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Multipole Moments (multipole + moment)
Selected AbstractsMultipole moments and polarizability of molecular systems with D3h symmetry in orbitally degenerate statesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2006I. Ya. Abstract It was proved, by ab initio studies, that the electronic ground states of the molecules MF3 (MV, Cr, Mn), M3 (MLi, Na, K), and C3H3, with D3h symmetry, have orbital degeneracy. It was shown that in the base functions of these degenerate states, the reduced matrix elements of the in-plane E,-type components of the dipole moment, of the quadrupole moments and of the nontotal symmetric components of the (hyper)polarizability are nonzero. The computed values of the dipole and quadrupole moments of the polarizability and hyperpolarizabilities are comparable to those of the molecular systems of the lower than D3h symmetry. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Interlayer coupling in magnetic superlattices with electron density inhomogeneitiesPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 1 2004W. Gruhn Abstract We discuss the influence of spatial inhomogeneities of the free electron density on the magnetic interaction between magnetic layers of the superlattice, mediated across nonmagnetic, metallic spacer. Using the modified total energy approach, we prove that the TM or RE superlattices the additional scattering of free electrons on magnetic ion multipole moment increases the ferroquadrupolar biquadratic coupling between magnetic layers. It is shown also that the nonuniform free electron density generates contribution to the interlayer coupling being of the Dzialoshinsky-Moriya type. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Computational linear dependence in molecular electronic structure calculations using universal basis setsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2005D. Moncrieff Abstract Distributed universal even-tempered basis sets have been developed over recent years that are capable of supporting Hartree,Fock energies to an accuracy approaching the sub-,Hartree level. These basis sets have also been exploited in correlation studies, in applications to polyatomic molecules, and in the calculation of electric properties, such as multipole moments, polarizabilities, and hyperpolarizabilities. Jorge and coworkers have also developed universal basis sets and have recently reported applications to diatomic molecular systems. In this article, we compare the molecular calculations reported by Jorge and coworkers with our previous studies. Particular attention is given to the degree of computational linear dependence associated with the various basis sets employed and the consequential effects of the accuracy of the calculated energies. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Linear augmented Slater-type orbital method for free standing clustersJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 8 2009K. S. Kang Abstract We have developed a Scalable Linear Augmented Slater-Type Orbital (LASTO) method for electronic-structure calculations on free-standing atomic clusters. As with other linear methods we solve the Schrödinger equation using a mixed basis set consisting of numerical functions inside atom-centered spheres and matched onto tail functions outside. The tail functions are Slater-type orbitals, which are localized, exponentially decaying functions. To solve the Poisson equation between spheres, we use a finite difference method replacing the rapidly varying charge density inside the spheres with a smoothed density with the same multipole moments. We use multigrid techniques on the mesh, which yields the Coulomb potential on the spheres and in turn defines the potential inside via a Dirichlet problem. To solve the linear eigen-problem, we use ScaLAPACK, a well-developed package to solve large eigensystems with dense matrices. We have tested the method on small clusters of palladium. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009 [source] Accuracy of distributed multipoles and polarizabilities: Comparison between the LoProp and MpProp modelsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 6 2007P. Söderhjelm Abstract Localized multipole moments up to the fifth moment as well as localized dipole polarizabilities are calculated with the MpProp and the newly developed LoProp methods for a total of 20 molecules, predominantly derived from amino acids. A comparison of electrostatic potentials calculated from the multipole expansion obtained by the two methods with ab initio results shows that both methods reproduce the electrostatic interaction with an elementary charge with a mean absolute error of ,1.5 kJ/mol at contact distance and less than 0.1 kJ/mol at distances 2 Å further out when terms up to the octupole moments are included. The polarizabilities are tested with homogenous electric fields and are found to have similar accuracy. The MpProp method gives better multipole moments unless diffuse basis sets are used, whereas LoProp gives better polarizabilities. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007 [source] Raman spectra and elastic properties of KPb2Cl5 crystalsPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 11 2004A. N. Vtyurin Abstract Raman scattering spectra and elastic constants of KPb2Cl5 crystals have been studied. The results obtained are interpreted in terms of the ab initio lattice dynamics model taking into account multipole moments of ionic electron envelopes. The experimental results have been found to be in good agreement with numerical simulation; the narrow phonon spectra are shown to be due to a considerable contribution of heavy cations into the eigenvectors of the higher frequency lattice modes. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Multipolar Ordering in Electro- and Magnetostatic Coupled NanosystemsCHEMPHYSCHEM, Issue 9 2008Elena Y. Vedmedenko Dr. habil. Abstract 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. [source] | |||||||||||||