  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 singular logarithmic dependence on $h$. We derive a general form for this
energy in terms of the singular capacitance of two spheres in near contact
$c(h)$, together with nonsingular geometric features of the cluster. Using this
form, we determine the energies of various clusters, finding that more compact
clusters are more stable. These energies are proposed to be significant for
metal-semiconductor binary nanoparticle lattices found experimentally. We
sketch how these effects should dictate the relative abundances of metal
nanoparticle clusters in nonpolar solvents.
