Dirac molecular orbital calculations on the octahedral paramagnetic Re6S8Cl63- cluster ion are reported. As the parent diamagnetic Re6S8Cl64- cluster, the calculated relativistic molecular orbitals indicate that the manifold of closely spaced unoccupied energy levels are mainly localized on the octahedral [Re6S8] core, while the cluster highest occupied molecular orbital is largely centered on the terminal chloride ligand. Thus, the probability distribution of the unpaired electron spin in Re6S8Cl63- is 3.5% on each Re-187 nuclei, 0.8% on each capping S-33 nuclei, and 12.1% on each terminal Cl-35 nuclei. The current calculations predicted an isotropic Zeeman interaction, which is in good agreement with single crystal solid state cluster EPR experiments. We also calculated the paramagnetic hyperfine interactions (A(hfi)) of the Re-187, Cl-35, and S-33 nuclei allowing us to describe that the metal and apical ligand hyperfine tensors are anisotropic, while the hyperfine tensors of the capping S ligands are small and isotropic. It is postulated that the reversible redox couple [Re6S8Cl64-/Re6S8Cl63-] could constitute a suitable molecular nanocell for applications in molecular electronics.