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Patrycja Stefanska - One of the best experts on this subject based on the ideXlab platform.
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magnetic field induced electric quadrupole Moment in the ground state of the relativistic hydrogen like atom application of the sturmian expansion of the generalized dirac coulomb green function
Physical Review A, 2012Co-Authors: Radoslaw Szmytkowski, Patrycja StefanskaAbstract:We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength B of the perturbing field, the only electric Multipole Moment induced by the field in the ground state of the atom is the quadrupole one. Using the Sturmian expansion of the generalized Dirac–Coulomb Green function [R. Szmytkowski, J. Phys. B 30 (1997) 825; erratum 30 (1997) 2747], we derive a closed-form expression for the induced electric quadrupole Moment. The result contains the generalized hypergeometric function 3F2 of the unit argument. Earlier calculations by other authors, based on the nonrelativistic model of the atom, predicted in the low-field region the quadratic dependence of the induced electric quadrupole Moment on B.
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magnetic field induced electric quadrupole Moment in the ground state of the relativistic hydrogenlike atom application of the sturmian expansion of the generalized dirac coulomb green function
Physical Review A, 2012Co-Authors: Radoslaw Szmytkowski, Patrycja StefanskaAbstract:We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength $B$ of the perturbing field, the only electric Multipole Moment induced by the field in the ground state of the atom is the quadrupole one. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [Szmytkowski, J. Phys. B 30, 825 (1997); Szmytkowski, J. Phys. B 30, 2747(E) (1997)], we derive a closed-form expression for an induced electric quadrupole Moment. The result contains the generalized hypergeometric function ${}_{3}{F}_{2}$ of the unit argument. Earlier calculations by other authors, based on a nonrelativistic model of the atom, predicted in the low-field region the quadratic dependence of the induced electric quadrupole Moment on $B$.
Elahe Parvini - One of the best experts on this subject based on the ideXlab platform.
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interactions of sodium polystyrene sulfonate with 4 methylpyridinium based ionic liquids in aqueous solution viscometry conductometry uv vis spectroscopy and density functional theory studies
The Journal of Chemical Thermodynamics, 2019Co-Authors: Abbas Mehrdad, Elahe ParviniAbstract:Abstract Viscosity ( η ) and molar conductivity (Λ) of aqueous solutions of sodium polystyrene sulfonate (NaPSS) in the presence of some 4-methylpyridinium based ionic liquids (1-Butyl-4-methylpyridinium bromide [BMPyr]Br, 1-Hexyl-4-methylpyridinium bromide [HMPyr]Br and 1-Octyl-4-methylpyridinium bromide [OMPyr]Br) were investigated at T = (288.15, 298.15 and 308.15) K. The viscosity values were correlated with the Wolf equation to obtain the intrinsic viscosity ( [ η ] ) of NaPSS. The intrinsic viscosity of NaPSS decreases by increasing the concentration of ionic liquids due to screens effects of ionic liquids and decreased with increasing alkyl chain length of ILs. The scaling theory is used for the description of electrical conductance of polyelectrolytes. The values of fractions of uncondensed counterions f have been estimated. The effects of the polyelectrolyte concentration, the relative permittivity of the medium, different alkyl chain length and the temperature on the fractions of uncondensed counterions of NaPSS aqueous solutions have been discussed. UV–Vis spectroscopy and Quantum chemical calculations studies are also used to confirm the existence of interactions between NaPSS and ILs. The UV–Vis spectra of NaPSS show that the conformation of NaPSS changes in the presence of ionic liquids; therefore the value of electric Multipole Moment decreases. Consequently, the absorption intensity of NaPSS was decreased with the addition of ionic liquids. Density functional theory (DFT) has been used to investigate the interactions between [PSS]− anion and [RMPyr]+ cations. The molecular electrostatic potential, natural bond orbital methodologies and atoms in molecules are used to analyses the nature of interactions of the ion-pairs [RMPyr]+[PSS]−.
