The ionization potentials (IPs) of aluminum Al (clustersN) are investigated using density functional calculations based on the plane-wave basis set and the projector-augmented wave method. We discuss the size dependence of the IP in relation to the electron affinity, the chemical hardness of both the small-sized and large cuboctahedral AlN containing up to 923 atoms and compare the computational results with other models of Wood and Perdew based on the jellium model. We show that the IP and electron affinity of large clusters in this size region can be extrapolated to the value of the work function for the bulk aluminum. Expressions of the higher-order IP of metallic clusters are derived by the extension of the Perdew model. We discuss the IP of a collective system of metallic clusters as a simple model of clusters on a thin film in the framework of the Perdew model. The critical size of superconductivity of aluminium cluster is discussed by using the present results of the average energy-level spacing. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
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