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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 45, 1982 - Issue 2
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Original Articles

Cartesian expressions for electric multipole moment operators

Joseph Cipriani Laboratoire de Spectrochimie Moléculaire Université Pierre et Marie Curie, 4 Place Jussieu-F-75005, Paris, France
&
Bernard Silvi Laboratoire de Spectrochimie Moléculaire Université Pierre et Marie Curie, 4 Place Jussieu-F-75005, Paris, FranceView further author information
Pages 259-272 | Received 29 Sep 1980, Accepted 18 Sep 1981, Published online: 23 Aug 2006

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J. Niitsuma. (2013) Generalized integral formulation of electromagnetic Cartesian multipole moments. Journal of Electromagnetic Waves and Applications 27:12, pages 1525-1533.
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A. Lakhlifi. (1993) Analysis of the interaction potential of a molecule physisorbed on NaCl(100) surface. Molecular Physics 78:3, pages 659-672.
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Bernard Silvi & Najib Fourati. (1984) Coupled Hartree-Fock method for the calculation of Cauchy moments for atomic and molecular dynamic polarizabilities. Molecular Physics 52:2, pages 415-430.
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B. Silvi & V. Chandrasekharan. (1983) Dispersion coefficients for atoms in different states. Molecular Physics 48:5, pages 1053-1066.
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Articles from other publishers (35)

