Anisotropy total polarizabilities

Even for the case of isotropic polarizabilities, where ap = aq = a, it follows from Eq. (3-36) that the total polarizability will be anisotropic. If we want to define effective polarizabilities from Eq. (3-37) for the members, we must (arbitrarily ) distribute the interaction term. For ap = aq equipartitioning could work, leading to local anisotropy with a// (local)>a and a (local)[Pg.53]

Atomic-level response of sodium clusters to external electric field has also been studied recently [55] using a decomposition of the total cluster dipole moment and polarizability into contributions from atomic volumes. The atomic dipole moments and polarizabilities thus obtained have also been partitioned into the atomic dipole and charge-transfer components. The relative contribution of these two components as a function of the size and shape of the clusters have been studied. Also the contributions are shown to depend on the location of the atomic site in the cluster. Thus, the surface atoms have been shown to have larger contribution to the polarizability than the interior ones. The anisotropy of the total polarizabilities is also shown to correlate with the shape anisotropy of the clusters. These ab initio results on the atomic charge and dipole components that contribute to the overall cluster polarizability thus would enable one to validate the coarse-grained DFT-based results in a more detailed fashion since the coarse-grained approaches provide the atomic charges and atomic dipoles besides the overall polarizability. 

In the case of water, the anisotropy of the polarizability is less than 10% of the total value, and we can safely employ a spherical polarization,... 

The properties that are routinely computed and discussed are the mean (or average) static dipole polarizability (a), the anisotropy (Act) of the polarizability tensor, the vector component of the first hyperpolarizabUity tensor in the direction of the ground state permanent dipole moment (/3 ), the total first-order hyperpolarizabUity tot, and the scalar component of the second hyperpolarizability tensor y. Those quantities are related to the experiment and in terms of the Cartesian components are defined as... 

The prime on the mean and anisotropy parameters, a and y, respectively, denote values obtained from the polarizability derivative - defined in the sense of Equation [5], but in components of the tensor daij 8Q t rather than a j itself. In the case of gases and liquids, Pi is lower than for vibrations that are totally symmetric (vibrations transforming under the totally symmetric representation of the molecular point group), but exactly for for other vibrations that lower the molecular symmetry, since a is then zero. 

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