Polarizability distortion

Consider the interaction of a neutral, dipolar molecule A with a neutral, S-state atom B. There are no electrostatic interactions because all the miiltipole moments of the atom are zero. However, the electric field of A distorts the charge distribution of B and induces miiltipole moments in B. The leading induction tenn is the interaction between the pennanent dipole moment of A and the dipole moment induced in B. The latter can be expressed in tenns of the polarizability of B, see equation (Al.S.g). and the dipole-mduced-dipole interaction is given by... 

The spherical shell model can only account for tire major shell closings. For open shell clusters, ellipsoidal distortions occur [47], leading to subshell closings which account for the fine stmctures in figure C1.1.2(a ). The electron shell model is one of tire most successful models emerging from cluster physics. The electron shell effects are observed in many physical properties of tire simple metal clusters, including tlieir ionization potentials, electron affinities, polarizabilities and collective excitations [34]. 

Polarizability (Section 4 6) A measure of the ease of distortion of the electric field associated with an atom or a group A fluonne atom in a molecule for example holds its electrons tightly and is very nonpolanzable Iodine is very polanz able... 

In order for dipole—dipole and dipole-iaduced dipole iateractioas to be effective, the molecule must coataia polar groups and/or be highly polarizable. Ease of electronic distortion is favored by the presence of aromatic groups and double or triple bonds. These groups frequently are found ia the molecular stmcture of Hquid crystal compouads. The most common nematogenic and smectogenic molecules are of the type shown ia Table 2. 

Polarizability describes the ease of distortion of the electron cloud of the attacking atom of the nucleophile. Again, since the S f2 process requires bond formation by an electron pair from flie nucleophile, the more easily distorted the electric field of the atom, the higher is its nucleophilicity. Polarizability increases going down and to the left in the periodic table. 

These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa. By means of Koopmann s theorem (Section 3.4) the hardness is related to the HOMO-LUMO energy difference, i.e. a small gap indicates a soft molecule. From second-order perturbation theory it also follows that a small gap between occupied and unoccupied orbitals will give a large contribution to the polarizability (Section 10.6), i.e. softness is a measure of how easily the electron density can be distorted by external fields, for example those generated by another molecule. In terms of the perturbation equation (15.1), a hard-hard interaction is primarily charge controlled, while a soft-soft interaction is orbital controlled. Both FMO and HSAB theories may be considered as being limiting cases of chemical reactivity described by the Fukui ftinction. 

Remembering that the polarizabilities are expressed in units of it follows that the largest positive eigenvalue corresponds to the energetically most favorable second-order bond distortion, and the type... 

The dispersion forces that act between atoms of the noble gases depend on the polarizabilities of their electron clouds. The total electron counts for these atoms are 10 for neon and 54 for xenon. When two atoms approach each other, the smaller electron cloud of neon distorts less than the larger electron cloud of xenon, as a molecular picture illustrates ... 

Cul) is not due to point defects but to partial occupation of crystallographic sites. The defective structure is sometimes called structural disorder to distinguish it from point defects. There are a large number of vacant sites for the cations to move into. Thus, ionic conductivity is enabled without use of aliovalent dopants. A common feature of both compounds is that they are composed of extremely polarizable ions. This means that the electron cloud surrounding the ions is easily distorted. This makes the passage of a cation past an anion easier. Due to their high ionic conductivity, silver and copper ion conductors can be used as solid electrolytes in solid-state batteries. 

Based on the ionic radii, nine of the alkali halides should not have the sodium chloride structure. However, only three, CsCl, CsBr, and Csl, do not have the sodium chloride structure. This means that the hard sphere approach to ionic arrangement is inadequate. It should be mentioned that it does predict the correct arrangement of ions in the majority of cases. It is a guide, not an infallible rule. One of the factors that is not included is related to the fact that the electron clouds of ions have some ability to be deformed. This electronic polarizability leads to additional forces of the types that were discussed in the previous chapter. Distorting the electron cloud of an anion leads to part of its electron density being drawn toward the cations surrounding it. In essence, there is some sharing of electron density as a result. Thus the bond has become partially covalent. 

As was discussed in Chapter 6, the electronic polarizability, a, of species is very useful for correlating many chemical and physical properties. Values of a are usually expressed in cm3 per unit (atom, ion, or molecule). Because atomic dimensions are conveniently expressed in angstroms, the polarizability is also expressed as A3, so lCT24cm3 = 1 A3. The polarizability gives a measure of the ability of the electron cloud of a species to be distorted so it is also related to the hard-soft character of the species in a qualitative way. Table 9.6 gives the polarizabilities for ions and molecules. 

However, for other reactions an opposite trend is observed. There are undoubtedly several factors involved, which include F forming the strongest bridge but I being the best "conductor" for the electron being transferred because it is much easier to distort the electron cloud of I- (it is much more polarizable and has a lower electron affinity). Therefore, in different reactions these effects may take on different weights, leading to variations in the rates of electron transfer that do not follow a particular order with respect the identity of the anion. 

Further work on long polyenes, including vibrational distortion, frequency dispersion effects and electron correlation, would be important for evaluating more accurate asymptotic longitudinal polarizabilities and hyperpolarizabilities. 

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