*2s* state at $\sim$ -20 eV has also been observed by XPS [@180] although, given the precision of the measurement, this band is broadened out and appears to extend into the oxygen *2p* valence band, the distinction of which is not made by the authors. Calculations using the local-density approximation and full-potential linear muffin-tin orbitals (where all electrons are considered, not just the valence electrons as in the case of the VASP program) result in density of states spectra which are virtually identical to those we have obtained [@56; @111]. This is the case in both the cubic and hexagonal systems. An older paper by D.W. Bullet [@186], utilising a non-relativistic atomic orbital-based method shows a very similar band structure (oxygen *2p* as valence band and tungsten *5d* as conduction band).

Figure \[fig:dos\_cub\_MWO3\] shows a comparison of the density of states of the cubic bronzes with the parent oxide. The hydrogen bronze system shows a large peak feature at the bottom of the conduction band, which is attributed to the non-ionised hydrogen *1s* orbital. Because only one electron is contributed from the hydrogen, the Fermi level lies about in the middle of this sub-band. For the other bronze systems, analysis 