Polarizabilities cubic

The measured values of coherence lengths / i, l, and the corresponding cubic non-linear susceptibilities Fn, Fj., F,j for all the compounds investigated are shown in Table. The effective cubic polarizabilities > f, yf, y and y,j were calculated using the isotropic (Vuks) form for the local electric field. The value of (the projection of the vectorial part of the quadratic hyperpolarizability on the direction of the molecular dipole moment jl) was calculated from the formula ... 

Let us discuss data from Table I and begin with the isotropic phase. It is seen that the quadratic hyperpolarizabilities are almost equal for all the substances despite the pronounced difference in molecular structure. By the way, the values are approximately two times more than that for nitrobenzene. Probably, the main contribution to the /3 value results from the benzene rings of molecules containing conjugated chains of 7r-bonds. The value of the cubic polarizability y, depends linearly on the permanent dipole moment of molecules (the molecular dipole moments of 5CB, 8CB and HOPCS are nearly equal and markedly higher than that for MBBA). The latter result is consistent with increasing degree of the field orientation of the molecules which is proportional to the product (xE. 

The fundamental equation (1) describes the change in dipole moment between the ground state and an excited state jte expressed as a power series of the electric field E which occurs upon interaction of such a field, as in the electric component of electromagnetic radiation, with a single molecule. The coefficient a is the familiar linear polarizability, ft and y are the quadratic and cubic hyperpolarizabilities, respectively. The coefficients for these hyperpolarizabilities are tensor quantities and therefore highly symmetry dependent odd order coefficients are nonvanishing for all molecules but even order coefficients such as J3 (responsible for SHG) are zero for centrosymmetric molecules. Equation (2) is identical with (1) except that it describes a macroscopic polarization, such as that arising from an array of molecules in a crystal (10). 

There have been a few recent studies of the corrections due to nuclear motion to the electronic diagonal polarizability (a ) of LiH. Bishop et al. [92] calculated vibrational and rotational contributions to the polarizability. They found for the ground state (v = 0, the state studied here) that the vibrational contribution is 0.923 a.u. Papadopoulos et al. [88] use the perturbation method to find a corrected value of 28.93 a.u. including a vibrational component of 1.7 a.u. Jonsson et al. [91] used cubic response functions to find a corrected value for of 28.26 a.u., including a vibrational contribution of 1.37 a.u. In all cases, the vibrational contribution is approximately 3% of the total polarizability. 

Conductivity is a measure of the number of ions per unit volume and their average velocity in the direction of the applied field. Polarizability is a measure of the number of bound charged particles per cubic unit and their average displacement in the direction of the applied field. 

A particle is subdivided into a small number of identical elements, perhaps 100 or more, each of which contains many atoms but is still sufficiently small to be represented as a dipole oscillator. These elements are arranged on a cubic lattice and their polarizability is such that when inserted into the Clausius-Mossotti relation the bulk dielectric function of the particle material is obtained. The vector amplitude of the field scattered by each dipole oscillator, driven by the incident field and that of all the other oscillators, is determined iteratively. The total scattered field, from which cross sections and scattering diagrams can be calculated, is the sum of all these dipolar fields. 

It has been assumed16 27 that the neon atom and other atoms with an s2p outer shell also may be described as tetrahedral. However, the four spa electrons with positive spin are independent of the four with negaiive spin, and the two corresponding tetrahedra are free to assume arbitrary relative orientation.28 Correlation requires that the most stable relative orientation be the inverse one hence the neon atom and the other s2p6 atoms can be described as cubic. Their polarizability in a cubic multipole electric field is large and that in a tetrahedral field small.29... 

In general, the cadmium halides show in their crystal structure the relation between polarizing effect and si/e of anion. The tluoride has tile smallest and least polarizable anion of Ihe lour and forms a cubic structure, while the mure polarizable heavy halides have hexagonal layer structures, increasingly covalent and al increasing distances apart in inxler down tire periodic table, in solution the halides exhibit anomalous thermal and transport properties, due primarily to the presence of complex ions, such as CDlr and CdBr r. especially in concentrated solutions or those containing excess halide ions. 

The design of molecules, supermolecules and materials presenting NLO activity involves molecular and supramolecular engineering. At the molecular level, a high polarizability, leading to large quadratic ft and cubic y hyperpolarizability coeffi-... 

There is very little problem in calculating an acceptable measure of solute size. Simple calculations of either molecular volume or area based on either Bondi s (Bondi, 1964) or McGowan s (Abraham, 1987) methods work almost as well as those derived from molecular mechanics and quantum chemistry (Leo, 1993). When volume in cubic Angstroms is used, V is normally scaled by 0.01 to produce a coefficient comparable to the others in the equation polarity/polarizability. 

According to eq. (19) the refractive index increases with increasing density (increasing pressure) and increasing polarizability. However, this model is exactly valid only for point dipoles in a cubic arrangement. Therefore, the reliability of this model with respect to quantitative predictions is limited in many cases (Eremets, 1996). A further difficulty here is to estimate the change of the polarizability under pressure. 

The mean-polarizability approximation, discussed in detail by Agranovitch,16 presents the same advantages (simplicity, arbitrary concentrations, etc.), and the same limitations as the average-locator approximation in particular, this theory provides two bands of persistence behavior for all values of the parameters. This may be checked on the example of a cubic crystal, where the local field has a very simple form The modes of the mixed crystal are given by... 

Here, we provide the theoretical basis for incorporating the PE potential in quantum mechanical response theory, including the derivation of the contributions to the linear, quadratic, and cubic response functions. The derivations follow closely the formulation of linear and quadratic response theory within DFT by Salek et al. [17] and cubic response within DFT by Jansik et al. [18] Furthermore, the derived equations show some similarities to other response-based environmental methods, for example, the polarizable continuum model [19, 20] (PCM) or the spherical cavity dielectric... 

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