  We present a general scheme for finding the exact eigenstates of two
electrons, with on-site repulsive potentials U_i, on I impurities in a
macroscopic crystal. The model describes impurities in doped semiconductors and
artificial molecules in quantum dots. For quantum dots, the energy cost for
adding two electrons is bounded by the single-electron spectrum, and does not
diverge when U_i approaches infinity, implying limitations on the validity of
the Coulomb blockade picture. Analytic applications on a one-dimensional chain
yield quantum delocalization and magnetic transitions.
