The compounds ${\mathrm{InMO}}_{\mathrm{4}}$ (M=V, Nb, Ta) and ${\mathrm{BiVO}}_{\mathrm{4}}$ are promising photocatalysts which are able to induce hydrolysis of water molecules under visible light irradiation. By first principles calculations, supported by experiments, we inspect their peculiar electronic structure in an attempt to rationalize the link between the bulk crystal architecture of the materials and the related electronic properties. We find that the bottom of the conduction band of ${\mathrm{InMO}}_{\mathrm{4}}$ systems consists of a large contribution (about 20%) due to $\text{5s}$ orbitals of In atoms. Another dominant component comes from d orbitals of V, Nb, and Ta. On the other hand, the top of the valence band of the ${\mathrm{BiVO}}_{\mathrm{4}}$ shows a contribution from 6s orbitals of Bi of about 18% as well as a dominant component due to $\text{2p}$ states of O. We can infer that the photocatalytic activity could be improved by the large mobility coming from the s orbital component as well as by tuning the electron affinity (position of the bottom of the conduction band) and ionization potential (top of the valence band). The absorption process of a ${\mathrm{H}}_{\mathrm{2}}\mathrm{O}$ molecule in the ${\mathrm{InVO}}_{\mathrm{4}}$ system was studied by fully relaxing the structure via first principles calculations. Our simulations have shown that the lone pairs of the O atom belonging to the ${\mathrm{H}}_{\mathrm{2}}\mathrm{O}$ molecule have a strong tendency to bind to In, while, at the same time, at least one of the H atoms of the water molecule forms a hydrogen bond with the O of the ${\mathrm{InVO}}_{\mathrm{4}}$ catalyst surface. When a water molecule absorption occurs, it induces a shortening of the In–In and In–V bond lengths around at the surface layer. This might suggest that the electron mobility is locally enhanced due to the resulting larger orbital overlap of $\mathrm{In\_}\text{5s–}\mathrm{In}\text{\_5s}$ and $\mathrm{In}\text{\_5s–}\mathrm{V}\text{\_3d}$ with respect to the case of absence of water.

We report a first-principle study of the $E_1^{\prime }$ defect in $\alpha$-quartz and of the analogous $E_{\gamma }^{\prime }$ defect in amorphous ${\mathrm{SiO}}_2$. Our calculation supports the attribution of both these defects to a positively charged oxygen vacancy. The ground-state configuration of these defects is characterized by a large local relaxation of the atomic network, which leads to a localization of the unpaired electron on a Si dangling bond. Using the calculated electronic spin densities, we fully characterize the hyperfine interactions with nearby ${}^{29}\mathrm{Si}$. Our results explain well both the strong and the weak features that are observed in the experimental spectra.

Recent studies suggest that the carbon-alloy catalyst with doped nitrogen may be a powerful candidate for cathode catalyst of fuel cell. In this paper, we aim to clarify the microscopic mechanisms of the enhancement in the catalyst activity caused by nitrogen doping using a simple graphene cluster model. Our analysis is based on the density-functional electronic-structure calculations. We analyze modifications in the electronic structures and the energetical stability for some different configurations of N doping. We extend the analysis to the case of codoping of nitrogen and boron and propose two possible scenarios explaining the further enhancement of catalytic activity by N and B codoping.