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Journal articles on the topic 'Interaction multipolaire'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

SHIROKOV, M. I. "REGULARIZATION OF THE MULTIPOLAR FORM OF QUANTUM ELECTRODYNAMICS." International Journal of Modern Physics A 07, no. 28 (November 10, 1992): 7065–77. http://dx.doi.org/10.1142/s0217751x92003240.

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The multipolar form of quantum electrodynamics has been proposed by Power, Zienau et al. It is widely used in nonrelativistic calculations but has the deficiency: its Hamiltonian has a divergent operator term. It is shown that the divergency can be removed by a regularization of the unitary transformation which converts the Coulomb gauge into the multipolar form. The regularized multipolar form is proven to have the same ultraviolet radiative divergencies as the Coulomb gauge electrodynamics. It is also demonstrated that the interaction with soft photons is represented by the usual electric dipole term e qE and interatomic Coulomb interactions persist to be absent.

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2

Jones, T. B., R. D. Miller, K. S. Robinson, and W. Y. Fowlkes. "Multipolar interactions of dielectric spheres." Journal of Electrostatics 22, no. 3 (September 1989): 231–44. http://dx.doi.org/10.1016/0304-3886(89)90011-9.

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3

Chiu, Shuo-Feng, and Sheng Chao. "Coarse-Grained Simulations Using a Multipolar Force Field Model." Materials 11, no. 8 (July 31, 2018): 1328. http://dx.doi.org/10.3390/ma11081328.

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This paper presents a coarse-grained molecular simulation for fullerenes based on a multipolar expansion method developed previously. The method is enabled by the construction of transferable united atoms potentials that approximate the full atomistic intermolecular interactions, as obtained from ab initio electronic structure calculations supplemented by empirical force fields and experimental data, or any combination of the above. The resultant series contains controllable moment tensors that allow to estimate the errors, and approaches the all-atom intermolecular potential as the expansion order increases. We can compute the united atoms potentials very efficiently with a few interaction moment tensors, in order to implement a parallel algorithm on molecular interactions. Our simulations describe the mechanism for the condensation of fullerenes, and they produce excellent agreement with benchmark fully atomistic molecular dynamics simulations.

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4

d'Etat, B., J. Grumberg, E. Leboucher, H. Nguyen, and A. Poquérusse. "Theoretical and experimental study of complete spectral series as a diagnostic tool for dense plasmas." Laser and Particle Beams 5, no. 1 (February 1987): 155–62. http://dx.doi.org/10.1017/s0263034600002561.

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A theoretical and experimental study of line broadening and merging is presented and suggested for diagnosis of high density laser plasmas. For densities larger than 1022 cm−3 the hydrogenlike sequence is reduced to four lines for the emitter ion with ZE = 9. The perturbation effects on the latter come mainly from the interaction with plasma ions and electrons (Stark effect, multipolar interactions, ionization by tunnel effect, polarization line shift …).

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5

Kadlubanski, Pawel, Katherine Calderón-Mojica, Weyshla A. Rodriguez, D. Majumdar, Szczepan Roszak, and Jerzy Leszczynski. "Role of the Multipolar Electrostatic Interaction Energy Components in Strong and Weak Cation−π Interactions." Journal of Physical Chemistry A 117, no. 33 (August 13, 2013): 7989–8000. http://dx.doi.org/10.1021/jp404245q.

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6

Sakurai, Gen’ya, and Yoshio Kuramoto. "Multipolar interactions in the Anderson lattice." Physica B: Condensed Matter 359-361 (April 2005): 720–22. http://dx.doi.org/10.1016/j.physb.2005.01.205.

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7

Panagiotidis, E., E. Almpanis, N. Stefanou, and N. Papanikolaou. "Multipolar interactions in Si sphere metagratings." Journal of Applied Physics 128, no. 9 (September 7, 2020): 093103. http://dx.doi.org/10.1063/5.0012827.

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8

RADWAŃSKI, R. J., and J. J. M. FRANSE. "SPECIFIC HEAT OF UPd2Al3." International Journal of Modern Physics B 07, no. 01n03 (January 1993): 38–41. http://dx.doi.org/10.1142/s021797929300010x.

