The electronic polarization

(17) indicates that the induced dipole moment is directly proportional to the applied electric field. The polarizability a is defined as the ratio between the induced dipole moment m and the applied electric field E 

(20) shows that polarizability increases quickly with the increase of the orbit radius, a/r is large, the polarizability is larger too. The ions of a large a/r should have a large dielectric constant. 

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The underlying principle of the PEOE method is that the electronic polarization within the tr-bond skeleton as measured by the inductive effect is attenuated with each intervening o -bond. The electronic polarization within /r-bond systems as measured by the resonance or mesomeric effect, on the other hand, extends across an entire nr-system without any attenuation. The simple model of an electron in a box expresses this fact. Thus, in calculating the charge distribution in conjugated i -systems an approach different from the PEOE method has to be taken. 

The treatment of electrostatics and dielectric effects in molecular mechanics calculations necessary for redox property calculations can be divided into two issues electronic polarization contributions to the dielectric response and reorientational polarization contributions to the dielectric response. Without reorientation, the electronic polarization contribution to e is 2 for the types of atoms found in biological systems. The reorientational contribution is due to the reorientation of polar groups by charges. In the protein, the reorientation is restricted by the bonding between the polar groups, whereas in water the reorientation is enhanced owing to cooperative effects of the freely rotating solvent molecules. 

One of the most important characteristics of these components is the time of their response to varying electric fields. The electronic polarization has the shortest time 10 s All other components are related with the nuclei motion and are characterized by longer times, from to x , X(,> 10 s Another impor-... 

Therefore, the electronic polarization induced by the transferable electron in the medium can follow any instant position of the electron without delay. This means that at any position of the transferable electron between the donor and acceptor, the electronic polarization of the medium induced by this electron is practically the same, and therefore the energy of the interaction of the electron with this polarization is... 

This component of solvent polarization is c WoAfast or inertialess polarization, Pfjjst, since it follows in an inertialess way the motion of the electron. It involves, however, only part of the electronic polarization ... 

Therefore, the other types of polarization do not change their configuration when the electron changes its spatial position. This polarization is called slow or inertial polarization, (= P the subscript slow is omitted below). It reacts only to the average position of the transferable electron (in the donor or in the acceptor). The inertial polarization includes all other components and part of the electronic polarization ... 

Inclusion of part of the electronic polarization into the inertial polarization is due to strong interaction between the nuclei and electrons of the medium. The (slow) change in the nuclei positions inevitably produces polarization of the electron shells of the solvent molecules. Therefore, the latter also contribute to the slow polarization. 

In Figs. 20 and 21 we compare the experimental and CDW-EIS results [38] for 40-keV H+ projectiles incident on H2 and He and for emission of electrons at 0° [doubly differential with respect to the electron polar angle of emission and the energy of the ejected electron d2a/dfldE (10-16 cm2 eV 1 sr 1)]. Both sets of results which did not require normalization are seen to be in very good accord, with the spectra being completely dominated by the ECC cusp. 

According to Hohenberg-Kohn theorem, 8p(F) given in Eq (36) does never vanishes because pA(r) and pY(r) are determined by different external potentials [26], Moreover, 8p(r) represents the electronic polarization contribution due to the isoelectronic change under the influence of the external electrostatic field. 

We shall now show that the insertion energy may be cast into a form completely equivalent to Bom formula. This may be easily done by using the well known relationship between the electrostatic ion-solvent interaction energy and the electronic polarization energy [3,14], Namely... 

Here the term involving e0 determines the spectral shift due to dipole-dipole interactions. This effect will be smaller, the greater the electronic polarization of the medium, which is expressed by the term involving n2. 

One must account for the screening of the external field by the electronic polarization of the adsorbed molecules. This screening gives rise to a reduced infrared absorption. Taking it into account in a proper way shows... 

In the first model, the mnneling electron mainly interacts with the electronic polarization of water ( = 1.88) since tunneling was assumed to be fast in comparison with the orientational response of the dipolar molecules of the liquid. Considering water as a dielectric continuum between a jellium spherical tip and planar substrate yields an effective barrier for tunneling that is about 1 eV lower than that for the vacuum case [95]. This result is consistent with photoemission studies of metal/aqueous interfaces, which reveal electron emission into water at 1 eV below the vacuum level [95-97]. Similar models have been employed to examine the effect of thermal fluctuations on the tunneling current [98-100]. Likewise, a related model assessing the noise associated with the reorientation of adsorbed molecules has been presented [101]. 

Atomic polarization contributes to the relative motion of atoms in the molecule affected by perturbation by the applied field of the vibrations of atoms and ions having a characteristic resonance frequency in the IR region. The atomic polarization is large in inorganic materials which contain low-energy conductive bonds and approaches zero for nonconductive polymers. The atomic polarization is rapid, and this, as well as the electronic polarization, constitutes the instantaneous polarization components. 

The electronic polarization is so rapid that there is no observable effect of time or frequency on the dielectric constant until frequencies are reached which correspond to the visible and ultraviolet spectra. For convenience, the frequency range of the infrared through the ultraviolet region is called the optical frequency range, whereas that including the radio and the audio range is called the electric frequency range. 

The electronic polarization is an additive property of atomic bonds, such as C-H, OC, and C-F. Thus the electronic polarizations and related properties per unit volume are similar for both small molecules and macromolecules. 

The atomic polarization is rapid, and this and the electronic polarizations constitute the instantaneous polarization components. The remaining types of polarization are absorptive types with characteristic relaxation times corresponding to relaxation frequencies. 

The sign of the energy shift is determined by the electric polarizability and has a clear physical origin. The electron polarizes the nucleus, an additional attraction between the induced dipole and the electron emerges, and shifts the energy level down. 

This energy shift is negative because when the electron polarizes the nucleus this leads to an additional attraction of the induced dipole to the electron. 

The high-frequency dielectric constant is determined by the effects of electronic polarization. An accurate estimate of this property lends confidence to the modeling of the electronic polarization contribution in the piezoelectric and pyroelectric responses. The constant strain dielectric constants (k, dimensionless) are computed from the normal modes of the crystal (see Table 11.1). Comparison of the zero- and high-frequency dielectric constants indicates that electronic polarization accounts for 94% of the total dielectric response. Our calculated value for k (experimental value of 1.85 estimated from the index of refraction of the P-phase of PVDF. ... 

Thus, fluorine substitution in polyimides can affect the total polarizability in different directions. It is the combined changes to the orientational and electronic polarizations, at a given frequency of interest, that must be considered. Since the orientation polarization can either go up or remain unchanged and the electronic polarization is always decreased, the net dielectric constant can go in either direction upon fluorination. However, it is more often observed that the net dielectric constant is decreased with fluorination. 

Applied electric fields, whether static or oscillating, distort (polarize) the electron distribution and nuclear positions in molecules. Much of this volume describes effects that arise from the electronic polarization. Nuclear contributions to the overall polarization can be quite large, but occur on a slower time-scale than the electronic polarization. Electronic motion can be sufficiently rapid to follow the typical electric fields associated with incident UV to near IR radiation. This is the case if the field is sufficiently off resonance relative to electronic transitions and the nuclei are fixed (see ref 5 for contributions arising from nuclear motion). Relaxation between states need not be rapid, so... 

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