole polarizabilities of arbitrary order is presented. In the multipolar framework of quantum electrodynamics, the interaction energy is viewed as arising from two-photon exchange and calculated using fourth order perturbation theory. It is shown how the energy may be expressed in terms of derivatives of the Casimir–Polder formula written in a special form as an integral over imaginary frequency. Explicit formulas are presented for (a) an electric dipole polarizable molecule interacting with an electric quadrupole polarizable molecule, (b) an electric dipole polarizable molecule interacting with an electric octupole polarizable molecule, and (c) an electric quadrupole polarizable molecule interacting with another electric quadrupole polarizable molecule. The results are expressed in terms of reducible and irreducible components of multipole moments. For case (b) it is shown that in addition to the weight-3 components of the octupole moments, weight-1 components contribute to the interaction energy. For cases (a) and (c) traceless components (weight-2) of the quadrupole moments contribute. The results are compared with other calculations and discrepancies pointed out.

Fundamental relationships in the theory of electric multipole moments and multipole polarizabilities in static fields (Chemical Physics 85 (1984) 279–290)

Fundamental relationships in the theory of electric multipole moments and multipole polarizabilities in static fields (Chemical Physics 85 (1984) 279–290)

Electric moments, polarizabilities and hyperpolarizabilities for carbon disulfide (SCS) from accurate SCF calculations

Electric multipole moments, polarizabilities and hyperpolarizabilities for carbon disulfide (SCS) were calculated from accurate SCF wavefunctions. The best values obtained for the quadrupole and hexadecapole moment are Θ zz =2.4254 e a 2 0 and Φ zzzz =140.12 e a 4 0, respectively. For the longitudinal and transversal component of the dipole polarizability, α zz =93.14 and α xx =36.58 e 2 a 2 0 E − h. For the mean values of the quadrupole polarizability ( C αβ,γδ), the dipole hyperpolarizability (γ αβγδ) and the quadrupole hyperpolarizability ( B αβ,γδ), C̄=412 e 2 a 4 0 E − 1 h, ▪ = 10520 e 4 a 4 0 E −3 h and B̄=−1580 e 3 a 4 0 E −2 h, respectively. For the dipole—octopole polarizability, E z, zzz =1026.7 and E x, xxx =−398.1 e 2 a 4 0 E −1 h.

Dynamic toroid polarizability of atomic hydrogen

The concept of toroid polarizability introduced in previous work is examined within the familiar context of nonrelativistic quantum Coulomb systems, in a way unbiased by approximations. The dynamic (i.e., frequency (ω) dependent) toroid dipole polarizability γ(ω) of a (nonrelativistic, spinless, ground-state) hydrogenlike atom is calculated analytically in terms of (essentially) one Gauss hypergeometric function. The static result takes on the simple form γ(ω = 0) = 23 60 α 2Z −4a 0 5 (α = fine structure constant, Z = nucleus charge number, a 0 = Bohr radius). γ(ω) characterizes the linear response of the system to a conduction and/or displacement (time dependent) external current. The method of calculation (based on the use of the integral representation for the nonrelativistic Coulomb Green's function) is presented in detail. The imaginary part of γ(ω) above ionization threshold is also computed in a simple closed form. Comparing γ(ω = 0) with the already known (exact) results for the electric multipole polarizabilities (for which, as a byproduct, we present in an Appendix a considerably simplified expression, to our knowledge the simplest reported as yet), one sees that although for H-like atoms the toroid effects appear as very small indeed, they are however increasing with Z. A comparison with analogous (but, this time, only order of magnitude) evaluations for (charged) pions, indicates that the role of the induced toroid moments (as against that of the usual electric ones) increases drastically when passing from atomic to hadron physics; it is argued that this trend might continue further, at the sub-hadronic level.

Dynamic toroid polarizability of atomic hydrogen: A. Costescu. Department of Physics, University of Bucharest, P.O. Box Mg-11, Bucharest, Romania; and E. E. Radescu. International Center for Theoretical Physics, Trieste, Italy, and Institute of Atomic Physics, P.O. Box Mg-6, Bucharest, Romania

Abstract The concept of toroid polarizability introduced in previous work is examined within the familiar context of nonrelativistic quantum Coulomb systems, in a way unbiased by approximations. The dynamic (i.e., frequency (ω) dependent) toroid dipole polarizability γ(ω) of a (nonrelativistic, spinless, ground-state) hydrogenlike atom is calculated analytically in terms of (essentially) one Gauss hypergeometric function. The static result takes on the simple form γ(ω = 0) = 23 60 α 2 Z −4 a 0 5 (α = fine structure constant, Z = nucleus charge number, a0 = Bohr radius). γ(ω) characterizes the linear response of the system to a conduction and/or displacement (time dependent) external current. The method of calculation (based on the use of the integral representation for the nonrelativistic Coulomb Green's function) is presented in detail. The imaginary part of γ(ω) above ionization threshold is also computed in a simple closed form. Comparing γ(ω = 0) with the already known (exact) results for the electric multipole polarizabilities (for which, as a byproduct, we present in an Appendix a considerably simplified expression, to our knowledge the simplest reported as yet), one sees that although for H-like atoms the toroid effects appear as very small indeed, they are however increasing with Z. A comparison with analogous (but, this time, only order of magnitude) evaluations for (charged) pions, indicates that the role of the induced toroid moments (as against that of the usual electric ones) increases drastically when passing from atomic to hadron physics; it is argued that this trend might continue further, at the sub-hadronic level.

Fundamental relationships in the theory of electric multipole moments and multipole polarizabilities in static fields

Abstract New derivations are given of equations relating molecular electric multipole moments and polarizabilities of general order to the electrostatic energy. The unabridged moment convention is shown to yield relatively simple relations between derivatives of the energy with respect to field gradients and the multipole moments and polarizabilities. Care is taken to distinguish various forms of these derivatives, and one form leads to a proof of a general symmetry of polarizability tensors with respect to permutations of rank indices. The condition of internal equilibrium is shown to be fundamental to the existence of this symmetry. The transformation of multipole moment and polarizability tensors under translation of the coordinate origin is expressed in relatively simple general form. The traceless multipole and polarizability tensors of Buckingham and McLean and Yoshimine are obtained as linear combinations of the unabridged tensors and their traces.