The structures of ion clusters have been investigated for the restrict
ed primitive model in the low density limit. The calculations have bee
n accomplished by a Monte Carlo integration over the probability funct
ion of the cluster configuration. The size of the clusters ranges from
dimer to octamer. Properties related to the structure, such as the nu
mber of associating bonds, the cluster volumes and the multipole momen
ts including ion polarizability, have been calculated. Two qualitative
ly different approaches for the Bjerrum distance have been investigate
d and compared with respect to its physical relevance. The Bjerrum dis
tance is the crucial and arbitrary parameter in the ion cluster theory
. As a result it was found that a considerable small constant Bjerrum
distance is superior to Bjerrum's original temperature dependent appro
ach.