Polarizabilities electron distribution

The alkali metals tend to ionize thus, their modeling is dominated by electrostatic interactions. They can be described well by ah initio calculations, provided that diffuse, polarized basis sets are used. This allows the calculation to describe the very polarizable electron density distribution. Core potentials are used for ah initio calculations on the heavier elements. 

Polarizability (Section 5.4) The measure of the change in a molecule s electron distribution in response to changing electric interactions with solvents or ionic reagents. 

According to Fig. 2, as M comes in contact with S,3 4 the electron distribution at the metal surface (giving the surface potential XM) will be perturbed X ) The same is the case for the surface orientation of solvent molecules (Xs + SXS). In addition, a potential drop has to be taken into account at the free surface of the liquid layer toward the air (xs). On the whole, the variation of the electron work function (if no charge separation takes place as assumed at the pzc of a polarizable electrode) will measure the extent of perturbation at the surfaces of the two phases, i.e.,... 

The ease with which the electron distribution around an atom or molecule can be distorted is called its polarizability. ... 

A satisfactory feature of (116) is that the first-order term, which describes the interaction between the external charge and the unperturbed molecule, continues to disappear if the electron distribution is highly uniform as in an alternant hydrocarbon in such cases the propensities for reaction are still dominated by the polarization term, but this now has a less simple form, depending upon all atom-atom polarizabilities and on the position of the attacking ion with respect to all conjugated centres. 

Robinson (1967) has used the Unsold approximation for the energy levels to express the polarizabilities in terms of the electrostatic moments of the ground-state electron distribution. The expressions have been applied to X-ray charge densities by Zyss, Baert, and coworkers (Fkyerat et al. 1995 F. Hamzaoui, F. Baert and J. Zyss, private communication). A detailed description of the derivation and the approximations involved is beyond the scope of this treatise. However, it should be mentioned that the severe approximations are made that all excited-state energy levels are equal, and that the exciting light frequency is equal to zero. 

Within models of the sparkle family the effect of the external Coulomb field does not reduce to the renormalization of the orbital energies as it is within the RLMO model (see above). By contrast, the electron distribution also changes when the ligand molecules are put into the field. We model this by classical polarizability. Accordingly the difference between effective charge on atom A in the complex (polarized) and that in the free ligand (non-polarized) is ... 

The Hamaker coefficient. A, is a measure of the interaction and is dependent on the material of the particle as well as on the surrounding medium. Heavy atoms, which are generally more polarizable (i.e., the electron distribution can be more... 

Generally, molecules exhibit 1 values between 8 and 12 eV (i.e., 1.3 and 2 x 10 18 J), and the separations between molecules must be related to the molecular sizes. The polarizability, a, of a molecule is related to its ability to develop uneven electron distributions in response to imposed electric fields on femtosecond timescales. Since visible light corresponds to electromagnetic radiation with frequencies around... 

The electron distribution of the helium atom in field-free space is, of course, spherically symmetric. The atom has, however, a large polarizability in a quadrupole electric field, which we may ascribe to the partial orientation of the prolate ellipsoid. 

In a simple model a neutral molecule can be described through two properties related to its electron distribution, the permanent dipole moment i and the average polarizability oc. There are therefore four electrostatic interactions between a solute molecule and the surrounding solvent molecules, as shown in Table 3.1. 

Just as a is the linear polarizability, the higher order terms p and y (equation 19) are the first and second hvperpolarizabilities. respectively. If the valence electrons are localized and can be assigned to specific bonds, the second-order coefficient, 6, is referred to as the bond (hyper) polarizability. If the valence electron distribution is delocalized, as in organic aromatic or acetylenic molecules, 6 can be described in terms of molecular (hyper)polarizability. Equation 19 describes polarization at the atomic or molecular level where first-order (a), second-order (6), etc., coefficients are defined in terms of atom, bond, or molecular polarizabilities, p is then the net bond or molecular polarization. 

Because the p value is positive, negatively charged carbon ions are considered to be the primary transition state complex (TSC). The TSC will dissociate to a substituted phenol radical and a stable anion. It may also be neutralized by the toluene, resulting in the addition of a proton, H+ (Arai and Dorfman, 1964) therefore, eaq is considered to interact with the ir-orbital of the ring as in electrophilic substitution rather than to affect electron distribution and polarizability of a certain substituent. 

The polarizability, a, is a measure of the extent to which the electronic distribution over a molecule can be distorted by the electric field of charged particles, or dipolar molecules. 

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 e j rate constants correlate better with normal o- values derived from electrophilic substitution than with a para values obtained from data of nucleophilic reactions. This is not surprising in view of the fact that the e]fq reactions constitute an interaction of an electron with the 77-orbitals of the ring, as in electrophilic substitution, rather than with effects on electron distribution and polarizability of a certain substituent. 

By taking as a reference the calculation in vacuo, the presence of the solvent introduces several complications. In fact, besides the direct effect of the solvent on the solute electronic distribution (which implies changes in the solute properties, i.e. dipole moment, polarizability and higher order responses), it should be taken into account that indirect solvent effects exist, i.e. the solvent reaction field perturbs the molecular potential energy surface (PES). This implies that the molecular geometry of the solute (the PES minima) and vibrational frequencies (the PES curvature around minima in the harmonic approximation) are affected by the presence of a solvating environment. Also, the dynamics of the solvent molecules around the solute (the so-called nonequilibrium effect ) has to be... 

Merocyanine dyes 50-55 (Fig. 5.18) possess an electronic structure at the meso-meric center between neutral and zwitterionic electron distribution and have high polarizabilities and dipole moments and exhibit absorption spectra with sharp bands that give rise to exceptionally brilliant magenta hues [60],... 

The local response model of the van der Waals interaction implies a corresponding model of the polarization potential, hence of the long-range limit of the bound-free correlation potential for an electron outside a polarizable charge distribution [12]. The implications of this observation are discussed in the present paper. 

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