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interactions of sodium polystyrene sulfonate with some imidazolium based ionic liquids in aqueous solutions
Journal of Molecular Liquids, 2017Co-Authors: Abbas Mehrdad, Elahe ParviniAbstract:Abstract In this work, the effect of temperature and concentration of imidazolium-based ionic liquids ([BMIm]Br, [HMIm]Br, and [OMIm]Br) on the intrinsic viscosity of sodium polystyrene sulfonate (NaPSS) was investigated, and the excellent conformance of obtained data to Wolf's equation was observed. Moreover, addition of ionic liquids screened the electrostatic repulsion between charges along the backbone of the polyelectrolyte chain, leading to the declined intrinsic viscosity of NaPSS by increasing concentration of ionic liquids. The results also revealed that the intrinsic viscosity of NaPSS in the presence of ionic liquids is in the order of [BMIm]Br > [HMIm]Br > [OMIm]Br. The UV–vis spectra of NaPSS show that the absorption intensity of NaPSS was decreased with the addition of ionic liquids. Because of the decreased the expansion factor of polymer chains in the presence of ionic liquids, the value of electric Multipole Moment showed a consequent decrease. As a result, the absorption intensity of NaPSS was decreased with the addition of ionic liquids.
Radoslaw Szmytkowski - One of the best experts on this subject based on the ideXlab platform.
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magnetic field induced electric quadrupole Moment in the ground state of the relativistic hydrogen like atom application of the sturmian expansion of the generalized dirac coulomb green function
Physical Review A, 2012Co-Authors: Radoslaw Szmytkowski, Patrycja StefanskaAbstract:We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength B of the perturbing field, the only electric Multipole Moment induced by the field in the ground state of the atom is the quadrupole one. Using the Sturmian expansion of the generalized Dirac–Coulomb Green function [R. Szmytkowski, J. Phys. B 30 (1997) 825; erratum 30 (1997) 2747], we derive a closed-form expression for the induced electric quadrupole Moment. The result contains the generalized hypergeometric function 3F2 of the unit argument. Earlier calculations by other authors, based on the nonrelativistic model of the atom, predicted in the low-field region the quadratic dependence of the induced electric quadrupole Moment on B.
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magnetic field induced electric quadrupole Moment in the ground state of the relativistic hydrogenlike atom application of the sturmian expansion of the generalized dirac coulomb green function
Physical Review A, 2012Co-Authors: Radoslaw Szmytkowski, Patrycja StefanskaAbstract:We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength $B$ of the perturbing field, the only electric Multipole Moment induced by the field in the ground state of the atom is the quadrupole one. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [Szmytkowski, J. Phys. B 30, 825 (1997); Szmytkowski, J. Phys. B 30, 2747(E) (1997)], we derive a closed-form expression for an induced electric quadrupole Moment. The result contains the generalized hypergeometric function ${}_{3}{F}_{2}$ of the unit argument. Earlier calculations by other authors, based on a nonrelativistic model of the atom, predicted in the low-field region the quadratic dependence of the induced electric quadrupole Moment on $B$.
Taylor L Hughes - One of the best experts on this subject based on the ideXlab platform.
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many body electric Multipole operators in extended systems
Physical Review B, 2019Co-Authors: William Wheeler, Lucas K Wagner, Taylor L HughesAbstract:The quantum mechanical position operators, and their products, are not well-defined in systems obeying periodic boundary conditions. Here we extend the work of Resta [Phys. Rev. Lett. 80, 1800 (1998)], who developed a formalism to calculate the electronic polarization as an expectation value of a many-body operator, to include higher Multipole Moments, e.g., quadrupole and octupole. We define $n\mathrm{th}$-order Multipole operators whose expectation values can be used to calculate the $n\mathrm{th}$ Multipole Moment when all of the lower Moments are vanishing (modulo a quantum). We show that changes in our operators are tied to flows of $n\ensuremath{-}1\mathrm{st}$ Multipole currents, and encode the adiabatic evolution of the system in the presence of an $n\ensuremath{-}1\mathrm{st}$ gradient of the electric field. Finally, we test our operators on a set of tight-binding models to show that they correctly determine the phase diagrams of topological quadrupole and octupole models, capture an adiabatic quadrupole pump, and distinguish a bulk quadrupole Moment from other mechanisms that generate corner charges.
