Polarisation electrons

If an atom or covalent molecule is placed in an electric field there will be a displacement of the light electron cloud in one direction and a considerably smaller displacement of the nucleus in the other direction (Figure 6.1 (b)). The effect of the electron cloud displacement is known as electron polarisation. In these circumstances the centres of negative and positive charge are no longer coincident. 

In the case of symmetrical molecules such as carbon tetrachloride, benzene, polyethylene and polyisobutylene the only polarisation effect is electronic and such materials have low dielectric constants. Since electronic polarisation may be assumed to be instantaneous, the influence of frequency and temperature will be very small. Furthermore, since the charge displacement is able to remain in phase with the alternating field there are negligible power losses. 

In the dielectric of a condenser the dipole polarisation would increase the polarisation charge and such materials would have a higher dielectric constant than materials whose dielectric constant was only a function of electronic polarisation. 

There is an important practical distinction between electronic and dipole polarisation whereas the former involves only movement of electrons the latter entails movement of part of or even the whole of the molecule. Molecular movements take a finite time and complete orientation as induced by an alternating current may or may not be possible depending on the frequency of the change of direction of the electric field. Thus at zero frequency the dielectric constant will be at a maximum and this will remain approximately constant until the dipole orientation time is of the same order as the reciprocal of the frequency. Dipole movement will now be limited and the dipole polarisation effect and the dielectric constant will be reduced. As the frequency further increases, the dipole polarisation effect will tend to zero and the dielectric constant will tend to be dependent only on the electronic polarisation Figure 6.3). Where there are two dipole species differing in ease of orientation there will be two points of inflection in the dielectric constant-frequency curve. 

For non-polar materials (i.e. materials free from dipoles or in which the dipoles are vectorially balanced) the dielectric constant is due to electronic polarisation only and will generally have a value of less than 3. Since polarisation is instantaneous the dielectric constant is independent of temperature and frequency. Power losses are also negligible irrespective of temperature and frequency. 

Relation of Structure to Electrical and Optical Properties It may be shown that for electron polarisation... 

The lowest dielectric constant (1.83-1.93) of any known plastics material. (It is to be noted that this is in spite of the fact that the dielectric constant is more than the square of the refractive index, indicating that polarisations other than electronic polarisations are present—see Section 6.3). 

Thus, in contrast to preceding MM approaches explicit treatment of electronic polarisability is integral to a semi-empirical QM approach and promises excellent prospects for quantitative theoretical modelling of carbohydrates across a range of condensed phase environments. The results of the PM3CARB-1 model do however indicate in line with classical force field approaches [65, 73] that perhaps greater... 

The electronic polarisability of a spherical atom may be calculated in a number of simplified ways. In the oldest approximation, an atom is regarded as a conductive sphere of radius R, when the polarisability may be shown to be 4k 0R3, a quantity that is closely related to the actual volume of a molecule. In the more realistic semi-classical Bohr model of a hydrogen atom, the application of a field normal to the plane of the electron orbit, radius R, will produce a small shift, — x, in the orbit, as shown in Fig. 2.2. To a first approximation the distance of the orbit from the nucleus will still be R and the dipole moment p. induced in the atom will have magnitude ex. At equilibrium, the external field acting on the electron is balanced by the component of the Coulombic field from the positive nucleus in the field direction ... 

We can understand how anisotropy of electronic polarisation arises in molecules in terms of a simple diatomic molecule, consisting of two similar atoms of radius R at separation L, in an applied field E. 

Equation (2.35), known as the Lorenz-Lorentz relation, provides a method of calculating the molecular polarisability from a macroscopic, observable quantity, the refractive index. We must make the proviso that we stay away from any resonant absorption frequency, where the refractive index is anomalously high. If the refractive index refers to optical frequencies, the polarisability a will be purely electronic in origin. In practice, electronic polarisabilities derived in this way are remarkably insensitive to temperature and pressure, even for highly condensed phases in which intermolecular forces must be large. This is illustrated for the particular case of xenon in Table 2.1. 

Optical detection of intermediates produced in the reactions of triplet carbonyl compounds with electron donors has some obvious limitations. However, the technique of CIDNP is proving particularly effective at elucidating the reaction pathways in these systems. The outstanding work of Hendriks et al. (1979) illustrates the power of the technique. Not only was the role of radical ions in the reactions of alkyl aryl ketones with aromatic amines defined but the rate constants for many of the processes determined. The technique has been used to show that trifluoracetyl benzene reacts with electron donors such as 1,4-diazabicyclo[2.2.2]octane and 1,4-dimethoxy-benzene by an electron-transfer process (Thomas et al., 1977 Schilling et al., 1977). Chemically induced dynamic electron polarisation (CIDEP) has been... 

An ensemble of electrons is said to be polarised if there is a preferential orientation of the electron spins. If there are N- electrons with spins parallel to a particular direction or axis of quantisation and N[ with spins antiparallel to that direction, then the component of the electron polarisation vector P = (Px,Py,Pz) in that direction is defined by... 

The magnetic coil shown in figs. 2.15 and 2.16 was used to orient the electron polarisation vector P parallel to the axis of the analysing target—Mott detector system. The deflection system is part of the differential pumping stage which is necessary for the maintenance of the required ultra-high vacuum in the source chamber. 

Fig. 2.22. Schematic of the polarised electron—polarised atom scattering apparatus of McClelland et al. (1986, 1989).

The reduced matrix element of the two-electron polarisation potential (7.115,7.116) is... 

Due to parity conservation A a)x = 0 for a = 45° and 135°. These parameters can be related to the state multipoles T j)) (8.22) describing the atomic state, which depend on the electron polarisation components as follows (Bartschat et al, 1981)... 

The continuum electrostatic approach has been considered also appropriate for studying biomolecular systems when electronic polarisation effects, typically neglected by the additive pair-wise potentials commonly use in MD and MC, are dominant in relation to the conformational flexibility, and when changes in protonation states of tritable sites [193-198] or electron-proton coupling phenomena [199-204] occur. 

As pointed out before, electronic polarisation also presents a challenge. Basically this is because the QM region is polarised while the MM region lacks in explicit polarisation. Efforts to incorporate a polarised MM model into a... 

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