Here we report a DFT relativistic scalar and spin-orbit study that considers the structural optimization of the complete tungsten (V) cofactor by studying the paramagnetic site of the Pyrococcus furiosus tungsto-bispterin enzyme. The best-fit superimposed X-ray structure shows an important similarity with the aldehyde ferredoxin oxidoreductase (1AOR) structure, and, the W(V) cofactor exhibits a Kramers doublet as the ground state, which agrees with the EPR observations. We conclude that it is quite necessary to include relativistic scalar and spin-orbit effects to describe the whole tungsten (V) cofactor in the P. furiosus tungsto-bispterin enzyme. (C) 2010 Elsevier B. V. All rights reserved.