METAL-CLUSTER IONIZATION-ENERGY - A PROFILE-INSENSITIVE EXACT EXPRESSION FOR THE SIZE EFFECT

The ionization energy of a large spherical metal cluster of radius R i s l(R) = W + (1/2 + c)/R, where W is the bulk work function and c appr oximate to -0.1 is a material-dependent quantum correction to the elec trostatic size effect. We present ''Koopmans'' and ''displaced-profile change-in-self-consistent-field'' expressions for W and c within the ordinary and stabilized-jellium models. These expressions an shown to be exact and equivalent H hen the exact density profile of a large neu tral cluster is employed; these equivalences generalize the Budd-Vanni menus theorem. With an approximate profile obtained from a restricted variational calculation, the ''displaced-profile'' expressions are the mon accurate ones. This profile insensitivity is important, because i t is nor practical to extract c from solutions of the Kohn-Sham equati ons for small metal clusters.