Electronic Polarizabilities

The products of a large number of reactions of many types are correctly predicted by the hard-soft interaction principle. Some examples are as follows. 

In the first of these reactions, I is softer than F and As is softer than P. Therefore, the exchange takes place to provide a more suitable match of hard-soft properties. In the second reaction, Mg2+ is a small, hard ion, whereas Ba2+ is much larger and softer. The O2- ion bonds better to Mg2+, whereas S2-bonds better with Ba2+. The hard-soft interaction principle predicts correctly the direction of many reactions of diverse types. 

Although many applications of the hard-soft interaction will be presented in later chapters, two additional applications will be illustrated here. First, consider the interaction of the Lewis acid Cr3+ with the Lewis base SCN, which could donate an electron pair from either the S or N atom  

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. 

In Chapter 6, the polarizability of molecules was considered as one factor related to both London and dipole-induced dipole intermolecular forces. The data shown in Table 9.6 confirm many of the observations that can be made about physical properties. For example, in the case of F2, Cl2, and Br2, the London forces that arise from the increase in polarizability result in a general increase in boiling point. 

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We note that the expression in brackets is just the b c tensor element of the electronic polarizability in the ground electronic state,, (ttj)- Thus... 

Since the vibrational eigenstates of the ground electronic state constitute an orthonomial basis set, tire off-diagonal matrix elements in equation (B 1.3.14) will vanish unless the ground state electronic polarizability depends on nuclear coordinates. (This is the Raman analogue of the requirement in infrared spectroscopy that, to observe a transition, the electronic dipole moment in the ground electronic state must properly vary with nuclear displacements from... 

The molecular electronic polarizability is one of the most important descriptors used in QSPR models. Paradoxically, although it is an electronic property, it is often easier to calculate the polarizability by an additive method (see Section 7.1) than quantum mechanically. Ah-initio and DFT methods need very large basis sets before they give accurate polarizabilities. Accurate molecular polarizabilities are available from semi-empirical MO calculations very easily using a modified version of a simple variational technique proposed by Rivail and co-workers [41]. The molecular electronic polarizability correlates quite strongly with the molecular volume, although there are many cases where both descriptors are useful in QSPR models. 

The refractive index of a medium is the ratio of the speed of light in a vacuum to its speed in the medium, and is the square root of the relative permittivity of the medium at that frequency. When measured with visible light, the refractive index is related to the electronic polarizability of the medium. Solvents with high refractive indexes, such as aromatic solvents, should be capable of strong dispersion interactions. Unlike the other measures described here, the refractive index is a property of the pure liquid without the perturbation generated by the addition of a probe species. 

Hammett-Taft sigma constants Electron density TT-Bond reactivity Electron polarizability Dielectric constant Dipole moments Ionization potential Electron affinity... 

Tanner and Thakkar (12) have obtained ai,(oo) = 3.66325789. Then it is possible to deduce the continuum contribution of, = 0.8367, i.e. about 18.6% of the total electronic polarizability. 

FORMALISMS FOR THE EXPLICIT INCLUSION OF ELECTRONIC POLARIZABILITY IN MOLECULAR MODELING AND DYNAMICS STUDIES... 

Electronic polarizability is often included in force fields via the use of induced dipoles. Assuming that hyperpolarization effects are absent, the induced dipoles respond linearly relative to the electric field. In this case, the induced dipole p on an atom is the product of the total electric field E and the atomic polarizability tensor a. 

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