Multipole electric moments and higher polarizabilities of molecules: Methodology and some results of ab initio calculations
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Abstract There is an electric field around a molecule which can be described in terms of its multipole moments. The energy of another nearby molecule in this field involves its multipole moments, and the electrostatic interaction between them can be expressed as a sum of terms, each involving a product of multipole moments for each molecule and an interaction tensor. These interaction terms can be expressed in either cartesian or spherical tensor form, most conveniently using multipole moments defined in local axes, as they do not change with the molecular orientation. The dependence of the multipole—multipole terms on the relative orientation of the molecules is then described using new functions (S functions). The dipole--dipole, dipole--quadrupole and quadrupole--quadrupole interactions are discussed in detail, with examples.
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Abstract In vortex-like spin arrangements, multiple spins can combine into emergent multipole moments. Such multipole moments have broken space-inversion and time-reversal symmetries, and can therefore exhibit linear magnetoelectric (ME) activity. Three types of such multipole moments are known: toroidal; monopole; and quadrupole moments. So far, however, the ME activity of these multipole moments has only been established experimentally for the toroidal moment. Here we propose a magnetic square cupola cluster, in which four corner-sharing square-coordinated metal-ligand fragments form a noncoplanar buckled structure, as a promising structural unit that carries an ME-active multipole moment. We substantiate this idea by observing clear magnetodielectric signals associated with an antiferroic ME-active magnetic quadrupole order in the real material Ba(TiO)Cu 4 (PO 4 ) 4 . The present result serves as a useful guide for exploring and designing new ME-active materials based on vortex-like spin arrangements.
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By using a schematic model the quadrupole polarizability is analytically estimated for nuclei rapidly “rotating” about the symmetry axis. We discuss the dependence of the polarizability on the angular momentum of the vacuum I0 and the transition energy. In particular it is shown that the µ = ±2 static polarizability corresponds to the complete screening when I0 ≠ 0, while for I0 it is identical with the known result. We separately discuss the contribution of the high-frequency modes (giant quadrupole resonances) and that of the low-frequency modes peculiar to the case I0 ≠ 0. In the limit I0 → 0 the latter with µ = ±1 can be viewed as the polarizability resulting from the Coriolis coupling (the particle-rotation coupling).
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Abstract It is shown that the static multipole polarizability of hydrogen-like atoms can be obtained as the static limit of the dynamic multipole polarizability previously given by the author. Recent criticism by Jhanwar and Meath that this static limit leads to wrong results is unfounded.
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Quadrupole magnet
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In this work, the partitioning of higher multipole polarizabilities, such as dipole–quadrupole, quadrupole–dipole, and quadrupole–quadrupole polarizabilities, into atomic contributions is studied. Partitioning of higher multipole polarizabilities is necessary in the study of accurate interaction energies where dispersion interactions are of importance. The fractional occupation Hirhsfeld-I (FOHI) method is used to calculate the atomic polarizabilities and is briefly explained together with the methodology for partitioning of the polarizabilities. The atomic multipole polarizabilities are calculated for different sets of molecules, linear alkanes, water clusters, and small organic molecules with different functional groups. It is found that the atomic and group contributions of the dipole and quadrupole polarizabilities are transferable as a function of the functional groups.
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