Energetics of charged metallic particles: From atom to bulk solid

The energy of a spherical metallic particle of radius R, charged with Z excess electrons, is simply E_Z=E₀-ZW+Z²e²/2(R+a), where W is the bulk work function, e is the charge of one electron, and R+a is the radial centroid of the excess charge. Consequently, the ionization energy is I=W+e²/2(R+a), and the electron affinity is A=W-e²/2(R+a). These formulas apply even to the smallest microparticle, a single monovalent atom. Thus they may be used to estimate the bulk work function W=(I+A)/2 and density parameter (Wigner-Seitz radius) r_s from atomic values for I and A; r_s is the solution of the equation r_s+a(r_s)=e²/(I-A). The link between microcosm and macrocosm is further shown by the relationship ɛ_{coh≊σ4πrs²} between the cohesive energy ɛ_coh and the surface tension σ. These relationships are illustrated for atoms and small jellium spheres.