Shell-correction method for calculating the binding energy of metal clusters: Application to multiply charged anions

Utilizing the nuclear-physics concept of separating, as a function of size, the total energy of a finite system into two parts, a smooth contribution and a shell correction, we introduce a method of calculating the binding energy of metal clusters. The method consists of a determination of the smooth part of the total energy from an extended Thomas Fermi approach to density-functional theory, and of superimposing on it a shell correction introduced through the kinetic-energy contribution. While circumventing a self-consistent iterative solution of the effective single-particle Kohn-Sham equations, the present method yields results in excellent agreement with such self-consistent calculations, but with considerable savings in computation time, thus allowing for an efficient approach for accurate systematic investigations of cluster properties for a wide range of sizes. As an application of the method, we study energetics and decay modes of multiply charged anionic metal clusters. Singly charged anions are stable for all sizes, but multiply charged negative ions are stable against spontaneous electron decay only above certain critical sizes. Below the border of stability, the cluster anions are metastable against electron tunneling through a Coulombic barrier. Lifetimes for such decay processes are estimated. Fission channels, which may compete with electron autodetachment, are studied for the case of doubly charged anions.