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The energy of a spherical metallic particle of radius R, charged with Z excess electrons, is simply Eₙ=E₀-ZW+Z^2e^2/2 (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+e^2/2 (R+a), and the electron affinity is A=W-e^2/2 (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) rₒ from atomic values for I and A; rₒ is the solution of the equation rₒ+a (rₒ) =e^2/ (I-A). The link between microcosm and macrocosm is further shown by the relationship ₂₎₇₄ₑₒ^{2} between the cohesive energy ₂₎₇ and the surface tension. These relationships are illustrated for atoms and small jellium spheres.
John P. Perdew (1988) studied this question.