Energetics, structure and excess electrons in small sodium-chloride clusters

The structure and energetics of stoichiometric (NaCl)n, 1⩽n⩽4, clusters, and of halide-deficient clusters in the sequence Na4Clm, 0 ⩽m⩽3, are studied using local-spin-density functional calculations, with and without exchange-correlation gradient corrections. The energy optimized structures of (NaCl)n clusters for 1⩽n⩽3 are two-dimensional converting to a three-dimensional cuboid for n = 4. The optimal structures of Na4Cl3 and Na4Cl2 are three-dimensional, deriving from that of the stoichiometric (NaCl)4 parent cluster, with the excess electrons substituting for the missing halide atoms. The optimal structure of Na4Cl is two-dimensional with the metal ions forming an approximate rhombus, and the chlorine ion capping one of the edges. In analogy with color centers in bulk ionic crystals, the excess electrons in the halogen-deficient clusters occupy energy levels which are split from the bottom of the unoccupied ‘conduction band’ of (NaCl)4. Analysis of the electronic spatila distributions and participation ratios indicates that the excess electrons are of a more delocalized nature in comparison with the electrons occupying the p-like ‘valence band’.