Electron Distributions and Polarizabilities

The asymmetry of distributions of positive and negative charges in a molecule can have important effects on its physical properties as well as on its chemical reactivity. This asymmetry can have two quite different origins, illustrated by the permanent and induced dipole moments. A molecule such as HF has a permanent dipole moment which results from the electronegativities of the H and F atoms but even a symmetrical molecule such as H2C=CH2 can acquire an induced dipole moment in an external electric field. 

The polarizability is strongly related to the molecular volume. In simple electrostatic theory the polarizability of a perfectly conducting sphere of radius a is a = a3, but in real molecules of more complex shapes the average polarizability is still proportional to the size of the molecule the larger molecules have the higher polarizabilities. 

This brings us to consider the size of excited molecules. In the low-energy excited states this remains very close to that of the ground state species, but it increases gradually with the energy of the states the higher excited states are more polarizable, until the limiting case of ionization is reached when the molecule becomes theoretically of infinite size. 

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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 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. 

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],... 

Inelastic or Raman scattering of light can be understood classically as arising from modulation of the electron distribution, and hence the molecular polarizability, because of vibrations of the nuclei. For example, for a diatomic molecule, a can be represented adequately by the first two terms of a power series in the vibrational coordinate Q ... 

At even higher frequencies, in the visible region, only the electrons are mobile enough to respond to the rapidly changing direction of the applied field, The polarization that remains is now due entirely to the distortion of the electron distribution, and the surviving contribution to the molecular polarizability is called the electronic polarizability. 

DFT can evaluate properties and mutual reactivity from the electron distribution. These relationships between qualitative concepts in chemistry, such as electronegativity and polarizability, suggest that DFT does incorporate fundamental relationships between molecular properties and structure. At this point, we want to emphasize the conceptual relationships between the electron density and electronegativity and polarizability. We can expect electrophiles to attack positions with relatively high electron density and polarizability. Nucleophiles should attack positions of relatively... 

Variations in the local environment of a residue such as Tip produce changes in the electronic distribution that are reflected in an alteration of the ZFS parameters D and E. As an example, a uniform increase in the polarizability of the local environment results in a more diffuse triplet state electronic distribution and a proportional reduction of both D and... 

The charge distribution in a molecule has moments, dipole, quadrupole, and so on, and these make for interaction of the molecule with an external electric field, field gradient, and so on. An external electrical potential (field, field gradient, etc.) may affect the electron distribution, and this is characterized by polarizabilities and hyper-polarizabilities. 

The long-range interactions between a pair of molecules are detemiined by electric multipole moments and polarizabilities of the individual molecules. MuJtipoJe moments are measures that describe the non-sphericity of the charge distribution of a molecule. The zeroth-order moment is the total charge of the molecule Q = Yfi- where q- is the charge of particle and the sum is over all electrons and nuclei in tlie molecule. The first-order moment is the dipole moment vector with Cartesian components given by... 

Polarizability Attraction. AU. matter is composed of electrical charges which move in response to (become electrically polarized in) an external field. This field can be created by the distribution and motion of charges in nearby matter. The Hamaket constant for interaction energy, A, is a measure of this polarizability. As a first approximation it may be computed from the dielectric permittivity, S, and the refractive index, n, of the material (15), where is the frequency of the principal electronic absorption... 

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