  Ab initio calculations using the Perturbed Ion model, with correlation
contributions included, are presented for nonstoichiometric (NaI)_nNa+ and
(CsI)_nCs+ (n=1-14) cluster ions. The ground state and several low-lying
isomers are identified and described. Rocksalt ground states are common and
appear at cluster sizes lower than in the corresponding neutral systems. The
most salient features of the measured mobilities seem to be explained by
arguments related to the changes of the compactness of the clusters as a
function of size. The stability of the cluster ions against evaporation of a
single alkali halide molecule shows variations that explain the enhanced
stabilities found experimentally for cluster sizes n=4, 6, 9, and 13. Finally,
the ionization energies and the orbital eigenvalue spectrum of two (NaI)_13Na+
isomers are calculated and shown to be a fingerprint of the structure.
