The Breit-Pauli Hamiltonian for many-electronic positron- and positronium-atom complexes is considered and is applied to the neutral positronium-atom complexes PsB-PsF, PsAl-PsCl, PsGa-PsBr, and PsIn-PsI. For these complexes, energy differences between the high-and low-spin states which arise from different positronic spin coupling schemes are estimated, and relativistic corrections for the dissociation energies into a positronium and a neutral atom. The relativistic effects are obtained from first-order perturbation theory based on the Hartree-Fock description. The influence of correlation effects on the dissociation energies for positronium halides are also discussed. (C) 2011 Elsevier B.V. All rights reserved.