Density-functional study of charge doping inWO3

The addition of electron donors to the vacant $A$ site of defect-perovskite structure tungsten trioxide causes a series of structural and chemical phase transitions; for instance, in the well-known case of the sodium tungsten bronzes $\left({\mathrm{Na}}_x{\mathrm{WO}}_3\right)$. Here we calculate the effect of the addition of electronic charge to ${\mathrm{WO}}_3$ without the complication of also including sodium ions. Our density-functional theory method enables isolation of electronic effects from the additional size, chemical, and disorder effects present in experimental samples. Our calculated low-temperature phase diagram between $x=0$ and $x=1$ moves from the initial low-temperature monoclinic phase through a second (centered) monoclinic phase, an orthorhombic phase, a tetragonal antiferroelectric, and an aristotypic cubic phase in broad agreement with the experimentally observed transformations in ${\mathrm{Na}}_x{\mathrm{WO}}_3$. Our work confirms that the observed structural transformations are driven primarily by electronic factors. We find that the dominant electronic effect is the covalent interaction between the tungsten $5d$ and oxygen $2p$ orbitals.