  The binding of clusters of metal nanoparticles is partly electrostatic. We
address difficulties in calculating the electrostatic energy when high charging
energies limit the total charge to a single quantum, entailing unequal
potentials on the particles. We show that the energy at small separation $h$
has a strong logarithmic dependence on $h$. We give a general law for the
strength of this logarithmic correction in terms of a) the energy at contact
ignoring the charge quantization effects and b) an adjacency matrix specifying
which spheres of the cluster are in contact and which is charged. We verify the
theory by comparing the predicted energies for a tetrahedral cluster with an
explicit numerical calculation.
