Structure and bonding in small neutral alkali halide clusters

The structural and bonding properties of small neutral alkali halide clusters, ${\mathrm{}\left(\mathrm{AX}\right)\mathrm{}}_n$ with $n<~10,$ $A$$={\mathrm{Li}}^{+}{,\mathrm{N}\mathrm{a}}^{+}{,\mathrm{K}}^{+}{,\mathrm{R}\mathrm{b}}^{+},$ and $X={\mathrm{F}}^{\mathrm{-}}{,\mathrm{C}\mathrm{l}}^{\mathrm{-}}{,\mathrm{B}\mathrm{r}}^{\mathrm{-}}{,\mathrm{I}}^{\mathrm{-}},$ are studied using the ab initio perturbed ion (PI) model and a restricted structural relaxation criterion. A trend of competition between rocksalt and hexagonal ringlike isomers is found and discussed in terms of the relative ionic sizes. The main conclusion is that an approximate value of $r_C{/r}_A=0.5\mathrm{}$ (where $r_C$ and $r_A$ are the cationic and anionic radii) separates the hexagonal from the rocksalt structures. The classical electrostatic part of the total energy at the equilibrium geometry is enough to explain these trends. The magic numbers in the size range studied are $n=4,$ 6, and 9, and these are universal since they occur for all alkali halides and do not depend on the specific ground-state geometry. Instead those numbers allow for the formation of compact clusters. Full geometrical relaxations are considered for $(\mathrm{LiF}{)}_n$ $(n=3\mathrm{}–7)$ and ${\mathrm{}\left(\mathrm{AX}\right)\mathrm{}}_3$ clusters, and the effect of Coulomb correlation is studied in a few selected cases. These two effects preserve the general conclusions achieved thus far.