Effective atomic radius

The Lewis dot formalism shows any halogen in a molecule surrounded by three electron lone pairs. An unfortunate consequence of this perspective is that it is natural to assume that these electrons are equivalent and symmetrically distributed (i.e., that the iodine is sp3 hybridized). Even simple quantum mechanical calculations, however, show that this is not the case [148]. Consider the diiodine molecule in the gas phase (Fig. 3). There is a region directly opposite the I-I sigma bond where the nucleus is poorly shielded by the atoms electron cloud. Allen described this as polar flattening , where the effective atomic radius is shorter at this point than it is perpendicular to the I-I bond [149]. Politzer and coworkers simply call it a sigma hole [150,151]. This area of positive electrostatic potential also coincides with the LUMO of the molecule (Fig. 4). 

Chemically they are extremely inert, being much more un-reactive even than the fluoroacetates. The inertness of the fluorocarbons and their nearly perfect physical properties arise from the strength of the F—C linkage and from their compact structure. The effective atomic radius of covalently bound fluorine is 0-64 A., which although greater than hydrogen (0-30) is smaller than other elements, e.g. Cl 0-99 A., Br 1-14 A. 

The final atomic radii equation that has to be solved in terms of Mulliken electronegativity is authors formulation above. However, before to arrive at the effective atomic radius equation, it should be first transformed according to the forms of atomic potential and associate homogeneous density. Performing this substitutions for the main ingredients of S-DFT electronegativity expression (4.354) we get successively (Putz, 2012b,c) ... 

What are the values of the effective atomic radius of neon, argon, krypton, and xenon given by the information in the preceding exercise ... 

Unfortunately, atomic radius is hard to define. We have seen that atomic orbitals extend, in principle, to infinity. Although the probability of finding an electron decreases with increasing distance from the nucleus, there is always nonzero probability of finding an electron at very large distances from the nucleus. Thus, an atom has no precise outer boundary. We might describe an effective atomic radius as, say, the distance from the nucleus within which 95% of the electron charge density is found, but this distance cannot be measured experimentally. 

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