Dirac molecular orbital calculations on the octahedral Re6Se8Cl64- and Re6Se8I64- cluster ions are reported. These cluster ions have singlet ground state. The estimated clusters electronegativity, chi, and their HOMO-LUMO energy gap suggest that Re6Se8I64- is softer and more reactive than Re6Se8Cl64-. The calculated relativistic molecular orbitals indicate that the manifold of closely spaced unoccupied energy levels is mainly localized on the octahedral rhenium core with some contributions from the mu(3)-Se ligands, while all the cluster highest occupied molecular orbitals are largely centered on the apical halide ligands. The electronic features of their ground and excited states are similar to the intensely luminescent hexanuclear tungsten halide W6X8X62- cluster ions. Our calculations suggest that the Re6Se8Cl64- and Re6Se8I64-cluster ions should be diamagnetic and luminescent.