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electric Multipole Moments topological Multipole Moment pumping and chiral hinge states in crystalline insulators
Physical Review B, 2017Co-Authors: Wladimir A Benalcazar, Andrei B Bernevig, Taylor L HughesAbstract:We extend the theory of dipole Moments in crystalline insulators to higher Multipole Moments. In this paper, we expand in great detail the theory presented in Ref. 1, and extend it to cover associated topological pumping phenomena, and a novel class of 3D insulator with chiral hinge states. In quantum-mechanical crystalline insulators, higher Multipole bulk Moments manifest themselves by the presence of boundary-localized Moments of lower dimension, in exact correspondence with the electromagnetic theory of classical continuous dielectrics. In the presence of certain symmetries, these Moments are quantized, and their boundary signatures are fractionalized. These Multipole Moments then correspond to new SPT phases. The topological structure of these phases is described by "nested" Wilson loops, which reflect the bulk-boundary correspondence in a way that makes evident a hierarchical classification of the Multipole Moments. Just as a varying dipole generates charge pumping, a varying quadrupole generates dipole pumping, and a varying octupole generates quadrupole pumping. For non-trivial adiabatic cycles, the transport of these Moments is quantized. An analysis of these interconnected phenomena leads to the conclusion that a new kind of Chern-type insulator exists, which has chiral, hinge-localized modes in 3D. We provide the minimal models for the quantized Multipole Moments, the non-trivial pumping processes and the hinge Chern insulator, and describe the topological invariants that protect them.
I I Guseinov - One of the best experts on this subject based on the ideXlab platform.
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comment on evaluation of multicenter electric Multipole Moment integrals over integer and noninteger n stos
Journal of The Chinese Chemical Society, 2004Co-Authors: I I GuseinovAbstract:Ozdoǧan (J. Chin. Chem. Soc. 2004, 51, 13) published formulas for evaluating the multicenter electric Multipole Moment (EMM) integrals over Slater-type orbitals (STOs). It is demonstrated that all of the formulas presented in this work are not original and they are available in our already published papers or can easily be derived by means of a simple algebra (I. I. Guseinov, J. Mol. Struct. (Theochem) 1996, 367, 83; 1998, 427, 263; Int. J. Quantum Chem. 1998, 68, 145; I. I. Guseinov, B. A. Mamedov, Int. J. Quantum Chem. 2003, 93, 9.
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calculation of molecular electric and magnetic Multipole Moment integrals of integer and noninteger n slater orbitals using overlap integrals
International Journal of Quantum Chemistry, 2003Co-Authors: I I Guseinov, B A MamedovAbstract:Closed 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.
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calculation of three center electric and magnetic Multipole Moment integrals using translation formulas for slater type orbitals
Theoretical Chemistry Accounts, 2000Co-Authors: I I Guseinov, B A Mamedov, Metin OrbayAbstract: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.
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calculation of electric Multipole Moment integrals using translation formulas for slater type orbitals
Communications in Theoretical Physics, 2000Co-Authors: I I Guseinov, Telhat Ozdogan, B A Mamedov, Metin Orbay, A M Rzaeva, A G GasanovAbstract: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.
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calculation of magnetic Multipole Moment integrals using translation formulas for slater type orbitals
Pramana, 1999Co-Authors: I I Guseinov, Telhat Ozdogan, B A Mamedov, Metin OrbayAbstract:Using translation formulas for Slater type orbitals (STO’s) the infinite series through the overlap integrals are derived for the magnetic Multipole Moment integrals. By the use of the derived expressions the magnetic Multipole Moment integrals, therefore, the magnetic properties of molecules can be evaluated most efficiently and accurately. The convergence of the series is tested by calculating concrete cases. An accuracy of 10−5 for the computer results is obtained in the case 2 p -pole magnetic Moment integrals for 1 ≤ v ≤ 5, and for the arbitrary values of internuclear distances and screening constants of atomic orbitals.
