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The existence of a topological Dirac nodal loop is predicted for hydrogenated monolayer boron sheets with a nonsymmorphic symmetry. The three-center two-electron bonds in boron compounds restrict the electronic system to be insulating or semimetallic with a Dirac nodal loop. Two types of electronic structures are distinguished by the Z_2 topological index and confirmed by first-principles total-energy calculations. The topological taxonomy, developed in this research, can be applied to other two-dimensional materials and to seek novel Dirac fermions.

Semiconductor photocatalysts that can produce hydrogen from water splitting are of great interest. Among the various possibilities, nitrogen (N)-doped $\mathrm{SrTi}{\mathrm{O}}_{3}$ is a promising candidate for hydrogen evolution under visible-light irradiation. In this study, hybrid density-functional calculations are employed to investigate the stability and impact of nitrogen impurities on the electronic and optical properties in $\mathrm{SrTi}{\mathrm{O}}_{3}$. We find that the substitutional N on O site (${\mathrm{N}}_{\mathrm{O}}$) is a deep acceptor in $\mathrm{SrTi}{\mathrm{O}}_{3}$. Moreover, ${\mathrm{N}}_{\mathrm{O}}$ predominates over other N-related defects under equilibrium growth conditions in $n$-type $\mathrm{SrTi}{\mathrm{O}}_{3}$. Our results reveal that ${\mathrm{N}}_{\mathrm{O}}$ gives rise to visible-light absorption in agreement with experimental observations. In addition, we find that hydrogen can bind to ${\mathrm{N}}_{\mathrm{O}}$, forming ${\mathrm{N}}_{\mathrm{O}}\ensuremath{-}{\mathrm{H}}_{i}$ complex which leads to a blueshift in the optical absorption. Other N configurations can also contribute to optical absorption in the visible range. The vibration frequencies of different N configurations are provided to support identification using vibrational spectroscopy techniques.

The electronic structures of ${[\mathrm{SrTiO}}_{3}]{}_{1\ensuremath{-}x}{[\mathrm{LaCrO}}_{3}]{}_{x}$ perovskite solid solutions are studied using hybrid density functional calculations to investigate their potential photocatalytic activity. The introduction of ${\mathrm{Cr}}^{3+}$ into ${\mathrm{SrTiO}}_{3}$ not only creates occupied states inside the band gap but can adversely narrow the conduction band. However, if ${\mathrm{Cr}}^{3+}$ and ${\mathrm{Ti}}^{4+}$ ions are segregated in alternating [001] layers, the conduction band remains highly dispersive. This suggests that the electronic structure can be tuned by controlling the cation arrangement. We predict that ${[\mathrm{SrTiO}}_{3}]{}_{0.5}{[\mathrm{LaCrO}}_{3}]{}_{0.5}$ with alternating ${\mathrm{TiO}}_{2}$ and ${\mathrm{CrO}}_{2}$ layered along the [001] direction, which has not been experimentally realized yet, will exhibit strong absorption of visible light response and excellent electronic transport properties.

Hybrid density functional calculations are carried out to investigate the behavior of holes in ${\mathrm{Sr}\mathrm{Ti}O}_{3}$. As in many other oxides, it is shown that a hole tend to localize on one oxygen forming an ${\mathrm{O}}^{\ensuremath{-}}$ anion with a concomitant lattice distortion; therefore a hole polaron. The calculated emission energy from the recombination of the localized hole and a conduction-band electron is about 2.5 eV, in good agreement with experiments. Therefore the localization of the hole or self-trapping is likely to be responsible for the green photoluminescence at low temperature, which was previously attributed to an unknown defect state. Compared to an electron, the calculated hole polaron mobility is three orders of magnitude lower at room temperature. In addition, two ${\mathrm{O}}^{\ensuremath{-}}$ anions can bind strongly to form an O${}_{2}{}^{2\ensuremath{-}}$ peroxide anion. No electronic states associated with the ${O}_{2}{}^{2\ensuremath{-}}$ peroxide anion are located inside the band gap or close to the band edges, indicating that it is electronically inactive. We suggest that in addition to the oxygen vacancy, the formation of the ${O}_{2}{}^{2\ensuremath{-}}$ peroxide anion can be an alternative to compensate acceptor doping in ${\mathrm{Sr}\mathrm{Ti}O}_{3}$.

