Dirac-Slater multiple scattering and its non-relativistic limit calculations on the reduced octahedral (20e) [W6S8(CN)(6)](6-) cluster ion are reported. The non-relativistic limit calculations predict a paramagnetic cluster with a triplet ground state, while the relativistic calculations predict a diamagnetic cluster with a singlet ground state, which is in agreement with the single sharp signal seen in C-13 NMR experiments in deoxygenated D2O at room temperature. We have also calculated the relativistic electronic structure of the oxidized 19e [W6S8(CN)(6)](5-) cluster ion. The calculated relativistic local density of states at the Fermi level of the [W6S8(CN)(6)](6-) cluster ion differs from those calculated for the 24e [Re6S8(CN)(6)](4-) cluster ion. This may explain the different role played by the axial cyanide ligands in their cluster reactivities. (C) 2004 Elsevier B.V. All rights reserved.