Anisotropy polarizability

Craven IE, Hesling MR, Laver DR et al (1989) Polarizability anisotropy, magnetic anisotropy, and quadrupole moment of cyclohexane. J Phys Chem 93 627-631... 

The isotropic dipole polarizability a, the dipole polarizability anisotropy Aa and the isotropic traceless quadrupole polarizability C are defined as... 

In addition to the nonzero a and P tensor components, we also consider the isotropic average polarizability (a) and the polarizability anisotropy Aa defined as ... 

Figures 1-3 display the basis set dependence of the average polarizability, (a), the polarizability anisotropy, Aa, and the vector component of the first hyperpolarizability,...

Fig. 2. Basis set dependence of the static polarizability anisotropy (in a.u.) for the eight reference molecules evaluated at the SOS/CIS level of approximation.

The SOS/CIS scheme leads to larger a tensor components than the TDHF/CPHF approach and, in most cases, to larger polarizability anisotropy. This can easily be understood by refereeing to the differences between the RPA and TDA schemes. In the latter which is equivalent to SOS/CIS, the excitation energies are smaller because the ground state is not stabilized by interactions with doubly-excited states [21-22]. This... 

A = solv, pol. The striking similarity in the spectra and their components is evident, justifying the use of OKE data to model SD in this liquid. It should be noted that the two experiments have very (tifierent dynamical origins in some liquids such as, for example, water, where SD is strongly dominated by rotational dynamics, " whereas OKE probes mainly translational motions due to the very small molecular polarizability anisotropy. ... 

By the same procedure are obtained the corresponding biphenyl isocyanide derivatives (Figure 7.20) [18]. Now, the free isonitriles are already liquid crystals displaying nematic and SmA phases with a short range of existence at moderate temperatures (40-85 °C), while the complexes show a marked increase in the melting points and also an expansion ofthe range of existence of the mesophase (up to 140 °C N and SmA phases). The exception is the shortest iodo-derivative, which is not a mesogen. Most of the complexes decompose into the isotropic state (above 220 °C). The biphenyl moiety increases the polarizability anisotropy compared to the phenyl and hence facilitates liquid crystal behavior. 

Based on their thermal properties, polymeric and glassy molecular PR materials can be classified as high-7 and low-7), materials. The Tg values of polymer composites can be lowered by doping small molecules as plasticizer. Introduction of a long alkyl side chain can effectively reduce the Tg of fully functionalized polymers. The glassy molecular materials usually possess low Tg if they are amorphous. For the high-7 and low-7), materials, the figures of merit of the NLO chromophores are defined by Eqs. (35) and (40), respectively. The latter are obviously enhanced by contributions from the polarizability anisotropy of the NLO chromophore. 

The Lorentz-Lorenz equation can be used to express the components of the refractive index tensor in terms of the polarizability tensor. Recognizing that the birefringence normalized by the mean refractive index is normally very small, ( A/i / 1), it is assumed that Aa /a 1, where the mean polarizability is a = (al + 2oc2)/3 and the polarizability anisotropy is Aa = a1-a2. It is expected that the macroscopic refractive... 

FIGURE 26 Nomogram of the dimensionless alignment parameter A > as a function of laser intensity, field strength, and polarizability anisotropy. [Reproduced with permission from Freidrich, B., and Herschbach, D. R. (1995). J. Phys. Chem. 99,15686. Copyright American Chemical Society.]... 

There exist various reviews of the methods by which the electric and magnetic polarizabilities of atoms and molecules can be establidied. Particularly valuable are the comprehensive artides of Le Ffevre on the determination of the anisotropy of optical polarizability from molecular refraction measurements and Kerr effect and, recently, on the role of molecular polarizability in chemistry. Bothorel reviews the method of deternuning optical anisotropy from direct measurements of depolarized scattered laser light intensity and its particular utility in the study of n-alkanes. Stein et al have latdy discussed the polarizability anisotropy of macromolecules. 

Table 17 Permanent electric dipole moments and electric polarizability anisotropies for some macromolecules and particles...

Linear electric polarizabilities of atoms and polarizability anisotropies of molecules have been rather extensively evaluated by using more or less approximate wavefunctions and various perturbation methods. Note-... 

The elements of o(co) are determined from studies of molecular refraction, anisotropic li t scattering, the Kerr effect, and optical birefiringence. Frequency-dependent polarizabilities can also be calculated directly to various orders of approximation by methods of quantum mechanics. Research has of late been developing on the spectra of depolarized li t in simple gases and liquids, " leading to the detemunation of pair polarizabOity of atoms or molecules - as wdl as of the polarizability anisotropies induced by multiple correlations. ... 

ISS data have been recorded in many pure and mixed molecular liquids [34,49, 75, 83, 83-85], In most cases, the data are not described precisely by Eq. (27). Rather, an additional decay component appears at intermediate times (decay times 500 fs). This has been interpreted [49, 84] in terms of higher order polarizability contributions to C (t) which represent translational motions, an interpretation supported by observations in CCI4 (whose single-molecule polarizability anisotropy vanishes by symmetry). This interpretation is not consistent with several molecular dynamics simulations of CSj [71, 86]. An alternative analysis has been presented [82] that incorporates theoretical results showing that even the single-molecule orientational correlation function C (t) should in fact show decay on the 0.5-ps time scale of cage fluctuations [87, 88]. 

F. Barocchi, M. Zoppi, U. Bafile, and R. Magli. The pair polarizability anisotropies of Kr and Xe from depolarized interaction induced light scattering spectra. Chem. Phys. Lett., 97 135-138 (1983). 

A. D, Buckingham and K. L. Clarke-Hunt. The pair polarizability anisotropy of SF in the point-atom-polarizability approximation. Molec. Phys., 40 643-648 (1980). 

P. R. Hilton and D. W. Oxtoby. Charge transfer in atomic collisions The pair polarizability anisotropy. J. Chem. Phys., 72 4Ti-4n (1980). 

N. Meinander, G. C. Tabisz, and M. Zoppi. Moment analysis in depolarized light scattering Determination of a single-parameter empirical pair polarizability anisotropy for Ne, Ar, Kr, Xe and CH. J. Chem. Phys., 54 3005-3013 (1986). 

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