Inert gases overlap interaction

The Iluorite structure of Cah 2 was given in Section 13-A. Use the appropriate inert-gas overlap interaction from Table 13-3 (use the values based upon Table 12-2) and the electrostatic energy from Table 1.3-1 to estimate the nearest-neighbor distance of CaFa and compare with experiment. You can ignore the d term if you like it makes only a one-percent correction. Compare also with the sum of ionic radii. 

Neon, and the elements directly below it in the periodic table or the Solid State Table, form the simplest closed-shell systems. The electronic structure of the inert-gas solid, which is face-ccntercd cubic, is essentially that of the isolated atoms, and the interactions between atoms are well described by an overlap interaction that includes a correlation energy contribution (frequently described as a Van der Waals interaction). The total interaction, which can be conveniently fitted by a two-parameter Lennard-Jones potential, describes the behavior of both the gas and the solid. Electronic excitations to higher atomic states become excitons in the solid, and the atomic ionization energy becomes the band gap. Surprisingly, as noted by Pantelides, the gap varies with equilibrium nearest-neighbor distance, d, as d... 

Their weak interatomic interaction is responsible for the condensation of the normal inert gases into solids. Atoms of normal inert gas are brought together until the repulsive terms in the overlap interaction prevent further contraction. The attraction favors a close-packed structure, and all of the normal inert gases form face-centered cubic lattices. These two contributions to the total interaction will remain almost the same in the ionic crystals, but with added Coulomb interactions, so it is desirable to understand all of these contributions with some care. 

We next consider the interactions at the second level, in terms of Lennard-Jones potentials. We considered the electronic structure of a system like KCI by beginning with the inert gas Ar and transferring protons between alternate nuclei to produce K and Cl. Certainly, the extra proton will reduce the size of the K ion in comparison to Ar, but the Cl" ion will be correspondingly expanded, and we may hope that the Cl" overlap interaction will not be changed too much. 

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