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Particularities in the specific heat of UPd 2 Al 3, a λ-type of peak with a maximum at 14.5 K and a Schottky-type of peak with a broad maximum at 55 K, has been attributed to the 5f-subsystem of the U atoms. The U-5f contribution has been found to be described surprisingly well within a single-ion Hamiltonian that includes the charge multipolar (CMP) interactions and the antiferromagnetic (AF) exchange interaction between the U 3+ ions. The AF exchange parameter and the full set of the CMP parameters associated with the hexagonal symmetry have been evaluated. The energy-level scheme (ELS) of this Kramers ion is constructed. The ground-state function Γ8 of the 5f 3 electrons is highly anisotropic. This state results from higher-order charge multipolar interactions. Magnetic properties resulting from this scheme including the metamagnetic-like transition at 18 T, the strongly-reduced value for the U-ion moment and its field dependence are found to be in good agreement with experimental observations.

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9

Molčanov, Krešimir, and Biserka Kojić-Prodić. "Towards understanding π-stacking interactions between non-aromatic rings." IUCrJ 6, no. 2 (February 2, 2019): 156–66. http://dx.doi.org/10.1107/s2052252519000186.

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The first systematic study of π interactions between non-aromatic rings, based on the authors' own results from an experimental X-ray charge-density analysis assisted by quantum chemical calculations, is presented. The landmark (non-aromatic) examples include quinoid rings, planar radicals and metal-chelate rings. The results can be summarized as: (i) non-aromatic planar polyenic rings can be stacked, (ii) interactions are more pronounced between systems or rings with little or no π-electron delocalization (e.g. quinones) than those involving delocalized systems (e.g. aromatics), and (iii) the main component of the interaction is electrostatic/multipolar between closed-shell rings, whereas (iv) interactions between radicals involve a significant covalent contribution (multicentric bonding). Thus, stacking covers a wide range of interactions and energies, ranging from weak dispersion to unlocalized two-electron multicentric covalent bonding (`pancake bonding'), allowing a face-to-face stacking arrangement in some chemical species (quinone anions). The predominant interaction in a particular stacked system modulates the physical properties and defines a strategy for crystal engineering of functional materials.

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10

Kumar, Prashant, Małgorzata Katarzyna Cabaj, and Paulina Maria Dominiak. "Intermolecular Interactions in Ionic Crystals of Nucleobase Chlorides—Combining Topological Analysis of Electron Densities with Energies of Electrostatic Interactions." Crystals 9, no. 12 (December 11, 2019): 668. http://dx.doi.org/10.3390/cryst9120668.

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Understanding intermolecular interactions in crystals of molecular ions continues to be difficult. On the one hand, the analysis of interactions from the point of view of formal charges of molecules, similarly as it is commonly done for inorganic ionic crystals, should be performed. On the other hand, when various functional groups are present in the crystal, it becomes natural to look at the interactions from the point of view of hydrogen bonding, π…π stacking and many other kinds of non-covalent atom–atom bonding. Often, these two approaches seem to lead to conflicting conclusions. On the basis of experimental charge densities of cytosinium chloride, adeninium chloride hemihydrate, and guanine dichloride crystals, with the help of theoretical simulations, we have deeply analysed intermolecular interactions among protonated nucleobases, chloride anions and water molecules. Here, in the second paper of the series of the two (Kumar et al., 2018, IUCrJ 5, 449–469), we focus on applying the above two approaches to the large set of dimers identified in analysed crystals. To understand electrostatic interactions, we analysed electrostatic interaction energies (Ees) computed directly from molecular charge densities and contrasted them with energies computed only from net molecular charges, or from a sum of electric multipolar moments, to find the charge penetration contribution to Ees. To characterize non-covalent interactions we performed topological analyses of crystal electron densities and estimated their interaction energies (EEML) from properties of intermolecular bond critical points. We show that the overall crystal architecture of the studied compounds is governed by the tight packing principle and strong electrostatic attractions and repulsions between ions. Many ions are oriented to each other in a way to strengthen attractive electrostatic interactions or weaken strong repulsion, but not all of them. Numerous bond critical points and bond paths were found between ions, including nucleobase cations despite their overall repulsive interactions. It is clear there is no correlation between EEML and Ees. However, strong relation between EEML and the charge penetration component of Ees is observed. The relation holds regardless of interaction types or whether or not interacting molecules bear the same or opposite charges. Thus, a charge density-based approach for computing intermolecular interaction energies and the atom–atom approach to analyse non-covalent interactions do complement each other, even in ionic systems.

