The adsorption profiles and electronic structures of Pt n ͑n =1-4͒ clusters on stoichiometric, reduced and reconstructed rutile TiO 2 ͑110͒ surfaces were systematically studied using on site d-d Coulomb interaction corrected hybrid density-functional-theory ͑DFT͒ calculations. The atomic structure of small Pt cluster adsorbates mainly depends on the stoichiometry of the corresponding titania support. The cluster shapes on the bulk terminated ideal surface look like their gas phase low-energy structures. However, for instance, they get significantly distorted on the reduced surfaces with increasing oxygen vacancies. On nonstoichiometric surfaces, Pt-Ti coordination becomes dominant in the determination of the adsorption geometries. The electronic structure of Pt n / TiO 2 ͑110͒ systems cannot be correctly described by pure DFT methods, particularly for nonstoichiometric cases due to the inappropriate treatment of the correlation for d electrons. We performed DFT+ U calculations to give a reasonable description of the reconstructed rutile ͑110͒ surface. Pt clusters induce local surface relaxations that influence band edges of titania support and bring a number of band-gap states depending on the cluster size. Significant band gap narrowing occurs upon Pt n -surface interaction due to adsorbate driven states on the bulk terminated and reduced surfaces. On the other hand, they give rise to a band-gap widening associated to partial reoxidation of the reconstructed surface. No metallization arises even for Pt 4 on rutile.

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We studied the electronic and atomic structures of anatase TiO2 codoped with Cr and N using hybrid density functional theory calculations. The nonlocal screened Hartree-Fock exchange energy is partially mixed with the traditional semilocal exchange energy. This not only patches the bandgap underestimation but also improves the description of the anion/cation-driven impurity states and the magnetization of the dopants. Cr and/or N doping modifies the valence and conduction band edges of TiO2, leading to significant bandgap reduction. Hence, Cr, N and Cr-N doped TiO2 are promising for enhanced visible light absorbance.

In this study, oxygen vacancies and adatoms have been considered on the surface of both hexagonal and triangular ZnO nanowires. Their effect on the electronic structure and optical spectra of the nanowires have been investigated using the exact exchange hybrid density functional theory calculations. A surface oxygen vacancy gives rise to appearance of a band gap state at almost 0.7 eV above the valence band of the both types of the nanowires while an oxygen adatom show bulk-like electronic properties. A shape dependence is also indicated by the calculated physical quantities of oxygen related point defects on ZnO nanowires.

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