Polarization of electrons

The symbol —> represents the direction of polarization of electrons m the H—F bond)... 

On the other hand the polarization of electron density map unsaturated carbonyl compounds makes their p carbon atoms rather electrophilic Some chemical conse quences of this enhanced electrophilicity are described m the following section... 

Radicals escaping from a radical pair become uncorrelated as approaches zero. In the free (doublet) state they are detectable by e.s.r. spectroscopy. However, just as polarization of nuclear spins can occur in the radical pair, so polarization of electron spins can be produced. Provided that electron spin-lattice relaxation and free radical scavenging processes do not make the lifetime of the polarized radicals too short. 

The isotropic Fermi contact field B, which arises from a net spin-up or spin-down -electron density at the nucleus as a consequence of spin-polarization of -electrons by unpaired valence electrons [63] ... 

Dispersion forces result from temporary dipoles caused by polarization of electron clouds... 

Moving down halogen family, shielding effect and greater distance from nucleus would cause easier polarization of electron cloud. 

Therefore, greater polarization of electron cloud would cause greater attractive force (van der Waals force), resulting in higher boiling points. 

Thiete 2 shows a doublet (IH) at S 6.50, a multiplet (IH) at 3 5.60, and a doublet (2H) at 8 3.80. In the spectrum of thiete 1,1-dioxide, the signal of the j -olefinic proton is at lower field than that of the a-olefinic proton. The P atom has a lower electron density than the a atom, because of the polarization of electrons in the ring by the sulfone group. 

In Chap. A, we have seen that, in the Stoner model, (ferromagnetic) spin-polarization of electrons originates two electron states E+ and E from each electron state E of a non-spin-polarized electron band, the difference between the two being (E+ - E ) = Im, where I is the Stoner parameter and m = n+ - n is the magnetization density. 

These are the Fourier components of the polarization vector which are connected with the oscillations of the ions that are present in eqns. (44)-(46). In addition to this polarization which results from the motion of the nuclei, purely electronic polarization (i.e. the polarization of electrons at equilibrium positions of the nuclei) is also of importance. In the frequency region below the optical range, the purely electronic polarization can be expressed through the optical dielectric permeability (i.e. the dielectric permeability corresponding to the frequencies which are less than those in the optical absorption region, but exceed those of the nuclei vibrations). Optical frequencies considerably exceed those of the nuclear vibrations therefore, in the optical frequency region the nuclei do not, in practice, contribute to polarization. The connection of the Fourier component of purely electronic polarization with that of the induction of the electric field has the usual form... 

The modern form of the stopping power includes two corrections. The first correction applies at high energies at which polarization of electrons by the electric held of the moving ion tends to shield distant electrons this correction depends on the electron density it is subtractive and given the symbol 8. The second correction applies at low energies when the collisions are no longer adiabatic, similar to the limit applied by Bohr. This correction is termed the shell correction as it depends... 

In this introductory chapter the concepts of linear and nonlinear polarization are discussed. Both classical and quantum mechanical descriptions of polarizability based on potential surfaces and the "sum over states" formalism are outlined. In addition, it is shown how nonlinear polarization of electrons gives rise to a variety of useful nonlinear optical effects. 

Classical anharmonic spring models with or without damping [9], and the corresponding quantum oscillator models seem well removed from the molecular problems of interest here. The quantum systems are frequently described in terms of coulombic or muffin tin potentials that are intrinsically anharmonic. We will demonstrate their correspondence after first discussing the quantum approach to the nonlinear polarizability problem. Since we are calculating the polarization of electrons in molecules in the presence of an external electric field, we will determine the polarized molecular wave functions expanded in the basis set of unperturbed molecular orbitals and, from them, the nonlinear polarizability. At the heart of this strategy is the assumption that perturbation theory is appropriate for treating these small effects (see below). This is appropriate if the polarized states differ in minor ways from the unpolarized states. The electric dipole operator defines the interaction between the electric field and the molecule. Because the polarization operator (eq lc) is proportional to the dipole operator, there is a direct link between perturbation theory corrections (stark effects) and electronic polarizability [6,11,12]. 

As a direct application of electric molecular terms we calculate the corresponding magnetic moments by studying the polarization of electronic (hole) states in a small external magnetic field. For a field H in z-direction we add to the potential (5) a... 

Theory indicates that the J x term is composed of several contributions that characterize the effect of orbital electronic motions, the polarization of electronic spins, and the Fermi contact term. The last contribution is the most significant, and affects mainly the s valence orbitals. 

In their work on the insertion of triplet oxygen to the hydrogen molecule, Bader and Gangi138 found it necessary to use the UHF method in order to investigate the changes of polarization of electron spins at various points on the potential energy surface. The spin density distribution function [Pg.43]

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