Polarizability atomic-level response

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. 

From Eq, (1) it is clear that a model of crystal polarization that is adequate for the description of the piezoelectric and pyroelectric properties of the P-phase of PVDF must include an accurate description of both the dipole moment of the repeat unit and the unit cell volume as functions of temperature and applied mechanical stress or strain. The dipole moment of the repeat unit includes contributions from the intrinsic polarity of chemical bonds (primarily carbon-fluorine) owing to differences in electron affinity, induced dipole moments owing to atomic and electronic polarizability, and attenuation owing to the thermal oscillations of the dipole. Previous modeling efforts have emphasized the importance of one more of these effects electronic polarizability based on continuum dielectric theory" or Lorentz field sums of dipole lattices" static, atomic level modeling of the intrinsic bond polarity" atomic level modeling of bond polarity and electronic and atomic polarizability in the absence of thermal motion. " The unit cell volume is responsive to the effects of temperature and stress and therefore requires a model based on an expression of the free energy of the crystal. 

Saue and Jensen used linear response theory within the random phase approximation (RPA) at the Dirac level to obtain static and dynamic dipole polarizabilities for Cu2, Ag2 and Au2 [167]. The isotropic static dipole polarizability shows a similar anomaly compared with atomic gold, that is, Saue and Jensen obtained (nonrelativ-istic values in parentheses) 14.2 for Cu2 (15.1 A ), 17.3 A for Ag2 (20.5 A ), and 12.1 A for Au2 (20.2 A ). They also pointed out that relativistic and nonrelativistic dispersion curves do not resemble one another for Auz [167]. We briefly mention that Au2 is metastable at 5 eV with respect to 2 Au with a barrier to dissociation of 0.3 eV [168, 169]. 

The molecule is often represented as a polarizable point dipole. A few attempts have been performed with finite size models, such as dielectric spheres [64], To the best of our knowledge, the first model that joined a quantum mechanical description of the molecule with a continuum description of the metal was that by Hilton and Oxtoby [72], They considered an hydrogen atom in front of a perfect conductor plate, and they calculated the static polarizability aeff to demonstrate that the effect of the image potential on aeff could not justify SERS enhancement. In recent years, PCM has been extended to systems composed of a molecule, a metal specimen and possibly a solvent or a matrix embedding the metal-molecule system in a molecularly shaped cavity [62,73-78], In particular, the molecule was treated at the Hartree-Fock, DFT or ZINDO level, while for the metal different models have been explored for SERS and luminescence calculations, metal aggregates composed of several spherical particles, characterized by the experimental frequency-dependent dielectric constant. For luminescence, the effects of the surface roughness and the nonlocal response of the metal (at the Lindhard level) for planar metal surfaces have been also explored. The calculation of static and dynamic electrostatic interactions between the molecule, the complex shaped metal body and the solvent or matrix was done by using a BEM coupled, in some versions of the model, with an IEF approach. 

Since second hyperpolarizabilities depend in addition to the first-order also on the second-order response of the wavefunction, the minimal requirements with respect to the choice of basis sets are for y somewhat higher than for the linear polarizabilities a and the first hyperpolarizabilities j8, in particular for atoms and small molecules. For the latter at least doubly-polarized basis sets augmented with a sufficient number of diffuse functions (e.g. d-aug-cc-pVTZ or t-aug-cc-pVTZ) are needed to obtain qualitatively correct results. Highly accurate results at a correlated level will in general only be obtained in quadruple- or better basis sets. 

Pluta and Sadlej have calculated the dipole moment and static a, P and y and y tensors of urea and thiourea using three high level basis sets of increasing flexibility. Excellent agreement is found with experimental determinations of the dipole moment and linear polarizability. Frequeney-dependent polarizabilities and hyperpolarizabilities are ealeulated in the TDHF approximation and the results are then scaled to allow for electron correlation and the effect of basis set extension. Estimates of the response flmctions for non-linear optical processes are obtained. The introduction of the sulfur atom is found to produce a large increase in the predicted efficiency for third order effects. 

High polarizability of electrons in Ceo is one of the reasons for which ions and polar molecules are stabilized when trapped in endohedral complexes [3,30]. The dipole polarizability (a) measures the electronic response to a static electric field of a constant strength. Experimental data on polarizability of Ceo or other fullerenes are currently lacking however, a lower bound to a equal to 442.1 au was established by Fowler et al. [31] with the help of ab initio electronic structure calculations carried out at the HF/6-3lG(d) level. Based on this result, one may conclude that, atom for atom, Ceo is at least as polarizable as benzene. A similar (but with a much worse basis set) estimate was obtained for the C70 cluster [32], which was found to be more polarizable than Ceo ... 

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