To use solar irradiation or interior lighting efficiently, we sought a photocatalyst with high reactivity under visible light. Films and powders of TiO _{2- x} N _x have revealed an improvement over titanium dioxide (TiO ₂ ) under visible light (wavelength < 500 nanometers) in optical absorption and photocatalytic activity such as photodegradations of methylene blue and gaseous acetaldehyde and hydrophilicity of the film surface. Nitrogen doped into substitutional sites of TiO ₂ has proven to be indispensable for band-gap narrowing and photocatalytic activity, as assessed by first-principles calculations and x-ray photoemission spectroscopy.

When determining machine-learning models for inter-atomic potentials, the potential energy surface is often described as a non-linear function of descriptors representing two- and three-body atomic distribution functions. It is not obvious how the choice of the descriptors affects the efficiency of the training and the accuracy of the final machine-learned model. In this work, we formulate an efficient method to calculate descriptors that can separately represent two- and three-body atomic distribution functions, and we examine the effects of including only two- or three-body descriptors, as well as including both, in the regression model. Our study indicates that non-linear mixing of two- and three-body descriptors is essential for an efficient training and a high accuracy of the final machine-learned model. The efficiency can be further improved by weighting the two-body descriptors more strongly. We furthermore examine a sparsification of the three-body descriptors. The three-body descriptors usually provide redundant representations of the atomistic structure, and the number of descriptors can be significantly reduced without loss of accuracy by applying an automatic sparsification using a principal component analysis. Visualization of the reduced descriptors using three-body distribution functions in real-space indicates that the sparsification automatically removes the components that are less significant for describing the distribution function.

We have performed the first-principles calculations on $\left({\mathrm{Ca}}_2{\mathrm{CoO}}_3{)}_4\right({\mathrm{CoO}}_2{)}_6$ to understand electronic structures of the misfit-layered calcium cobaltite, $({\mathrm{Ca}}_2{\mathrm{CoO}}_3{)}_x{\mathrm{CoO}}_2,$ within the generalized gradient approximation. The optimized structure, consisting of a triple rocksalt-type ${\mathrm{Ca}}_2{\mathrm{CoO}}_3$ subsystem and a ${\mathrm{CdI}}_2$-type ${\mathrm{CoO}}_2$ subsystem in which their respective octahedra are significantly distorted, shows good agreement with recent experiment. The calculated electronic structures include two-dimensionally dispersive $e_g$ bands across the Fermi energy, which yield the p-type conductivity in the rocksalt subsystem, while the Fermi energy lies in the crystal-field gap of the d states in the ${\mathrm{CoO}}_2$ subsystem. The spin-polarized calculations show that antiferromagnetic or ferrimagnetic ordering with a small net magnetic moment within the rocksalt subsystem is found to be the ground state, which gives a reasonable explanation of low-temperature behavior of the resistivity and the susceptibility observed in experiment.

Ab initio density functional calculations of the response of V, Nb, and Ta to tensile and shear loading have been performed. We find that the behavior of all three metals of the V group under large strains differs considerably from that reported for the other body-centered cubic (bcc) transition metals (Mo, W, and Fe). Under unaxial ⟨100⟩ tensile loading, V and Nb undergo a bifurcation from a tetragonal to an orthorhombic deformation path, associated with a shear instability, before reaching the stress maximum. The bifurcation strongly reduces the ideal tensile strengths to 11.5 GPa for V and 12.5 GPa for Nb. For Ta the bifurcation point coincides with the stress maximum of 13.6 GPa along the tetragonal path so that the metal fails under tensile strain by shear and not by cleavage. The stress-strain curves calculated for the {110}⟨111⟩ and {211}⟨111⟩ slip systems are strongly asymmetric; the ideal shear strengths for both slip systems are 6.5 (5.5) GPa for V and 7.8 (6.0) GPa for Nb. Hence the ideal shear strengths are only half as large as for the bcc metals Mo and W, but much larger than expected on the basis for the low shear moduli of V and Nb. Ta shows a behavior intermediate between these two groups of metals, with a calculated ideal shear strength of 7.1 (6.5) GPa, in excellent agreement with the experimental estimate from nanoindentation experiments. The saddle-point structure determining the shear strength for both slip systems is a special body-centered-tetragonal structure. This structure is identical to the saddle-point structure identified on the orthorhombic deformation path under uniaxial tension. Hence also V and Nb will fail under uniaxial tension not by cleavage, but by shear.

We have performed first-principles calculations for the $\mathrm{Ag}{\mathrm{Pb}}_m\mathrm{Sb}{\mathrm{Te}}_{2+m}$ ($m=6$, 14, and 30) to clarify the effect of simultaneous doping of Ag and Sb on PbTe. The atomic positions were optimized for the model structures with $m=6$, 14, and 30. We calculated the formation energy and the lattice constant by varying the distance between Ag and Sb atoms in each model structure and revealed that the Ag-Sb pair is stabilized when it forms the nearest neighbor in the PbTe matrix, which is consistent with recently reported experimental data. The temperature dependence of the Seebeck coefficient for $\mathrm{Ag}{\mathrm{Pb}}_{14}\mathrm{Sb}{\mathrm{Te}}_{16}$ was also calculated in the framework of the Bloch-Boltzmann transport theory. The calculated Seebeck coefficient for $\mathrm{Ag}{\mathrm{Pb}}_{14}\mathrm{Sb}{\mathrm{Te}}_{16}$ turned out to be close to that of PbTe below $300\mathrm{K}$. However, the value at high temperatures tends to be saturated and becomes less in magnitude than that of PbTe. The lattice thermal conductivity is found to be significantly lowered with increasing the Ag-Sb doping as a result of a shortening of the mean free path. We conclude that there exists an optimum Ag-Sb concentration, at which the thermal conductivity is substantially reduced but a large Seebeck coefficient of PbTe is essentially preserved, so that the dimensionless figure of merit can be increased beyond that of PbTe at high temperatures around $800\mathrm{K}$.