Optical polarizability

R. Spreiter, C. Bosshard, G. Knopfle, P. Gunter, R. R. Tykwinski, M. Schreiber, F. Diederich, One- and Two-Dimensionally Conjugated Tetraethynylethenes Structure versus Second-Order Optical Polarizabilities , J. Phys. Chem B. 1998,102,29-32... 

Calculations which ascribe nonlinear optical polarizabilities in LilOa to the individual I-O bonds and relate experimentally measured second harmonic generation coefficients x 311 and X313 to theoretical results for the structure of LilOs, have been performed by Jeggo ii). 

Table 1.22 lists the values of optical polarizability a and static polarizability calculated by Lasaga and Cygan (1982) for various silicates on the basis of... 

The quantity dn/dc is the specific refractive index increment and it represents the incremental change in solution refractive index with sample concentration at the wavelength, temperature, and pressure of the LALLS measurements. Since dn/dc reflects the optical characteristics of the polymer and solvent (their different optical polarizabilities), its value strongly depends on the chemical composition of both components ( 0). 

The process of THG is driven by third-order optical nonlinearity, which defines the nonlinear optical polarizability at the frequency 3[Pg.128]

Cheng, L. T., Tam, W., Stevenson, S. H., Meredith, G. R., Rikken, G., Marder, S. R., Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives. J. Phys. Chem. 1991,95, 10631-10643. 

Four frequently used conventions exist for the definition of non-linear optical polarizabilities, leading to confusion in the realm of NLO. This has been largely clarified by Willets et al. (1992) and in their nomenclature we have used the Taylor series expansion (T convention), originally introduced by Buckingham (1967), where the factorials n are explicitly written in the expansion. Here the polarizabilities of one order all extrapolate to the same value for the static limit w— 0. /3 values in the second convention, the perturbation series (B), have to be multiplied by a factor of 2 to be converted into T values. This is the convention used most in computations following the sum-over-states method (see p. 136). The third convention (B ) is used by some authors in EFISHG experiments and is converted into the T convention by multiplication by a factor of 6. The fourth phenomenological convention (X) is converted to the T convention by multiplication by a factor of 4. 

To add to the confusion noted for conventions of polarizabilities, both cgs and recommended SI units for linear and non-linear optical polarizabilities coexist in the literature. We strongly advocate the use of SI units. The SI unit of the electric dipole moment is Cm (Cohen and Giacomo, 1987). Thus, consistent SI units of an nth-order polarizability are defined as C m(mV )" = C m " V ", cf. (34)-(37). Conversions from the SI to the esu system for the dipole moment, the first-, second-, and third-order polarizability, are given in (38)-(41). 

The molecular polarizabilities can be interpreted quantum mechanically by using the methods of time-dependent perturbation theory. Under the influence of the electric fleld, the molecular ground state ( g)) is changed by admixture of excited states ( /), m). ..). Collections of such expressions are available in the literature (Ward, 1965 Orr and Ward, 1971 Bishop, 1994b). A comprehensive treatment has also been given by Flytzanis (1975). Here, we only quote the results for the linear optical polarizability a(-a) a)) and the second-order polarizability /3(-2a) o), co). The linear optical polarizability may be represented by the sum of two-level contributions (45). 

These equations are used in semiempirical quantum chemical calculations of non-linear optical polarizabilities by applying perturbation theoretical expressions [the so-called sum-over-states (SOS) method]. Here we use them to derive some qualitative and very general trends in a few simple model systems. To this end we concentrate on the electronic structure, i.e. on the LCAO coefficients. We do not explicitly calculate the transition frequencies. This is justified for the qualitative discussion below since typical transition energies... 

The simplest model consists of two centres, one donor (D) and one acceptor (A), separated by a distance I and contains two electrons. Here we consider this simple system to illustrate some general relations between charge transfer, transition intensities and linear as well as non-linear optical polarizabilities. We will show below that the electro-optic parameters and the molecular polarizabilities may be described in terms of a single parameter, c, that is a measure of the extent of coupling between donor and acceptor. Conceptually, this approach is related to early computations on the behaviour of inorganic intervalence complexes (Robin and Day, 1967 Denning, 1995), Mulliken s model for molecular CT complexes (Mulliken and Pearson, 1969) and a two-form/two-state analysis of push-pull molecules (Blanchard-Desce and Barzoukas, 1998). 

In the reaction field model expression (94) is obtained for the effective linear optical polarizability. 

The effective polarizability a was defined in (93). The relation between and the refractive index n was given in (13). Concentration-dependent measurements of the refractive index yield experimental information about the optical polarizability of the molecules. 

This basicity concept (further discussed in Chapter 8) may be quantified by study of the spectra of probe ions such as Pb +, leading to values of optical basicity. These optical basicities can be correlated with polarizabilities, either macroscopic optical polarizabilities or the molecular-level polarizabilities, which influence the Auger parameter. 

More recently, the Faraday eflfect (particulariy its dispersion and absorption) has been found to provide new ways of studying the structure of molecules and, even more so, of macromolecules and biopolymers. This is because the Faraday eflfect is primarily due to the direct influence of the electric field on the optical polarizability of the microsystems (it thus differs essentially from natural optical activity). The theoretical and experimental results obtained in these studies are presented in the articles of Buckingham and Stephen, and Schatz and McCaflfery. Existing laser and high-magnetic-fidd techniques permit studies of non-linear variations in the Faraday eflfect, particularly with regard to macromolecular and colloidal substances. ... 

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. 

In the case of axially symmetric molecules the optical polarizability tensor a has the form (86) (similar to electric polarizability), and ... 

Translational-orientational fluctuations. Re-writing the expansion (195) of the optical polarizability deviation tensor in a manner adapted to multi-component systems (as done previously for electric polarizability), one obtains from the general formula an additional contribution from binary correlations of axially symmetric molecules, of the form ... 

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