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11

Boateng, H. A., and I. T. Todorov. "Arbitrary order permanent Cartesian multipolar electrostatic interactions." Journal of Chemical Physics 142, no. 3 (January 21, 2015): 034117. http://dx.doi.org/10.1063/1.4905952.

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12

Diederich, F., K. Müller, and R. Paulini. "Multipolar interactions in structural chemistry and biology." Acta Crystallographica Section A Foundations of Crystallography 61, a1 (August 23, 2005): c27. http://dx.doi.org/10.1107/s0108767305098855.

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13

Giraud, M., P. Morin, and D. Schmitt. "Multipolar interactions in cubic rare earth intermetallics." Journal of Magnetism and Magnetic Materials 52, no. 1-4 (October 1985): 41–46. http://dx.doi.org/10.1016/0304-8853(85)90224-0.

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14

Mun, Jungho, and Junsuk Rho. "Importance of higher-order multipole transitions on chiral nearfield interactions." Nanophotonics 8, no. 5 (May 17, 2019): 941–48. http://dx.doi.org/10.1515/nanoph-2019-0046.

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AbstractSurface-enhanced circular dichroism (SECD) of chiral molecules adsorbed on plasmonic nanostructures can substantially enhance chiroptical molecular signals by several orders, which is otherwise very weak to be directly measured. Several mechanisms were proposed to explain this extreme enhancement, but the exact mechanism is still controversial. We investigate strong higher-order multipole contribution to SECD near plasmonic nanostructures using the superposition T-matrix method and discuss how 3-dimensional full-field simulations implementing a homogeneous chiral medium have succeeded in the reconstruction of the extreme enhancement. We also discuss how theoretical studies modeling chiral molecules based on dipole approximation have failed to reconstruct the extreme enhancement and show that SECD enhancement of such chiral dipoles is directly governed by optical chirality enhancement. In addition, strong multipolar transitions in subwavelength chiral plasmonic nanoparticles are discussed based on the T-matrix. This work reviews theoretical frameworks describing chiral molecules, demonstrates significant contribution of a multipolar transition on the extreme SECD enhancement near plasmonic nanostructures, and emphasizes the importance of a multipolar transition in chiral nearfield interaction.

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15

González-Calderón, José Alfredo, and Fernando del Río. "A new combining rule for fluid mixtures." Collection of Czechoslovak Chemical Communications 74, no. 2 (2009): 363–91. http://dx.doi.org/10.1135/cccc2007198.

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We present evidence for the regular behaviour of the Boyle temperature TB in gaseous binary mixtures of small molecules with negligible multipolar moments. We use this regularity to construct a new combining rule for the prediction of the cross interaction u12(r) in those mixtures. The combining rule gives TB of the cross interaction as the harmonic mean of the Boyle temperatures of the pure components. The validity of this harmonic rule is based on experimental data of 28 binary mixtures, whose TB have been obtained from experimental data of the cross virial coefficient B12(T). In determining TB we make use of non-conformal potentials that have been proven to represent very accurately the effective interactions of the molecules investigated. The new combining rule is used to give interaction parameters of several dozens of binary mixtures involving noble gases (Ne, Ar, Kr and Xe), diatomic molecules (N2, O2 and CO) and n-alkanes (from methane to n-octane). These interaction parameters lead to a prediction of cross virial coefficients B12(T) within experimental error. Electrostatic interactions, originating in permanent dipolar, quadrupolar, octupolar and hexadecapolar moments and exemplified by molecules of HCl, CO2, CF4 and SF6, depart from the regular non-polar behaviour.

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16

Noheda, Beatriz, Marceli Koralewski, Ginés Lifante, and Julio A. Gonzalo. "Dielectric discontinuities and multipolar interactions in ferroelectric perovskites." Ferroelectrics Letters Section 17, no. 1-2 (February 1994): 25–31. http://dx.doi.org/10.1080/07315179408203369.

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17

Ikeda, S., K. Umeo, H. Tou, M. Sera, F. Iga, and S. Kunii. "Unusual pressure dependence of the multipolar interactions in." Journal of Magnetism and Magnetic Materials 310, no. 2 (March 2007): e163-e165. http://dx.doi.org/10.1016/j.jmmm.2006.10.120.

