Crystallographic van der Waals Radii

In principle, the vdW radius of an atom must depend on its effective charge. However, Pauling [82] found that vdW radius of a nonmetal coincide with its anionic radius, inasmuch as the bonded atom presents the same face to the outside world in directions away from its bond as the ion does in aU direction and used this rule to suggest vdW radii for some elements. He also noticed that vdW radii exceed the covalent radii (r) of the same elements by S 0.8 A Bondi used this rule in constructing his system of radii (he assumed S = 0.76 A), as well as some other physical properties (e.g. critical volumes). This value can be deduced from covalent radii using the equations 

324 A (from Eq. 4.16 [82]) or 0.460 A (from Eq. 4.17 [75,87]). If upon a molecule-to-metal phase transition R decreases by the same amount, then R — r will be twice this, i.e. 0.78 0.15 A. For compounds with Ac = 4 the difference between vdW and covalent radii is 0.70 0.07 A [89]. The crystallographic vdW radii of nonmetals obtained by different authors from organic or inorganic compounds are very close, see Table S4.11. 

This refers to the coordination number Ac = 1. If these molecules are fused into a close-packed (fee or hep) metallic stmeture, Ac increases to 12 while the number of valence electrons remains the same, hence the overlap of each pare of spheres will diminish, 

Experiments show that a phase transition of molecular solid into metal is indeed accompanied by shortening of intermolecular and a simultaneous elongation of intramolecular bonds, so that each coordination number is characterized by the R and r values of its own. Thus, Eq. 4.19 can be solved to determine the vdW radii of metals, listed in Table S4.13 [102]. 

By similar reasoning (Fig. 4.6), vdW radii of metals can be estimated fromM-X bond distances d. 

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