Silver orthophosphate (Ag${}_{3}$PO${}_{4}$) exhibits extremely high photocatalytic activity under visible light. Gaining insight into the behavior of point defects would open opportunities for new applications. Our hybrid density-functional calculations show that intrinsic point defects are unlikely to cause carrier trapping. Charge neutrality analysis suggests that Ag${}_{3}$PO${}_{4}$ possibly behaves as a weak $n$-type semiconductor under the O-poor condition and as a weak $p$-type semiconductor under the O-rich condition. Unlikely to other oxides, unintentionally incorporated hydrogen does not necessarily lead to strong $n$-type conductivity. Migration properties of some Ag-related defects and hydrogen are also discussed.

We report total-energy electronic-structure calculations based on density functional theory performed on graphene adsorbed on the (111) surface of hafnium dioxide (HfO${}_{2}$). We find that the graphene is bound to the HfO${}_{2}$ surface with an interlayer spacing of 3.05 \AA{} with a binding energy of about $\ensuremath{-}$110 meV per C atom. The electronic structure of the HfO${}_{2}$-adsorbed graphene originates primarily from that of the graphene near the Fermi level. However, a detailed analysis of the electronic structure shows that the linear bands on the Dirac cone are slightly split because of the interaction between the graphene and the HfO${}_{2}$ substrate. The physical origin of this splitting is the hybridization between the $\ensuremath{\pi}$ states of the graphene and the O 2$p$ state with Hf $d$ character.

The recent discovery of an excellent photocatalyst, Ag${}_{3}$PO${}_{4}$, motivated us to clarify the origin of its high performance. Our comprehensive study using density-functional-theory-based calculations has revealed that the formation of PO${}_{4}$ tetrahedral units with strong P-O bonds weakens the covalent nature of Ag-O bonds, inhibiting hybridization of Ag $d$ and O $p$. This excludes the $d$ character from the conduction-band minimum (CBM), leaving highly dispersive Ag $s$-Ag $s$ hybrid bands. The delocalized charge distribution of the CBM results in a small effective mass of the electron, which is advantageous for the carrier transfer to surface.

The electronic and structural properties of the oxygen vacancy $({V}_{\text{O}})$ in rutile ${\text{TiO}}_{2}$ are studied using generalized Kohn-Sham theory with the Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional for exchange and correlation. The HSE approach corrects the band gap and allows for a proper description of defects with energy levels close to the conduction band. According to the HSE calculations, ${V}_{\text{O}}$ is a shallow donor for which the $+2$ charge state is lower in energy than the neutral and $+1$ charge states for all Fermi-level positions in the band gap. The formation energy of ${V}_{\text{O}}^{2+}$ is relatively low in $n$-type ${\text{TiO}}_{2}$ under O-poor conditions but it rapidly increases with the oxygen chemical potential. This is consistent with experimental observations where the electrical conductivity decreases with oxygen partial pressure.

We have investigated the correlation energy for the homogeneous electron gas given by the transcorrelated (TC) method. In the TC method, the energy is defined by an expectation value of an effective Hamiltonian constructed by similarity transformation of the original Hamiltonian with respect to a Jastrow factor. In our calculation, a two-body Jastrow factor, which is the simplest function representing the electronic correlation effects, was adopted. Two parameters in the Jastrow factor are determined by the cusp conditions, which restricts the short-range electronic interactions and the long-range asymptotic condition resulted from the random-phase approximation. The energy is expressed within three-body integrals using the two-body Jastrow factor and so it is easily applied to the homogeneous electron gas without Monte Carlo sampling. We found that the TC method yields a fairly good estimate of the correlation energy, and so that of the total energy, especially for near the region of metallic densities (2