$x = 0.2$. Lastly, three compounds of a layered WO$_4\cdot\alpha$,$\omega$-diaminoalkane hybrid series were studied and found to be insulating, with features in the band structure similar to those of the parent WO$_3$ compound which relate well to experimental UV-visible spectroscopy results.
address:
- '$^1$Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand'
- '$^2$Industrial Research Ltd., P.O. Box 31310, Lower Hutt, New Zealand'
author:
- 'B. Ingham$^1$, S.C. Hendy$^{1,2}$, S.V. Chong$^2$ and J.L. Tallon$^{1,2}$'
bibliography:
- 'vasp.bib'
title: 'Density-functional studies of tungsten trioxide, tungsten bronzes, and related systems'
---

Introduction
============

Tungsten trioxide has long been studied for its interesting structural, electronic, and electrochromic properties. Tungsten trioxide is most stable in a pseudo-cubic, distorted ReO$_3$ structure [@90] but can also form metastable hexagonal [@106], tetragonal [@15] and pyrochlore [@22; @507] structures. For all of these structures it is possible to intercalate mono- or di-valent cations in the vacancies or channels within the structures to form the so-called ‘tungsten bronzes’ [@15; @17; @151; @163]. The resulting materials exhibit a continuous colour change [@12] and often a large increase in the electrical conductivity, which becomes metallic in nature [@9]. The most-studied system is that of the cubic alkali bronzes (M$_x$WO$_3$, M 