Nils W. Schween & Brian Reville. (2022) Converting between the Cartesian tensor and spherical harmonic expansion of solutions to the Boltzmann equation. Journal of Plasma Physics 88:5.
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Johanna Klein, Paul Fleurat‐Lessard & Julien Pilmé. (2021) New insights in chemical reactivity from quantum chemical topology. Journal of Computational Chemistry 42:12, pages 840-854.
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Sılay Aytaç Yükçü, Niyazi Yükçü & Emin Öztekin. (2021) Analytical treatments for magnetic multipole moment integrals. Chemical Physics Letters 771, pages 138466.
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Mohamed Amaouch, Dumitru-Claudiu Sergentu, David Steinmetz, Rémi Maurice, Nicolas Galland & Julien Pilmé. (2017) The bonding picture in hypervalent XF 3 (X = Cl, Br, I, At) fluorides revisited with quantum chemical topology . Journal of Computational Chemistry 38:32, pages 2753-2762.
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Péter R. Nagy, Gyula Samu & Mihály Kállay. (2016) An Integral-Direct Linear-Scaling Second-Order Møller–Plesset Approach. Journal of Chemical Theory and Computation 12:10, pages 4897-4914.
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E. Galbis, E. Giglio & B. Gervais. (2013) A diabatic parameterization of the twofold ground state potential energy surface of the H2O-OH molecular complex. The Journal of Chemical Physics 139:16.
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P.V. Makhlaichuk, M.P. Malomuzh & I.V. Zhyganiuk. (2013) Potential in the Multipole Approximation. Ukrainian Journal of Physics 58:3, pages 278-288.
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Dennis M. Elking, Lalith Perera & Lee G. Pedersen. (2012) HPAM: Hirshfeld partitioned atomic multipoles. Computer Physics Communications 183:2, pages 390-397.
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Dennis M. Elking, Lalith Perera, Robert Duke, Thomas Darden & Lee G. Pedersen. (2011) A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank. Journal of Computational Chemistry 32:15, pages 3283-3295.
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Massimiliano Bartolomei, Estela Carmona‐Novillo, Marta I. Hernández, José Campos‐Martínez & Ramón Hernández‐Lamoneda. (2010) Long‐range interaction for dimers of atmospheric interest: dispersion, induction and electrostatic contributions for O 2 O 2 , N 2 N 2 and O 2 N 2 . Journal of Computational Chemistry 32:2, pages 279-290.
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Telhat Özdoğan. (2006) Unified Treatment for Arbitrary-rank Cartesian Electric and Magnetic Multipole Moment Operators. Journal of Mathematical Chemistry 42:2, pages 201-214.
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Karol M. Langner, Pawel Kedzierski, W. Andrzej Sokalski & Jerzy Leszczynski. (2006) Physical Nature of Ethidium and Proflavine Interactions with Nucleic Acid Bases in the Intercalation Plane. The Journal of Physical Chemistry B 110:19, pages 9720-9727.
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Daniel S. Lambrecht & Christian Ochsenfeld. (2005) Multipole-based integral estimates for the rigorous description of distance dependence in two-electron integrals. The Journal of Chemical Physics 123:18.
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Konstantin N. Kudin & Gustavo E. Scuseria. (2000) Analytic stress tensor with the periodic fast multipole method. Physical Review B 61:8, pages 5141-5146.
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Eric Schwegler & Matt Challacombe. (1999) Linear scaling computation of the Fock matrix. IV. Multipole accelerated formation of the exchange matrix. The Journal of Chemical Physics 111:14, pages 6223-6229.
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Konstantin N. Kudin & Gustavo E. Scuseria. (1999) Range definitions for Gaussian-type charge distributions in fast multipole methods. The Journal of Chemical Physics 111:6, pages 2351-2356.
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Anders Wallqvist & Raymond D. Mountain. 1999. Reviews in Computational Chemistry. Reviews in Computational Chemistry 183 247 .
Eric Schwegler, Matt Challacombe & Martin Head-Gordon. (1998) A multipole acceptability criterion for electronic structure theory. The Journal of Chemical Physics 109:20, pages 8764-8769.
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Christof Hättig. (1996) Recurrence relations for the direct calculation of spherical multipole interaction tensors and Coulomb-type interaction energies. Chemical Physics Letters 260:3-4, pages 341-351.
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Matt Challacombe, Eric Schwegler & Jan Almlöf. (1995) Recurrence relations for calculation of the Cartesian multipole tensor. Chemical Physics Letters 241:1-2, pages 67-72.
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K. Esselink. (1995) A comparison of algorithms for long-range interactions. Computer Physics Communications 87:3, pages 375-395.
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Itai Panas. (2004) Practical expressions for the two‐center multipole expansion of r . International Journal of Quantum Chemistry 53:3, pages 255-263.
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P.-O. Åstrand, A. Wallqvist & G. Karlström. (1994) Nonempirical intermolecular potentials for urea–water systems. The Journal of Chemical Physics 100:2, pages 1262-1273.
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K. Hinsen & B. U. Felderhof. (1992) Dielectric constant of a suspension of uniform spheres. Physical Review B 46:20, pages 12955-12963.
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K. Hinsen & B. U. Felderhof. (1992) Reduced description of electric multipole potential in Cartesian coordinates. Journal of Mathematical Physics 33:11, pages 3731-3735.
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George Maroulis. (1991) Hyperpolarizability of H2O. The Journal of Chemical Physics 94:2, pages 1182-1190.
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Joseph D. Augspurger & Clifford E. Dykstra. (2004) General quantum mechanical operators. An open‐ended approach for one‐electron integrals with Gaussian bases. Journal of Computational Chemistry 11:1, pages 105-111.
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J Applequist. (1989) Traceless cartesian tensor forms for spherical harmonic functions: new theorems and applications to electrostatics of dielectric media. Journal of Physics A: Mathematical and General 22:20, pages 4303-4330.
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Christian Girard & Claude Girardet. (1987) Potential energy calculations for argon and methane adsorbed on MgO(001) substrate. Chemical Physics Letters 138:1, pages 83-89.
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Bernard Silvi & Emmanuel Bernard. (1987) On the determination of atom-atom potentials in silicates from quantum chemical calculations. Chemical Geology 62:1-2, pages 125-130.
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B. Silvi & M. Allavena. (1986) Properties of monomers in dimers, an analysis of dimerization effect: Ab initio calculations on HClN2 and HClCO2 complexes. Journal of Molecular Structure: THEOCHEM 135, pages 225-233.
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Jon Applequist. (1985) A multipole interaction theory of electric polarization of atomic and molecular assemblies. The Journal of Chemical Physics 83:2, pages 809-826.
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N. Fourati, B. Silvi & J. P. Perchard. (1984) The carbon dioxide–hydrogen chloride complexes. A matrix isolation study and an a b   i n i t i o calculation on the 1–1 species . The Journal of Chemical Physics 81:11, pages 4737-4745.
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Claude Girardet, Luce Abouaf-Marguin, Béatrice Gauthier-Roy & Daniel Maillard. (1984) NH3 trapped in nitrogen and rare gas matrices. I. Potential surface analysis. Chemical Physics 89:3, pages 415-430.
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A. Lakhlifi & C. Girardet. (1984) Interaction potential for symmetric top-diatom or atom pairs. Journal of Molecular Structure: THEOCHEM 110:1-2, pages 73-96.
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