LIQUID-DROP MODEL FOR CHARGED SPHERICAL METAL-CLUSTERS

The average ground-state energy of a charged spherical metal cluster w ith N atoms and z excessive valence electrons, i.e., with net charge Q = -ez and radius R = r(s)N(1/3), is presented in the liquid drop mode l (LDM) expansion E(N, z) = (2/3)+a(c)N(1/3)+a(0)(z)+a(-1)(z)N--1/3+O( N--2/3). We derive analytical expressions for the leading LDM coeffici ents a(v) a(s), a(c), and, in particular, for the charge dependence of the further LDM coefficients a(0) and a(-1), using the jellium model and density functional theory in the local density approximation. We o btain for the ionization energy I(R) = W+alpha(e(2)/R)+O(R(-2)), with the bulk work function W = [Phi(+infinity)-Phi(0)]-e(b), given first b y Mahan and Schaich in terms of the electrostatic potential Phi and th e bulk energy per electron e(b), and a new analytical expression for t he dimensionless coefficient alpha. We demonstrate that within classic al theory alpha = 1/2 but, in agreement with experimental information, alpha tends to similar to 0.4 if quantum-mechanical contributions are included. In order to test and confirm our analytical expressions, we discuss the numerical results of semiclassical density variational ca lculations in the extended Thomas-Fermi model. (C) 1996 Academic Press , Inc.