  The Coulomb energy of a small metallic island coupled to an electrode by a
tunnel junction is investigated. We employ Monte Carlo simulations to determine
the effective charging energy for arbitrary tunneling strength. For small
tunneling conductance, the data agree with analytical results based on a
perturbative treatment of electron tunneling, while for very strong tunneling
recent semiclassical results for large conductance are approached. The data
allow for an identification of the range of validity of various analytical
predictions.
