Restricted Hartree-Fock calculations for the ground electronic states of BrH/sup +/, KrH/sup +/, and RbH/sup +/ have been carried out using carefully selected nominal atomic basis sets for the heavy atoms, supplemented with an additional orbital designed to allow for a better description of atomic distortion at intermediate internuclear separations. A flexible four-function basis set was used on the hydrogen atom. Molecular optimization was carried out for the heavy-atom distortion orbital and also for the hydrogen 2p orbital. The interatomic potentials obtained for the X /sup 2/PI state of BrH/sup +/ and the X /sup 1/..sigma../sup +/ state of KrH/sup +/ show strong molecular binding (i.e., 3-4 eV) relative to the neutral heavy atoms plus a proton. The RbH/sup +/ X /sup 2/..sigma../sup +/ calculations give a repulsive interatomic potential with dissociation to Rb/sup +/ and a neutral hydrogen atom.