Atomic polarization, static electric fields

Molecules with polar groups possess a permanent dipole moment pp. In these molecules, a static electric field produces an orientation polarizability, in addition to induced atomic or electron polarization i.e., the most probable rest position for the permanent dipole lies preferentially in the direction of the field. Molecules with permanent dipoles thus often store more electrical energy than those with induced dipoles. 

The Stark-PNC form of interference is utilized in experiments with heavy atoms at Berkeley and Paris, and in many experiments with hydrogen. Here we present a qualitative sketch of the scheme used at Paris and Berkeley. The basic idea, originally pointed out by Bouchiat and Bouchiat, is that an electronic polarization (i.e., a nonzero expectation value of the electronic angular momentum ])) in the excited state of the atom is induced by absorption of a circularly polarized photon directed perpendicular to an applied static electric field. 

High polarizability of electrons in Ceo is one of the reasons for which ions and polar molecules are stabilized when trapped in endohedral complexes [3,30]. The dipole polarizability (a) measures the electronic response to a static electric field of a constant strength. Experimental data on polarizability of Ceo or other fullerenes are currently lacking however, a lower bound to a equal to 442.1 au was established by Fowler et al. [31] with the help of ab initio electronic structure calculations carried out at the HF/6-3lG(d) level. Based on this result, one may conclude that, atom for atom, Ceo is at least as polarizable as benzene. A similar (but with a much worse basis set) estimate was obtained for the C70 cluster [32], which was found to be more polarizable than Ceo ... 

In the presence of a static, spatially uniform electric field Ea, the electronic cloud of atomic and molecular systems gets polarized. The energy, W, can be written as a Taylor series [1-3]... 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

Most properties of solids represent the response of the solid to some external electromagnetic field or mechanical force. The response of the electronic states to electromagnetic fields is so directly related to electronic structure that it is appropriate to discuss it first. We are interested in absorption and reflection of light as well as in the ordinary dielectric and diamagnetic properties of solids. When static or slowly varying electric fields act on a polar semiconductor, the two types of atoms in the semiconductor will move with respect to each other, giving a lattice... 

Derivatives of the dipole moment with respect to Qj can be expressed within a Cartesian reference frame via a similarity transformation, introducing atomic polar tensors (APTs) [13, 14], The connection between the latter and the electric shielding is obtained by means of the Hellmann-Feynman theorem. Within the Born-Oppenheimer approximation and allowing for the dipole length formalism, the perturbed Hamiltonian in the presence of a static external electric field E is given by Eqs. (6) and (35). 

The size of the fluorine atom allows the formation of a uniform and continuous sheath around the carbon-carbon bonds and protects them from attack, thus imparting chemical resistance and stability to the molecule. The fluorine sheath is also responsible for the low surface energy (18 dynes/cm)[ i and low coefficient of friction (0.05-0.08, static)[ i of PTFE. Another attribute of the imiform fluorine sheath is the electrical inertness (or non-polarity) of the PTFE molecule. Electrical fields impart only slight polarization to this molecule, so volume and surface resistivity are high. Table 1.1 summarizes the fundamental properties of PTFE, which represents the ultimate polymer among all fluoroplastics. 

So far we have been dealing with various forms of the "response" to displacements of atoms. In Section 6 also certain electric fields have been studied, we benefited from the fact that displacing atoms in GaAs generates dipoles and therefore electric fields all the reasonings of Section 6 were, however, limited to polar crystals and e.g. determination of static dielectric constant e as in Section 6.2 would be impossible in Ge or other homopolar substances. From the point of view of studying dielectric properties, the main drawback of Section 6 was our dependence upon the various displacement patterns the electric fields could not be varied at will, as an independent variable. The present Section summarizes the most recent applications of the DF which tend to fill this blank and to open the way to "direct" treatment of dielectric properties of semiconductors, within the framework of the Density Functional. They are the treatment of constant macroscopic electric field imposed from outside (Section 8.1) and "direct" evaluation. of the individual elements of the inverse dielectric matrix s ("q + +"g ) (Section 8.2). 

Molecules consisting of atoms with different values of the electronegativity are polar. The dipole moment of a chemical bonding is a vector and therefore, a compensation or increase of the bond moments in a molecule can be observed [1, 2], Furthermore, the overall dipole moment of a molecule depends on the life time of different conformations. By the dielectric method, only a very small orientation of the molecular dipoles and the time for its reorientation can be measured as static dielectric constant and relaxation time T, respectively. Thereby the static dielectric constant can be produced by switching off an external electrical field in different steps as demonstrated in Fig. 1. 

At the surface, however, the inversion symmetry of the bulk is broken. Electric dipole contributions to the nonlinear polarization become possible due to the spatial structure of the surface and due to the discontinuity of the normal component of the electric field at the surface. In the case of a nonlocal interaction, the polarization at a given position r depends on the external field of the surroundings (i.e, "spatial dispersion"). In most cases, however, one assumes for the sake of simplicity a local interaction, in which case the susceptibility is independent of the polarization in the surroimdings. If one assumes that the main reason for this nonlinear polarization is the generation of a strong (static) dipole field at the surface, then it becomes clear that it should be localized in the uppermost atomic layers down to a depth of 0.5-1.5 nm (Sipe et al. 1987). 

Derivation of the Brossel-Bitter formula. In a static magnetic field the 6 P level of mercury splits into three magnetic sub-states which are essentially equally spaced for fields less than 10 G. Thus the simple result presented above does not apply for the detection scheme used in the Brossel-Bitter experiment and equation (16.20) must therefore be modified. The magnetic dipole transition probabilities for a system with a multiplicity of equally spaced levels have been calculated quantum mechanically by Majorana (1932) and Rabi (1932). However, we prefer to return to our classical model in which the excited atoms are represented as electric dipole oscillators. When iT-polarized excitation is used, as in the Brossel-Bitter experiment, the axes of the dipoles at the instant of excitation are parallel to the z-direction. Under the combined influence of the static and rotating magnetic... 

Refs. [i] Bottcher CJF (1973) Theory of electric polarization Dielectrics in static fields, vol. 1. (1978) Dielectrics in time-dependent fields, vol. 2. Elsevier, Amsterdam [ii] Tide DR (2003) Dipole Moments. In Tide DR (ed) CRC handbook of chemistry and physics, 84til edn. CRC Press, Boca Raton, pp 9-42 - 9-51 [Hi] Miller TM (2003) Atomic and molecular polarizabilities. In Tide DR (ed) CRC handbook of chemistry and physics, 84th edn. CRC Press, Boca Raton, pp 10-163 -10-177 [ivJFred-erikse HPR (2003) Polarizabilities of atoms and ions in solids. In LideDR (ed) CRC handbook of chemistry and physics, 84til edn. CRC Press, Boca Raton, pp 12-17 -12-18... 

---