The electronic structures for cubic WO 3 , LiWO 3 , NaWO 3 , HWO 3 , H 2 WO 3 , and hexagonal WO 3 have been calculated. The calculations rely on the local approximation to density functional theory and use a full-potential linear muffin-tin orbitals method. The incorporation of ions in tungsten oxide by chemical or electrochemical methods is the basis for several technological applications related to solid state ionics. Essentially, incorporation of alkali ions results in an s-band high above the Fermi level, and the charge-balancing electrons take part in a rigid band filling of the W d conduction band. Hydrogen forms a hydroxide unit with one oxygen atom, and we find a minimum in total energy for a bond length of 1.03 Å . The cubic phase of WO 3 can take up more than one hydrogen atom, and the formation of two hydroxide units is preferable to one water molecule. The calculated dielectric function and reflectance of Li x WO 3 and Na x WO 3 are presented, and the change in optical properties being the basis for reflective electrochromism is reproduced, although the reflectance curves show some deviations from experiments.

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We demonstrate, by means of Grst-principles calculations, that in the Geld-induced magnetic state of o,-cerium and cx-uranium the spin and orbital moments are coupled parallel rather than antiparallel as expected from Hund's third rule. This behavior gives a magnetic form factor for a-uranium in very good agreement with experiment. The calculated form factor of 0;-cerium, when assuming that the f electron is itinerant, is very diferent from the localized Ce + form factor, and we propose that a measurement of the magnetic form factor of a-Ce can indicate whether the f state is localized or itinerant. The Geld-induced magnetism of plutonium is shown to be almost exclusively of orbital character and the induced spin density of plutonium is highly anomalous.

An example of a breakdown of Hund's third rule for a system with less than a half filled electronic shell is presented. By means of spin polarized electronic structure calculations including the relativistic effects and a Zeeman term, we demonstrate that in the field induced magnetic state of uranium the spin and orbital moments are coupled parallel rather than antiparallel as stipulated by Hund's third rule. This provides an explanation for the measured field induced magnetic form factor of uranium metal.

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