Internuclear distances, and atomic radii

It is valuable to be able to predict the internuclear distance of atoms within and between molecules, and so there has been much work done in attempting to set up tables of "atomic radii" such that the sum of two will reproduce the internuclear distances. Unfortunately there has been a proliferation of these tables and a bewildering array of terms including bonded, nonbonded, ionic, covalent, metallic, and van der Wauls radii, as well as the vague term atomic radii. This plethora of radii is a reflection of the necessity of specifying what is being measured by an atomic radius. Nevertheless, it is possible to simplify the treatment of atomic radii without causing unwarranted errors. 

Successor complex0 (A B) Assumed ionic and atomic radii 1 Assumed internuclear distance R AGFC(kcai mole r ) X ... 

Isolated atoms show spherical symmetry, and it is natural to model atoms by spheres of some suitably defined radii. The potential energy of interaction between two atoms rises very sharply at short internuclear distances during atomic collisions, not unlike the potential energy increase in the collisions of hard, macroscopic bodies. In a somewhat crude, approximate sense, atoms behave as hard balls. This analogy can be used for a simple molecular model where atoms are represented by hard spheres. Once a choice of atomic radii is made, the approximate atomic surfaces can be defined as the surfaces of these spheres. 

Homonuclear pairs of noble gas atoms well depths, Dm minimum-energy internuclear distances, and van der Waals radii, rw. 

The radii are so ohosen that their sums represent average internuclear distances for bonded atoms in molecules and crystals at room temperature. The atoms carry out thermal oscillations, which cause the internuclear distances to vary about their average values. At room temperature these are only slightly different from the values corresponding to the minima in the potential energy functions. 

It is, of course, impossible to measure the absolute size of an isolated atom its electron cloud extends to infinity. It is possible to calculate the radius within which (say) 95% of its total electron cloud is confined but most measures of atomic/ionic size are based upon experimental measurements of internuclear distances in molecules and crystals. This means that the measurement is dependent on the nature of the bonding in the species concerned, and is a property of the atom or ion under scrutiny in a particular substance or group of substances. This must always be borne in mind in making use of tabulated radii of atoms or ions. The most important dictum to remember is that radii are significant only insofar as they reproduce experimental internuclear distances when added together. The absolute significance of a radius is highly suspect,... 

The determination of the sizes of ions has been a fundamental problem in inorganic chemistry for many years. Many indirect methods have been suggested for apportioning the internuclear distance between two ions, relatively easy to obtain, into cationic and anionic radii. Although these have been ingenious ai provide insight into atomic properties, they are no longer necessary. 

The concept of atomic or ionic size is one that has been debated for many years. The structure map of Figure 1 used the crystal radii of Shannon and Prewitt and these are generally used today in place of Pauling s radii. Shannon and Prewitt s values come from examination of a large database of interatomic distances, assuming that internuclear separations are given simply by the sum of anion and cation radii. Whereas this is reasonably true for oxides and fluorides, it is much more difficult to generate a self-consistent set of radii for sulfides, for example.A set of radii independent of experimental input would be better. The pseudopotential radius is one such estimate of atomic or orbital size. 

Table 9.3. Heteronuclear pairs of noble gas atoms well depths, Dm minimum-energy internuclear distances, Rta, and the sum of their van der Waals radii, rw(A) + r y(B). ...

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