A diatomics-in-molecules (DIM) model for the energy, shape and charge
distribution of metal cluster ions in the presence of a charged insula
ted conducting sphere is presented. The electrostatic interaction betw
een the sphere and the cluster-ion is introduced in a self-consistent
manner which allows the sphere to be polarized by the ion and the ion
by the sphere. This interaction appears in the diagonal elements of th
e model Hamiltonian matrix in such a way that the lowest eigenvalue in
cludes the correct electrostatic energy for the charge distribution in
the ground state. The model is applied to the calculation of fusion b
arriers for Na-2(+) and Na-3(+) ions. When both the charge distributio
n and the geometric configuration of the cluster-ion are allowed to re
lax freely, the energy as a function of distance from the sphere is ne
arly the same as that calculated from the electrostatic energy alone,
which implies that details of the molecular structure of the cluster-i
on can be neglected in calculating fusion barriers from charge polariz
ation alone. That the fusion barriers lie sufficiently far away from t
he sphere so that the molecule does not dissociate under the influence
of the Coulomb interaction confirms that it is meaningful to speak of
two separate entities at the barrier position.