Core electrons Covalent radius

The empirical concept of atomic radius has found an explanation in quantum chemistry. Thus, ab initio calculations have shown that the radial tunction of electron density of an atom has a minimum, which gives a physically meaningful boundary surface between the inner (core) and outer (valence) regions [107-112]. The distance from the nucleus at which the chemical potential is equal to the electrostatic potential of a free atom, has been calculated for a number of elements and proved to be proportional to the covalent radius [113]. The general theory of atoms in molecules (AIM), developed by Bader, has demonstrated that atoms in molecules or solids can be divided by physically meaningful boundary surfaces, rather than regarded as extending to infinity [114-117]. 

The sodium atom has an outer 3s electron and a neon core. Since the 3s electron is the outermost electron, and since it is shielded from the nuclear charge by the core electrons, it contributes greatly to the size of the sodium atom. The sodium cation, having lost the outermost 35 electron, has only the neon core and carries a charge of 1+. Without the 35 electron, the sodium cation (ionic radius = 95 pm) becomes much smaller than the sodium atom (covalent radius = 186 pm). The trend is the same with all cations and their atoms, as shown in Figure 8.12 t. 

The Octet Rule. To the isomorphism exhibited in Table 1 may be added the radius-ratio rules. The statement in crystal chemistry that rattling is bad , that the number of anions about a cation should not be so great as to create a cavity larger than the cation 72>, corresponds to the statement in covalent chemistry that the number of electron-pairs about an atomic core should not be so great as to exceed the number of low-lying, available, valence-shell orbitals. 

Sidgwick s discussion raises an important question What are the effective sizes and shapes of atoms in molecules From the viewpoint of the electride ion model of electronic structure, Sigdwick s circles for the fluoride ions in the first column of Fig. 15 are the wrong shape, if nearly the right overall size. In the electride-ion model a fluoride ion is composed of (approximately) spherical domains, but is not itself spherical, in the field of a cation, Fig. 16. Fig. 17 illustrates, correspondingly, the implied suggestion that, on the assumption that non-bonded interactions are not limiting, the covalency limits of an atom will be determined by the radius of the atom s core and by the effective radii, not of the overall van der Waals envelopes of the coordinated ions but, rather, by the radii of the individual, shared electron-pairs. 

The simplest model of a covalent bond is based on an electrostatic point-charge simulation of overlapping spherical valence-electron charge clouds that surround monopositive atomic cores. For a homonuclear pair of atoms with radius r and internuclear distance d, the dissociation energy D is calculated from... 

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