10.1 Nearly Stoichiometric Metal Halide Clusters

A salt like NaCl is composed of closed shell ions, Na ⁺ and Cl ^-, with electronic configurations similar to those of the rare gas atoms Ne (1 s ² 2 s ² 2 p ⁶) and Ar (1 s ² 2 s ² 2 p ⁶ 3 s ² 3 p ⁶), respectively. The cohesion in the crystal is explained as a balance between attractive and repulsive forces between the ions. The attractive interaction comes from the Coulombic attraction between anions and cations, which tend to be nearest neighbors. In contrast, cation-cation and anion-anion repulsion prevents these from being nearest neighbors. Although the electrostatic interaction between anions and cations is attractive, the overlap between the closed electronic shells leads to a strong short-range repulsion arising from the Pauli exclusion principle, and sets a minimal distance of approach between nearest neighbors. These effects can be taken into account by an interionic potential of the form

(10.1)

where r _ij indicates the separation between two ions i and j. The second term represents the short-range repulsion between ions with closed electronic shells, and the first one is the long range Coulombic interaction (attraction or repulsion) between point charges of magnitudes Z _ie and Z _je ( Z _i and Z _j can be positive or negative). The parameters A and ? are usually determined...