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18

Pustovit, Vitaly N., Juan A. Sotelo, and Gunnar A. Niklasson. "Coupled multipolar interactions in small-particle metallic clusters." Journal of the Optical Society of America A 19, no. 3 (March 1, 2002): 513. http://dx.doi.org/10.1364/josaa.19.000513.

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19

Paulini, Ralph, Klaus Müller, and François Diederich. "Orthogonal Multipolar Interactions in Structural Chemistry and Biology." Angewandte Chemie International Edition 44, no. 12 (February 11, 2005): 1788–805. http://dx.doi.org/10.1002/anie.200462213.

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20

Luding, S., H. Schn�rer, V. Kuzovkov, and A. Blutnen. "Bimolecular annihilation reactions: Immobile reactants and multipolar interactions." Journal of Statistical Physics 65, no. 5-6 (December 1991): 1261–67. http://dx.doi.org/10.1007/bf01049611.

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21

Fazleev, N. G. "Multipolar interactions in rare-earth metals and alloys." Journal of Magnetism and Magnetic Materials 104-107 (February 1992): 1525–26. http://dx.doi.org/10.1016/0304-8853(92)91438-y.

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22

Hosoi, Masashi, Tomonari Mizoguchi, Taichi Hinokihara, Hiroyasu Matsuura, and Masao Ogata. "Dzyaloshinskii–Moriya Interaction between Multipolar Moments in 5d1 Systems." Journal of the Physical Society of Japan 89, no. 7 (July 15, 2020): 074702. http://dx.doi.org/10.7566/jpsj.89.074702.

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23

Steffen, W., N. Koning, A. Esquivel, G. García-Segura, Ma T. García-Díaz, J. A. López, and M. Magnor. "A wind–shell interaction model for multipolar planetary nebulae." Monthly Notices of the Royal Astronomical Society 436, no. 1 (September 25, 2013): 470–78. http://dx.doi.org/10.1093/mnras/stt1583.

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24

Francisco, Evelio, Daniel Menéndez Crespo, Aurora Costales, and Ángel Martín Pendás. "A multipolar approach to the interatomic covalent interaction energy." Journal of Computational Chemistry 38, no. 11 (February 16, 2017): 816–29. http://dx.doi.org/10.1002/jcc.24758.

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25

Perdana, Nanda, Carsten Rockstuhl, and Alexander A. Iskandar. "Induced higher order multipolar resonances from interacting scatterers." Journal of the Optical Society of America B 38, no. 1 (December 18, 2020): 241. http://dx.doi.org/10.1364/josab.410860.

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26

Ido, K., A. Tobo, K. Ohoyama, H. Onodera, and Y. Yamaguchi. "Magnetic ordering affected by multipolar interactions in Ho1 xTbxB2C2." Journal of Physics: Condensed Matter 15, no. 28 (July 4, 2003): S2193—S2196. http://dx.doi.org/10.1088/0953-8984/15/28/350.

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27

Tronci, Cesare. "Hybrid models for perfect complex fluids with multipolar interactions." Journal of Geometric Mechanics 4, no. 3 (2012): 333–63. http://dx.doi.org/10.3934/jgm.2012.4.333.

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28

Sakurai, Gen'ya, and Yoshio Kuramoto. "Multipolar Interactions in the Anderson Lattice with Orbital Degeneracy." Journal of the Physical Society of Japan 73, no. 1 (January 15, 2004): 225–38. http://dx.doi.org/10.1143/jpsj.73.225.

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29

Sakurai, Gen'ya, and Yoshio Kuramoto. "Wavenumber Dependence of Multipolar Interactions in the Anderson Lattice." Journal of the Physical Society of Japan 74, no. 3 (March 2005): 975–82. http://dx.doi.org/10.1143/jpsj.74.975.

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30

Koga, Toshikatsu, and Mitsuru Uji-ie. "Some accurate nonadditive multipolar interaction constants for three hydrogen atoms." Physical Review A 39, no. 8 (April 1, 1989): 4272–73. http://dx.doi.org/10.1103/physreva.39.4272.

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31

Xing, Li, Christopher Keefer, and Matthew F. Brown. "Fluorine multipolar interaction: Toward elucidating its energetics in binding recognition." Journal of Fluorine Chemistry 198 (June 2017): 47–53. http://dx.doi.org/10.1016/j.jfluchem.2016.12.013.

