Theoretical study of the stability of X ⁿ _N (n=−1, 0, +1, +2; X=Ag, Cu;N≤25) clusters as a function of size using a non-local density functional formalism

Abstract

The spherical jellium model and self-consistent Weighted Density Approximation (WDA) to density functional theory have been used to study the stability of X ⁿ _N (n=−1, 0, +1, +2; X=Ag, Cu;N≤25) clusters. The calculated magic numbers coincide with the observed ones. The first (IP1) and second (IP2) ionization potentials of Ag _N and Cu _N as a function of size show the typical oscillations induced by the electronic shell-filling effect. IP1 of Cu _N is about 0.5 eV higher than IP1 of Ag _N in the range studied (N≤25). For both Cu _N and Ag _N , IP1 appears to converge well towards the respective experimental values of the work function. The use of WDA allows us to obtain bound negative clusters of small size or with a nearly empty external shell, which is not possible using the Local Density Approximation (LDA) [1, 2]. However the electron affinity of X _N clusters obtained as the difference of energies of the neutral and the negatively charged clusters, becomes negative forN=2, 3 and 8 (very close to zero forN=8), revealing that WDA needs further refinements.