Based on first principles within density-functional theory, we establish three models of N doped anatase TiO2, Sm doped anatase TiO2 and Sm-N codoped anatase TiO2 by using the plane-wave ultrasoft pseudopotential method. We calculate their densities of states, band structures and absorption spectra. Their results show that although the N doped anatase TiO2 takes the best redshift, the Sm-N codoped anatase TiO2 makes better lifespan of electron and the Sm-N codoped anatase TiO2 is more stable.

According to the plane wave ultra-soft pseudo potential technique of density function theory, we perform the first-principles study of the electronic structure and absorption spectrum of heavily Nd-doped anatase TiO2 with different Nd concentrations, along with those of pure anatase TiO2. The calculation results show that, within the concentration range of Nd set by this article, with the doping concentration decreasing, the band gap becomes narrow, and the absorption spectrum is red shifted more considerably. The experimental results are in accordance with the calculation results.

Based on first principles within the density-functional theory, we establish three different concentration Eu-doping anatase TiO2 models by using the plane-wave ultrasoft pseudopotential method. We calculate the density of states, the electron density difference, the band structure and the absorption spectrum. The results show that Eu creates an impurity level in the band gap of TiO2 and a redshift in absorption spectrum of anatase TiO2. By comparing the bands of anatase TiO2, with two different Eu-doping concentrations (1.39 at% and 2.08 at%) we find that more Eu atoms make the impurity level deeper, the recombination rate bigger, and the electron lifespan shorter.

The research on the photocatalytic properties of TiO2 by doping transition metals (Fe/Co/Ni) has achieved certain progress. However, the effects of Fe/Co/Ni doping and the coexistence of O vacancies on the photocatalytic properties of TiO2 have been rarely reported. Oxygen vacancies are the most common point defects in TiO2 materials, and the precise control of O vacancies in experiments presents difficulty. To solve this problem, this study used first principles under the framework of density functional theory to investigate the effects of Fe/Co/Ni doping and the coexistence of O vacancies on the magnetic and optical properties of rutile TiO2(110) surface. The findings indicated that the formation energy of the (110) surface of rutile TiO2 doped with transition metals Fe, Co, and Ni and coexisting with O vacancies was smaller under Ti-rich conditions than under O-rich conditions. Under Ti-rich conditions, the doping system easily formed and exhibited a high stability. The findings on magnetic properties indicated that the Fe/VO-TiO2, Co/VO-TiO2, and Ni/VO-TiO2 systems all exhibited magnetism on the (110) surface. The Fe/VO-TiO2(110) surface had the largest magnetic moment and the best magnetic properties. The study of optical properties showed that the Fe/VO-TiO2(110) surface had the longest carrier lifetime, strongest surface activity, and most evident red shift in the absorption spectrum. The oxidation capability of the Fe/VO-TiO2(110) surface was relatively the best. Fe doping and the coexistence of O vacancies are the most beneficial to the photocatalysts for the production of O2 by dissociation of water on the surface of rutile TiO2(110).