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32

Bae, Jinhye, Nakul P. Bende, Arthur A. Evans, Jun-Hee Na, Christian D. Santangelo, and Ryan C. Hayward. "Programmable and reversible assembly of soft capillary multipoles." Materials Horizons 4, no. 2 (2017): 228–35. http://dx.doi.org/10.1039/c6mh00531d.

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33

Liu, Tianji, Rongyang Xu, Peng Yu, Zhiming Wang, and Junichi Takahara. "Multipole and multimode engineering in Mie resonance-based metastructures." Nanophotonics 9, no. 5 (March 19, 2020): 1115–37. http://dx.doi.org/10.1515/nanoph-2019-0505.

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AbstractBenefited from the well-known Mie resonance, a plethora of physical phenomena and applications are attracting attention in current research on dielectric-based nanophotonics. High-index dielectric metastructures are favorable to enhance light-matter interaction in nanoscale with advantages such as low loss, optical magnetism, and multipolar responses, which are superior to their plasmonic counterpart. In this review, we highlight the important role played by Mie resonance-based multipolar and multimodal interaction in nanophotonics, introducing the concept of “multipole and multimode engineering” in artificially engineered dielectric-based metastructures and providing an overview of the recent progress of this fast-developing area. The scope of multipole and multimode engineering is restricted not only in multipolar interferences of meta-atom and meta-molecule but also in the nontrivial intermodal coupling (Fano resonance and bound states in the continuum), in the collective mode and the surface lattice mode appearing via periodic meta-lattices and aperiodic meta-assembly, in chiral enhancement via chiral and achiral dielectric metastructures, and in Mie resonance-mediated hybrid structures (Mie-plasmon and Mie-exciton). Detailed examples and the underlying physics of this area are discussed in-depth, in order to lead the multifunctional metastructures for novel applications in the future.

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34

Smith, G. B., and V. N. Pustovit. "Coupled multipolar interactions in clusters of nanoparticles with metal shells." Optics Communications 211, no. 1-6 (October 2002): 197–204. http://dx.doi.org/10.1016/s0030-4018(02)01902-8.

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35

Claro, F., and F. Brouers. "Dielectric anomaly of porous media: The role of multipolar interactions." Physical Review B 40, no. 5 (August 15, 1989): 3261–65. http://dx.doi.org/10.1103/physrevb.40.3261.

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36

Fazleev, N. G., and J. L. Fry. "Indirect multipolar interactions in rare‐earth metals and alloys (abstract)." Journal of Applied Physics 73, no. 10 (May 15, 1993): 5748. http://dx.doi.org/10.1063/1.353559.

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37

George, Shefin S., Mohit N. Shivdasani, Andrew K. Wise, Robert K. Shepherd, and James B. Fallon. "Electrophysiological channel interactions using focused multipolar stimulation for cochlear implants." Journal of Neural Engineering 12, no. 6 (September 24, 2015): 066005. http://dx.doi.org/10.1088/1741-2560/12/6/066005.

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38

Santini, Paolo, Stefano Carretta, Giuseppe Amoretti, Roberto Caciuffo, Nicola Magnani, and Gerard H. Lander. "Multipolar interactions inf-electron systems: The paradigm of actinide dioxides." Reviews of Modern Physics 81, no. 2 (June 2, 2009): 807–63. http://dx.doi.org/10.1103/revmodphys.81.807.

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39

Sera, Masafumi, Fumitoshi Iga, Shinichiro Kobayashi, Hiroki Sugamoto, Kenji Nagatomo, Kazunori Umeo, Shigenori Tsuji, Kenichi Kojima, Jun Akimitsu, and Yuji Zenitani. "Ce Site Substitution Effects on the Multipolar Interactions in CeB6." Journal of the Physical Society of Japan 71, Suppl (January 2002): 52–55. http://dx.doi.org/10.1143/jpsjs.71s.52.

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40

Yoshino, Yasuhiro, Shinichiro Kobayashi, Shigenari Tsuji, Hideki Tou, Masafumi Sera, Fumitoshi Iga, Yuji Zenitani, and Jun Akimitsu. "Nd Ion Doping Effects on the Multipolar Interactions in CeB6." Journal of the Physical Society of Japan 73, no. 1 (January 15, 2004): 29–32. http://dx.doi.org/10.1143/jpsj.73.29.

