Distances and Atomic Radii

It is valuable to be able to predict the intemuclear 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 intemuclear 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 Waals 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. 

Although the van der Waals radius of an atom might thus seem to be a simple, invariant quantity, such is not the case. The size of an atom depends upon how much it is compressed by external forces and upon substituent effects. For example, in XeF4 

Although we must therefore expect van der Waals radii to vary somewhat depending upon the environment of the atom, we can use them to estimate nonbonded distances with reasonable success. Table 8.1 lists the van der Waals radii of some atoms. 

Ionic radii are discussed thoroughly in Chapters 4 and 7. For the present discussion it is only necessary to point out that the principal difference between ionic and van der Waals radii lies in the difference in the attractive force, not the difference in repulsion. The interionic distance in LiF, for example, represents the distance at which the repulsion of a He core (Li+) and a Ne core (F ) counterbalances Ihe strong electrostatic or Madelung force. The attractive energy for Li+F is considerably over 500 kj mol-1 and the London energy of He-Ne is of the order of 4 kJ mol 1. The forces in the LiF crystal are therefore considerably greater and the interionic distance (201 pm) is less lhan expected for the addition of He and Ne van der Waals radii (340 pm). 

The intemudear distance in the fluorine molecule is 142 pm, which is shorter than the sum of two van der Waals radii. The difference obviously comes from the fact that the electron clouds of the fluorine atoms overlap extensively in the formation of the F—F bond whereas little overlap of the van der Waals radii occurs between Ihe molecules 

Covalent Radii The internuclear distance in the fluorine molecule is 142 pm. which is shorter than the 

---

The corrections which have to be applied to the ionic radii are very large in molecules with high ionic charges and lead to very considerable contractions, but, when they are applied, there is agreement with the values observed for many compounds. Where a compound has a much smaller distance than the sum of the ionic radii, this does not prove that the compound concerned is not composed of ions the contraction which takes place leads to a merging of values for the ionic and atomic radii. 

Predict the internudc.tr distance in the following molecules and lintices by use of the appropriate van dcr Wauls, ionic, covuleni. and atomic radii. In those cases where two or more sets of values are applicable, determine which yield ihc results closest to the experimental values... 

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

In the author s paper 68) it was shown that changing the nature of the metal catalyst (with the lattice A1 and A3) greatly affects the rate of dehydrogenation and the energy of activation e. A relationship between e and the interatomic distances or atomic radii is observed, as one should expect from the multiplet theory. This relationship proves to be linear (see Fig. 7). 

Using partial atomic charges in eq. (14.59) is often called the generalized Bom model, which has been used especially in connection with force field methods in the Generalized Born/Surface Area (GB/SA) model. In this case, the Coulomb interaction between the partial charges (eq. (2.20)) is combined with the Bom formula by means of a function fy depending on the intemuclear distance and Born radii for each of the two atoms,and aj. 

In crystal chemistry, particles sizes are represented by ionic and atomic radii. Admission of such size is related to the assumption that the ions and the atoms have spherical shapes and a determined volume, impenetrable to others ions or atoms. Thus, the inter-ionic or inter- atomic distance that is established between two particles in a network, i.e., the distance between the mass centers of these particles is equal to the sum of radius of the two particles. Based on this assumption certain determinations to establish the ionic and atomic radii are therefore possible. However, aiming to determine the size of the constitutive partieles of erystalline lattiee/networks numerous experimental or ealeulation methods have been proposed the present discussion follows (Chiriac-Putz-Chiriac, 2005). 

Owing to the many factors which influence interatomic distances, it is difficult to proportion such distances into atomic radii. This problem has been extensively discussed by Shannon and Prewitt and by Shannon. ... 

The wave function T i oo ( = 11 / = 0, w = 0) corresponds to a spherical electronic distribution around the nucleus and is an example of an s orbital. Solutions of other wave functions may be described in terms of p and d orbitals, atomic radii Half the closest distance of approach of atoms in the structure of the elements. This is easily defined for regular structures, e.g. close-packed metals, but is less easy to define in elements with irregular structures, e.g. As. The values may differ between allo-tropes (e.g. C-C 1 -54 A in diamond and 1 -42 A in planes of graphite). Atomic radii are very different from ionic and covalent radii. 

The atom radius of an element is the shortest distance between like atoms. It is the distance of the centers of the atoms from one another in metallic crystals and for these materials the atom radius is often called the metal radius. Except for the lanthanides (CN = 6), CN = 12 for the elements. The atom radii listed in Table 4.6 are taken mostly from A. Kelly and G. W. Groves, Crystallography and Crystal Defects, Addison-Wesley, Reading, Mass., 1970. 

Linus Pauling, Atomic Radii and Interatomic Distances in Metals, J. Am. Chem. 

---