Effective polarizability

Previous studies with a variety of datasets had shown the importance of charge distribution, of inductive effect), of r-electronegativity, resonance effect), and of effective polarizability, aeffi polarizability effect) for details on these methods see Section 7.1). All four of these descriptors on all three carbon atoms were calculated. However, in the final study, a reduced set of descriptors, shown in Table 3-4, was chosen that was obtained both by statistical methods and by chemical intuition. 

Figure 7-6. Graphical representation of the procedure for calculating the effective polarizability on the nitrogen atom of 2-aminopropane.

An effective polarizability, reflecting the stabilization of a positive charge on the protonated nitrogen atom through polarizability, is calculated by Eq, (16). 

The method for calculating effective polarizabilitie.s wa.s developed primarily to obtain values that reflect the stabilizing effect of polarizability on introduction of a charge into a molecule. That this goal was reached was proven by a variety of correlations of data on chemical reactivity in the gas phase with effective polarizability values. We have intentionally chosen reactions in the gas phase as these show the predominant effect of polarizability, uncorrupted by solvent effects. 

Thus, the values calculated for effective polarizability at the nitrogen atom for a series of 49 amines carrying only alkyl groups was correlated directly with their proton affinities, a reaction that introduces a positive charge on the nitrogen atom by protonation (Figure 7-7) [40. ... 

The pA of 1,3-dithiane is 36.5 (Cs" ion pair in THF). The value for 2-phenyl-1,3-dithiane is 30.5. There are several factors which can contribute to the anion-stabilizing effect of sulfur substituents. Bond dipole effects contribute but carmot be the dominant factor because oxygen substituents do not have a comparable stabilizing effect. Polarizability of sulfur can also stabilize the carbanion. Delocalization can be described as involving 3d orbitals on sulfur or hyperconjugation with the a orbital of the C—S bond. MO calculations favor the latter interpretation. An experimental study of the rates of deprotonation of phenylthionitromethane indicates that sulfur polarizability is a major factor. Whatever the structural basis is, there is no question that thio substituents enhance... 

Let us take the problem of a diatomic molecule, such as Cl2, with the two atoms as the two polarizable parts. Each atom has a polarizability ax parallel to and a2 perpendicular to the interatomic axis, respectively. The Silberstein theory yields for the effective polarizability of the molecule the values bx and b2, respectively, parallel and perpendicular to the axis. 

The significance of the values calculated for the effective polarizability was first established with physical data, among them relaxation energies derived from a combination of X-ray photoelectron and Auger spectroscopy, as well as N-ls ESCA data53, 54). From our point of view, however, the most important applications of effective polarizability are to be found in correlating chemical reactivity data. Thus, the proton affinity (PA) of 49 unsubstituted alkylamines comprising primary, secondary and tertiary amines of a variety of skeletal types correlate directly with effective polarizability values (Fig. 22). 

The signs of the coefficients in this equation are consistent with the interpretation of the two factors the negative sign of the coefficient for the x12 parameter indicates that an increase in the inductive effect destabilizes the corresponding ammonium ion and thereby leads to a decrease in the proton affinity. On the other hand, an increase in the effective polarizability, ad, stabilizes the ammonium ion and therefore... 

Figure 3. Deriving values for effective polarizability, a, from refractive index, n, molecular weight, MW, and density, d...

Simple linear equations could also be developed for the other three systems of Figure 4, PA of aldehydes and ketones(4e), and their hydride ion affinities, both of the neutral (4f) and protonated forms (4g), However, in addition to effective polarizability and electronegativity, hyperconjugation had also to be used as a parameter, as p-orbitals carrying a partial positive charge are involved in the reactions 4e to 4g (26),... 

A parameter used to characterize ER fluids is the Mason number, which describes the ratio of viscous to electrical forces, and is given by equation 14, where 8 is the solvent dielectric constant T 0, th solvent viscosity 7, the strain or shear rate P, the effective polarizability of the particles and E, the electric field (117). 

FIM can also be used to study properties, such as the surface induced dipole moment and the effective polarizability of some surface atoms, kink site atoms and adsorbed atoms etc. The charge distribution of a surface atom is obviously completely different from that of a free atom because of its interaction with the surface and in addition surface atoms are partially shielded by itinerant charges of the surface. The charge distribution of a surface atom can be described by the magnitudes of the electric multipoles of the atom. 

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. 

Magnetic susceptibilities Zeeman and Faraday effects polarizability 594... 

These results apply specifically to Rayleigh, or elastic, scattering. For Raman, or inelastic, scattering the same basic CID expressions apply but with the molecular property tensors replaced by corresponding vibrational Raman transition tensors between the initial and final vibrational states nv and rn . In this way a s are replaced by (mv aap(Q) nv), where aQ/3(<3) s are effective polarizability and optical activity operators that depend parametrically on the normal vibrational coordinates Q such that, within the Placzek polarizability theory of the Raman effect [23], ROA intensity depends on products such as (daaf3 / dQ)0 dG af3 / dQ) and (daaf3 / dQ)0 eajS dAlSf / dQ)0. 

The theory of PCM calculation of the effective polarizabilities is based on a time-dependent response theory that describes the interaction between the molecular solutes and the Maxwell electric field. We will review the method in three separate sections, the... 

In this section we compare the PCM formulation of the effective polarizabilities with the semiclassical Onsager-Wortmann-Bishop model [2] (from now on indicated as OWB). 

The effective polarizabilities of the OWB solute are finally obtained in terms of the cavity and reaction field factors for example, for the linear effective polarizability we obtain... 

Similarly, we have effective second- and third-order effective polarizabilities... 

The OWB equations obtained in this semiclassical scheme analyse the effective polarizabilities in term of solvent effects on the polarizabilities of the isolated molecules. Three main effects arise due to (a) a contribution from the static reaction field which results in a solute polarizability, different from that of the isolated molecules, (b) a coupling between the induced dipole moments and the dielectric medium, represented by the reaction field factors FR n, (c) the boundary of the cavity which modifies the cavity field with respect the macroscopic field in the medium (the Maxwell field) and this effect is represented by the cavity field factors /c,n. 

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