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41

Kusunose, Hiroaki, and Yoshio Kuramoto. "Non-Collinear Magnetism due to Orbital Degeneracy and Multipolar Interactions." Journal of the Physical Society of Japan 70, no. 6 (June 15, 2001): 1751–61. http://dx.doi.org/10.1143/jpsj.70.1751.

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42

Xiao-Feng, Zhou, and Gao Lei. "Effect of multipolar interaction on the effective thermal conductivity of nanofluids." Chinese Physics 16, no. 7 (July 2007): 2028–32. http://dx.doi.org/10.1088/1009-1963/16/7/037.

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43

DeCrescent, Ryan A., Naveen R. Venkatesan, Clayton J. Dahlman, Rhys M. Kennard, Xie Zhang, Wenhao Li, Xinhong Du, Michael L. Chabinyc, Rashid Zia, and Jon A. Schuller. "Bright magnetic dipole radiation from two-dimensional lead-halide perovskites." Science Advances 6, no. 6 (February 2020): eaay4900. http://dx.doi.org/10.1126/sciadv.aay4900.

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Light-matter interactions in semiconductors are uniformly treated within the electric dipole approximation; multipolar interactions are considered “forbidden.” We experimentally demonstrate that this approximation inadequately describes light emission in two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs), solution processable semiconductors with promising optoelectronic properties. By exploiting the highly oriented crystal structure, we use energy-momentum spectroscopies to demonstrate that an exciton-like sideband in 2D HOIPs exhibits a multipolar radiation pattern with highly directed emission. Electromagnetic and quantum-mechanical analyses indicate that this emission originates from an out-of-plane magnetic dipole transition arising from the 2D character of electronic states. Symmetry arguments and temperature-dependent measurements suggest a dynamic symmetry-breaking mechanism that is active over a broad temperature range. These results challenge the paradigm of electric dipole–dominated light-matter interactions in optoelectronic materials, provide new perspectives on the origins of unexpected sideband emission in HOIPs, and tease the possibility of metamaterial-like scattering phenomena at the quantum-mechanical level.

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44

Domagała, Sławomir, Parthapratim Munshi, Maqsood Ahmed, Benoît Guillot, and Christian Jelsch. "Structural analysis and multipole modelling of quercetin monohydrate – a quantitative and comparative study." Acta Crystallographica Section B Structural Science 67, no. 1 (December 18, 2010): 63–78. http://dx.doi.org/10.1107/s0108768110041996.

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The multipolar atom model, constructed by transferring the charge-density parameters from an experimental or theoretical database, is considered to be an easy replacement of the widely used independent atom model. The present study on a new crystal structure of quercetin monohydrate [2-(3,4-dihydroxyphenyl)-3,5,7-trihydroxy-4H-chromen-4-one monohydrate], a plant flavonoid, determined by X-ray diffraction, demonstrates that the transferred multipolar atom model approach greatly improves several factors: the accuracy of atomic positions and the magnitudes of atomic displacement parameters, the residual electron densities and the crystallographic figures of merit. The charge-density features, topological analysis and electrostatic interaction energies obtained from the multipole models based on experimental database transfer and periodic quantum mechanical calculations are found to compare well. This quantitative and comparative study shows that in the absence of high-resolution diffraction data, the database transfer approach can be applied to the multipolar electron density features very accurately.

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45

Im, Won Bin, Yong-Il Kim, Jong Hyuk Kang, Duk Young Jeon, Ha Kyun Jung, and Kyeong Youl Jung. "Neutron Rietveld Analysis for Optimized CaMgSi2O6:Eu2+ and its Luminescent Properties." Journal of Materials Research 20, no. 8 (August 1, 2005): 2061–66. http://dx.doi.org/10.1557/jmr.2005.0253.

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We optimized synthesis conditions of blue-emitting CaMgSi2O6:Eu2+ (CMS:Eu2+) with conventional solid-state reaction and successfully determined structure parameters by Rietveld refinement method with neutron powder diffraction data. The final weighted R-factor Rwp was 6.42% and the goodness-of-fit indicator S (= Rwp/Re) was 1.34. The refined lattice parameters of CMS:Eu2+ were a = 9.7472(3) Å, b = 8.9394(2) Å, and c = 5.2484(1) Å. The β angle was 105.87(1)°. The concentration quenching process was observed, and the critical quenching concentration of Eu2+ in CMS:Eu2+ was about 0.01 mol and critical transfer distance was calculated as 12 Å. With the help of the Rietveld refinement and Dexter theory, the critical transfer distance was also calculated as 27 Å. In addition, the dominant multipolar interaction of CMS:Eu2+ was investigated from the relationship between the emission intensity per activator concentration and activator concentration. The dipole–dipole interaction was a dominant energy transfer mechanism of electric multipolar character of CMS:Eu2+.

