Relativistic corrections for positronium-atom complexes

► The Breit-Pauli Hamiltonian is extended to positron-and positronium-atom complexes. ► The energy differences between the high- and low-spin states of PsB-PsO, PsAl-PsS, PsGa-PsSe, and PsIn-PsTe are obtained. ► Relativistic corrections to the dissociation energies of PsB-PsF, PsAl-PsCl, PsGa-PsBr, and PsIn PsI are obtained. ► In some cases the relativistic corrections are capable of changing positive dissociation energies to negative values.