Anisotropy polarizability measurements

The experimental values of the polarizability a = V2 (2a + of 1 and its anisotropy Aa = oL.-oL x 5.50 and -0.74 which have been obtained by extrapolating polarizabilities measured at optical frequencies to their static limits Amos and Williams calculated for a and Aa 5.03 and -0.67 at the HF/[5s3p2d/3slp] level, which are about 10% too small, typical of HF/large basis set calculations. As can be seen from Table 23, a = oiyy (components in the ring plane) is larger than a (perpendicular to the ring plane). Since an... 

According to (2.12) the optical anisotropy As = njf — n is completely defined by the anisotropy of polarizability, measured parallel and perpendicular to the long molecular axis A7. The values of optical anisotropy increase [14,28] with ... 

Zdzislaw, S. Gordon, T., Optical anisotropy in lipid bilayer membranes Coupled plasmon waveguide resonance measurements of molecular orientation, polarizability, and shape, Biophys. J. 2001, 80, 1557 1567... 

In the above experiments in which an electrode surface is examined, the electrode potential is fixed as the electrode surface is rotated and the SH anisotropy recorded. In a useful variation of this procedure, one can fix the angle of rotation and measure the SH response as a function of potential. Since the absolute orientation of the crystal is known, information can be derived about the various tensor elements describing the nonlinear polarizability from these crystalline surfaces. By fixing the angle and applying a transient potential pulse, one can perform time resolved measurements and watch the evolution of various adsorption and deposition processes along specific crystal axes. 

All of the studies discussed above for silver have been done with an incident beam of 1064 nm. These studies have proven that the anisotropy in the nonlinear polarizability from the silver surface is not purely free-electron-like at these wavelengths, that the anisotropy can be correlated with surface symmetry, and that the SH response measured in situ is nearly identical to that measured in UHV. The issue of the sensitivity of the rotational anisotropy to surface electronic properties has been the topic of very recent work which has been conducted by variation of the incident wavelengths to where optical resonances in the bulk or surface electronic structure can be accessed. 

The polarizability tensor, a, introduced in section 4.1.2, is a measure of the facility of the electron distribution to distortion by an imposed electric field. The structure of the electron distribution will generally be anisotropic, giving rise to intrinsic birefringence. This optical anisotropy reflects the average electron distribution whereas vibrational and rotational modes of the molecules making up a sample will cause the polarizability to fluctuate in time. These modes are discrete, and considering a particular vibrational frequency, vk, the oscillating polarizability can be modeled as... 

The simplified schematic in Figure 2a shows the essential features of the effect. Optically anisotropic molecules in the solution are preferentially oriented by the applied field E(t), resulting in a difference of refractive indices for components of polarized light parallel and perpendicular to the bias field which is measured as a birefringence. The basic theoretical problem is to evaluate this effect in terms of anisotropies of polarizability Aa. referred to molecular axes which produce a time dependent effect when the molecules are preferentially oriented by the field. For no anisotropy in absence of the field, the effect must be an evgn function of field strength, and at low fields proportional to E. A remarkable feature of the effect is that for molecules with permanent dipole moments the response af-... 

This invariant can be thought of as measuring the average deviation of the polarizability from its mean value, and is therefore known as the anisotropy of n. 

The authors used a [5 s4p 1 d/4s 1 p] basi s set in their calculations. In order to focus on the effects of the molecular interaction, they introduced the concept of a noninteracting dimer wherein the dimer wave function is a simple product (non-antisymmetrized) of the unperturbed monomer functions. The effects of the interaction are thus in evidence by comparison of the two columns in Table 3.31 from which it may be seen that the average polarizability is little affected, increasing from 16.48 to only 16.60. The anisotropy of the polarizability, however, as measured by y, undergoes a dramatic increase. Whereas the polarizability tensor is nearly spherical in the monomer, with all a.j values between 16.3 and 16.6, is increased up to 18 when the two molecules interact with one another. This increase is thus focused along the H-bond direction. 

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 general, the polarizability is a tensor whose invariants, trace and anisotropy, give rise to polarized and fully depolarized light scattering, respectively. Collision-induced light scattering is caused by the excess polarizability of a collisional pair (or a larger complex of atoms or molecules) that arises from the intermolecular interactions. In Section I.l, we are concerned with the definition, measurement, and computation of interaction-induced polarizabilities and their invariants. 

Measurements. The anisotropy of the pair polarizability has been determined from three types of measurements depolarized CILS spectra, pressure dependent depolarization ratios, and second virial Kerr coefficients. 

---