Effective polarizability, determination

The effective polarizability of surface atoms can be determined with different methods. In Section 2.2.4(a) a method was described on a measurement of the field evaporation rate as a function of field of kink site atoms and adsorbed atoms. The polarizability is derived from the coefficient of F2 term in the rate vs. field curve. From the rate measurements, polarizabilities of kink site W atoms and W adatoms on the W (110) surface are determined to be 4.6 0.6 and 6.8 1.0 A3, respectively. The dipole moment and polarizability of an adatom can also be measured from a field dependence of random walk diffusion under the influence of a chemical potential gradient, usually referred as a directional walk, produced by the applied electric field gradient, as reported by Tsong et a/.150,198,203 This study is a good example of random walk under the influence of a chemical potential gradient and will therefore be discussed in some detail. 

The dipole moment of a selected functional group in the polymer can also be calculated using the Clausius-Mossotti equation. According to Van Krevelan, (15) the "effective polarizability" of a functional group in the polymer is calculated from the measured dielectric constant, the polymer density and the number of moles of that group in the polymer repeat unit. Using the data for the six polyamide-imides listed in Table I, the effective polarizability of the amide group can be determined from... 

The interfacial electric polarizability y, being an important dynamic characteristic of the particle surface charge, can be easily determined from the electro-optical effect dependence on the square of the electric field strength (Eq. 6). A significant increase in the particle dimensions as well as the low surface charge of the colloid-polymer complex complicate the electric polarizability determination near to the system s isoelectric point (Figure 2). The electric polarizabilities are calculated in this review only for polymer covered particles in stabilized suspensions. One way to obtain correct values... 

The above expressions were derived for the polarizabilities of molecules in free space or in a dilute gas (mostly air). However, we often encounter molecules interacting in a liquid solvent medium, which reduces the interaction pair potential by around e, or more the extent of this reduction depends on several factors. First of all, the intrinsic polarizability and dipole moment of an isolated gas molecule may be different when it is itself in the liquid state, or alternatively when dissolved in a solvent medium. This is because of the difference in interaction strength and also the separation distance between molecules. Thus, the polarizability values are best determined by experiment. Second, a dissolved molecule can only move by displacing an equal volume of solvent from its path. If the molecule has the same polarizability as the solvent molecules, that is if no electric held is reflected by the molecule, it is invisible in the solvent medium and does not experience any induction force. Thus, the polarizability of the molecule, a, must represent the excess or effective polarizability of a molecule over that of the solvent. Landau and Lifshitz applied a continuum approach and modeled a molecule, i, as a dielectric sphere of radius, ah having... 

The term AWi (= Ajr ) is the first-order energy shift, and AW, (= Cjr ) is the second-order shift. Equation 16 has the form of (2), and in the region of validity of the rotational Stark effect the simple Langevin theory applies. However, the effective angular momentum is determined by the first two terms of (16), and the effective polarizability is determined by the last two terms. 

KL also considered the effective polarizability (otgff) which determines the refractive index of a fluidand the appropriate local field factors for the Kerr effect ). Cox et al obtained analagous expressions for the local field factors in the Raman... 

The experimental methods for polarizability determination based on the Stark effect use the displacements and splitting of rotational energy levels of small molecules under the influence of an external electric field [11-14]. The usual accuracy of these methods is in the range of 3-10 %. 

We are restricted here by the terms in (4.2.7) related to the modified DID model discussed above. In the framework of this model for (N2)2 and (02)2 complexes the effective polarizability of the atoms N and O is determined as a half of the polarizability for the N2 and O2 molecules respectively. It s evident, that the effective polarizability of atoms N and O determined by such a way is anisotropic and depends on the internuclear distance of the molecules, and, as a result, the polarizability of the complex is the function of the internuclear distances of the molecules forming it, which allows one to calculate the tensor of the polarizability derivatives of the complex for different configurations. 

The quality of the ) states has been tested through their energy and also their transition moment. Moreover from the natural orbitals and Mulliken populations analysis, we have determined the predominant electronic configuration of each ) state and its Rydberg character. Such an analysis is particularly interesting since it explains the contribution of each ) to the calculation of the static or dynamic polarizability it allows a better understanding in the case of the CO molecule the difficulty of the calculation and the wide range of published values for the parallel component while the computation of the perpendicular component is easier. In effect in the case of CO ... 

It can be seen from Figures 3.7 and 3.8 that the calculations reproduce very well not only the experimental spectra but also the experimentally observed isotopic shifts indicating a high reliability of the computational method. According to this comparison, definite attribution can be made for even the difficult Raman bands that cannot be assigned based solely on the experimental results. It is, however, necessary to mention at this point that the calculated Raman spectrum provided directly by the ab initio computations correspond to the normal Raman spectrum with the band intensity determined by the polarizability of the correlating vibration. Since the intensity pattern exhibited by the experimentally recorded resonance Raman spectrum is due to the resonance enhancement effect of a particular chromophore, with no consideration of this effect, the calculated intensity pattern may, in many... 

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