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46

Stewart, A. M. "General Gauge Independence of Diamagnetism plus Paramagnetism." Australian Journal of Physics 53, no. 4 (2000): 613. http://dx.doi.org/10.1071/ph99098.

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With the use of the generalised multipolar gauge, a completely general proof is obtained for a result asserted by J. H. Van Vleck in 1932 but never fully proved by him. Specifically it is demonstrated that the matrix elements of the magnetic moment operator are independent of the origin of the vector potential for electromagnetic fields that are non-uniform in space and non-constant in time. A general survey of the principles of the quantum mechanics of solid state and molecular magnetism is also given to set the problem in its context. Based on the multipolar gauge, a simple conversion of the interaction Hamiltonian from the form of A.p to E.r plus higher order terms is demonstrated.

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47

Avsec, Jurij, and Milan Marcic. "Influence of Multipolar and Induction Interactions on the Speed of Sound." Journal of Thermophysics and Heat Transfer 14, no. 4 (October 2000): 496–503. http://dx.doi.org/10.2514/2.6572.

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48

Stevenson, Peter R., Matthew Du, Charles Cherqui, Marc R. Bourgeois, Kate Rodriguez, Jacob R. Neff, Endora Abreu, et al. "Active Plasmonics and Active Chiral Plasmonics through Orientation-Dependent Multipolar Interactions." ACS Nano 14, no. 9 (July 30, 2020): 11518–32. http://dx.doi.org/10.1021/acsnano.0c03971.

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49

Aubert, Emmanuel, Florence Porcher, Mohamed Souhassou, and Claude Lecomte. "Characterization of intra-framework and guest/host interactions in the AlPO4-15 molecular sieve by charge-density analysis." Acta Crystallographica Section B Structural Science 59, no. 6 (November 25, 2003): 687–700. http://dx.doi.org/10.1107/s0108768103017075.

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Abstract:

The electron-density distribution of AlPO4-15 has been determined using high-resolution single-crystal X-ray diffraction, and the topological properties of the charge density have been calculated using the `atoms in molecules' (AIM) theory. Analysis of the topological properties at the bond critical points has been used to characterize the interactions within the framework, and between the framework and the extra-framework species (ammonium ions and water molecules), and to define atomic properties, such as volume and net charges, uniquely. A comparison between procrystal and multipolar representations of the density was performed in order to explore to what extent the former representation is likely to reflect the interactions in the solid. Correlation with geometrical properties (P—O and Al—O bond lengths, and Al—O—P angle) is found for topological charges obtained from the multipolar model, but not for the results from the procrystal representation.

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50

Guillot, Régis, Nicolas Muzet, Slimane Dahaoui, Claude Lecomte, and Christian Jelsch. "Experimental and theoretical charge density of DL-alanyl-methionine." Acta Crystallographica Section B Structural Science 57, no. 4 (July 24, 2001): 567–78. http://dx.doi.org/10.1107/s0108768101007212.

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Abstract:

X-ray diffraction data up to d = 0.50 Å resolution have been collected at 100 K for a DL-alanyl-methionine single crystal using a CCD area detector. Multipolar crystallographic refinement was carried out and the electron density of the molecule has been analyzed. The deformation electron density around the S atom reveals two lone pairs with an sp 3 hybridization and agrees with the results of density functional theory calculations. The topological properties of the covalent bonds and of the hydrogen bonds have been investigated. Two weak polar intramolecular interactions of the type C5 (pentagonal cyclic structure) have unfavorable geometrical parameters for hydrogen bonds and are devoid of critical points. The two electron lone pairs of the carbonyl oxygen appear asymmetric in the experimental deformation density. This could be attributed to the different strength of the hydrogen bond and intramolecular polar interaction involving the carbonyl oxygen. In the ab-initio-derived deformation maps, the asymmetry of the electron doublets is reproduced only very partially.

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