WO$_6$ octahedra) linked with organic diamine molecules [@us1; @us2]. The electronic structure of these materials will determine how they may be used in various electronic applications. This work presents *ab* *initio* computations on a variety of tungsten oxide derivatives, including a series of cubic and hexagonal alkali tungsten bronzes, variable doping Na$_x$WO$_3$ ($0 \leq x \leq 1$), oxygen-deficient WO$_{3-x}$, and some simple layered organic-inorganic tungsten oxide hybrid structures to aid in understanding the optical and electronic properties of the latter. During the course of completing this work another paper has recently appeared which treats some of the earlier materials [@521].

Computational details
=====================

We have applied density functional theory (DFT) within the generalized gradient approximation (GGA) [@PBE96] using the VASP package [@vasp1; @vasp2; @vasp3; @vasp4] which solves the DFT-GGA Kohn-Sham equations within the pseudopotential approximation. Here the valence electrons have been expanded in a plane wave basis set and the effect of the core on the valence electrons has been modelled with ultrasoft pseudopotentials. We used ultrasoft Vanderbilt type pseudopotentials [@ultra1] as supplied by G. Kresse and J. Hafner [@ultra2]. The pseudopotential valence states and cut-off energies for all elements used are given in Table \[table:pp\].

   Atom   Valence Electrons   Cut-off 