Equilibrium Radii of Atoms

The minimum of the potential curve of vdW interaction of two isolated atoms corresponds to the sum of their equilibrium radii, Since different interatomic potentials are used to calculate the vdW energy, the reported Re vary considerably, and are sometimes regarded as pure adjustable parameters in molecular-mechanics calculations, without any strict physical meaning. However, ab initio calculations show that the equilibrium vdW radii are physically meaningfiil, namely, they define the surface enclosing up to 99 % of the electron density of an atom or molecule [110-112], They also define the distance at which the steric repulsion energy becomes comparable to ambient thermal energy, [113], 

The difference between the equilibrium radii of identical elements used by different authors in the molecular mechanics calculations is very large (see Table S4.15) because these values were optimized for narrow ranges of compounds. Allinger et al. [49,114,115] have calculated the vdW radii for all of the atoms in the Periodic Table using experimental data for carbon and rare gases Table S4.16, upper lines. 

It is interesting to compare Allinger s results with Rm calculated from the available interatomic distances in of MXn molecules by Eq. 4.20, depending significantly on the M-X bond polarity. This dependence was described in [53] by an equation, similar to that suggested earlier (but for different purposes) by Blom and Haaland 

Tabulated equilibrium radii are close to the experimental radii of atoms in the M2 molecules of Groups 2 and 12, where bonds are close to the vdW type, or in the vdW complexes Rg A and M Rg calculated in [14, 18]. An important point in the latter case is that the distances in heteronuclear vdW molecules turned out to be larger than sums of the vdW radii because of the polarization effects, e.g. the loosening influence of the smaller atoms on the electron polarizability of the larger one  

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