A semi-empirical method for estimating molecular quadrupole polarizabilities
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A new scheme for decomposing the total dipole moment and polarizability of a system into site-specific contributions is presented. The scheme is based on partitioning the system volume into cells associated with its atoms or groups of atoms. The site-specific dipole moments and polarizabilities are computed from the charge densities within the individual cells and the responses of these densities to an external electric field. These dipole moments and polarizabilities are further partitioned into local/dipole and charge-transfer components. The utility of the scheme is illustrated through analysis of the structure-/shape- and size-specific aspects of the dipole moments and polarizabilities of silicon clusters. It is shown that the polarizabilities associated with the individual constituent Si atoms vary considerably with the structure/shape of the cluster and the location of the atom or site within a given structure. Surface atoms, and especially those at edges, have larger polarizabilities than interior atoms. The overall contribution of the charge-transfer components to the total cluster polarizability increases with the cluster size. Finally, the anisotropy of the total polarizability correlates with the anisotropy of the cluster shape, and the charge-transfer component is the part dominantly responsible for the polarizability anisotropy.
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Bond dipole moment
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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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The group–dipole interaction model is generalized to treat the molecular polarizability and the molecular first and second hyperpolarizabilities. A molecule is divided in groups; each group is characterized by a polarizability and by first and second hyperpolarizabilities, and it resides in an internal molecular electric field. The internal field is thought to arise from any charges or permanent moments within the molecule, and it is characteristic of the system being studied. In the point dipole approximation, all the dipole–dipole interactions are treated exactly, and all the molecular results are written in terms of only those quantities needed to calculate the molecular polarizability. Several approximate theories are considered, and the additivity of group polarizabilities and hyperpolarizabilities is discussed. Special formulas are derived to treat an assembly of interacting isotropic atoms.
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Abstract We use a previously proposed variation‐perturbation method to calculate the electric polarizabilities and the electric dipole moment at equilibrium nuclear distance of the BH molecule. We obtain 3.56 × 10 −24 cm 3 for the perpendicular polarizability α xx and 3.22 × 10 −24 cm 3 for the parallel polarizability α zz . Our result for the electric dipole moment μ 0 is 1.734 debye units; there is no reliable experimental result to compare it with.
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Abstract It is shown that even for pronouncedly anisotropic dipole molecules the mean polarizability in a homogeneous external electrical field, provided there is no saturation, is practically equal to (α 1 + α 2 + α 3 )/3 where α 1 , α 2 and α 3 are the polarizabilities in the three main directions.
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