there is also some additional oxygen *2p* contribution - particularly to the strong peak feature observed at 2.5 eV. The band gap (defined as the difference in energy between the top of the valence band and the bottom of the conduction band) is 0.4 eV in the cubic system and 0.5 eV in the hexagonal. This is much less than the observed band gap, which is typically reported in the range of 2.5 - 3 eV, and as being indirect [@177; @182; @184]. However this is not too surprising as DFT generally underestimates band gaps. The presence of peak features in the density of states can also lead to the phenomenon where even though the conduction band is being filled, there is a sudden increase in the population of the conduction band at these peaks and a sharp transition in the optical spectrum is observed.

It is worth taking pause here to point out the similarities between this work and that of experimental results and other calculations reported on the same structures. X-ray photoelectron spectroscopy (XPS) reveals that the valence band is comprised of oxygen *2p* states only, and the conduction band of tungsten *5d* states [@182; @252]. The oxygen 