Although the underlying all-electron calculations employed the correct local density approximation for exchange and correlation, the pseudopotential calculations for solids inadvertently used the local field correction for exchange alone. The corrected universal ͑U͒ and individual ͑I͒ pseudopotential parameters are given here.
We report the first reliable theoretical calculation of the quantum size correction c which yields the asymptotic ionization energy I(R)=W+(12+c)/R+O(R−2) of a simple-metal cluster of radius R. Restricted-variational electronic density profiles are used to evaluate two sets of expressions for the bulk work function W and quantum size correction c: the Koopmans expressions, and the more accurate and profile-insensitive ΔSCF expressions. We find c≈−0.08 for stabilized (as for ordinary) jellium, and thus for real simple metals. We present parameters from which the density profiles may be reconstructed for a wide range of cluster sizes, including the planar surface. We also discuss how many excess electrons can be bound by a neutral cluster of given size. Within a continuum picture, the criterion for total-energy stability of a negatively charged cluster is less stringent than that for existence of a self-consistent solution.
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