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Based on density functional theory (DFT), theoretical models of three kinds of lanthanide rare earth metal ion-doped γ-Bi2MoO6 were constructed (Ln-BMO (Ln=Gd, Ho, Yb)). The geometric structure, electronic structure, and optical properties of the model were calculated, and the influence of doped Ln3+ ions on the structures and properties of the system was analyzed. The results revealed that the substitution of smaller ionic radius Ln3+ ions for Bi3+ ions caused a contraction of the lattice parameters. At the same time, the contribution of the [Ln]4d near valence band and conduction band reduced the bandwidth of γ-Bi2MoO6, forming the Ln-O ionic bond with different strengths to obtain higher charge conductivity and charge-separation ability. Secondly, Ln3+ ions have a strongly ionic charge, which leads to the appearance of optical absorption bands in the infrared region and part of the visible region. This reduces the reflection in the visible region, improves the utilization rate, delays the loss of electron energy, and promotes phase matching in the visible region. And the Gd3+-doped system has better photocatalytic activity than the other Ln3+-doped system. This research provides theoretical insights into doped lanthanide rare earth ions and also provides strategies for the modification of γ-Bi2MoO6 nanomaterials.

The electronic structural and optical properties of CdGeAs2 crystals are calculated by using the Perdew–Burke–Ernzerhof (PBE) functional within generalized gradient approximation (GGA) and the Heyd–Scuseria–Ernzerhof (HSE06) functional. The results show that CdGeAs2 is an optical crystal with a direct bandgap of 0.71 eV by using the HSE06 functional method, which is closer to the experimental value. The Mulliken population and differential charge density analysis indicate that the Ge–As and Cd–As bonds have covalent properties, and that the covalent bond of Cd–As is visibly stronger than that of the Ge–As bond. The optical properties show that the CdGeAs2 crystal has strong absorption and reflection in the ultraviolet region and strong transmittance in the infrared region. The average static refractive index of CdGeAs2 is 2.96, and the static birefractive index is 0.08. The results show that CdGeAs2 is an excellent optical material of potential applications in the middle and far infrared.

Based on the density functional theory, the effect of rare-earth La doping at different concentrations on the electronic structure, optical properties, and magnetic properties of ZnO was calculated by using the GGA+U method under the condition of spin polarization. The calculation results show that the cell of a La-doped ZnO system is distorted, resulting in a formation energy less than zero, in which case it is easy to dope. After La doping, the band gap narrows, the Fermi level enters the conduction band, and the excess carriers induced by La atoms degenerate to form n-type degenerate semiconductor materials. In the visible light region, a blue shift in the optical absorption edge of the La-doped ZnO system causes an increased average static dielectric constant, stronger polarization ability, stronger binding ability on charges, and the photoconductivity of the doped ZnO system is improved. The magnetic moment of the La-doped ZnO system is zero, so it is not magnetic.

The first-principle calculation method based on the density functional theory (DFT) in combination with the LDA+U algorithm is employed to study the electronic structure and magnetic properties of Co/Mn co-doped ZnO nanowires. Special attention is paid to the optimal geometric replacement position, the coupling mechanism, and the magnetic origin of Co/Mn atoms. According to the simulation data, Co/Mn co-doped ZnO nanowires of all configurations exhibit ferromagnetism, and substitution of Co/Mn atoms for Zn in the (0001) inner layer brings nanowires to the ground state. In the magnetic coupling state, the obvious spin splitting is detected near the Fermi level, and strong hybridization effects are observed between the Co/Mn 3d and O 2p states. Moreover, the ferromagnetic ordering forming Co2+-O2−-Mn2+ magnetic path is established. In addition, the calculation results suggest that the magnetic moment mainly takes its origin from the Co/Mn 3d orbital electrons, and the size of the magnetic moment is related to the electronic configurations of Co/Mn atoms. Therefore, a realistic description of the electronic structure of Co/Mn co-doped ZnO nanowires, obtained via LDA+U method, shows their potential for diluted magnetic semiconductor materials.