In supercell calculations of defective crystals, it is common to place a point defect or vacancy in the atomic position with the highest possible point symmetry. Then, the initial atomic structure is often arbitrary distorted before its optimization, which searches for the total energy minimum. In this paper, we suggest an alternative approach to the application of supercell models and show that it is necessary to preliminarily analyze the site symmetry of the split Wyckoff positions of the perfect crystal supercell atoms (which will be substituted or removed in defective crystals) and then perform supercell calculations with point defects for different possible site symmetries, to find the energetically most favorable defect configuration, which does not necessarily correspond to the highest site symmetry. Using CeO as an example, it is demonstrated that this use of the site symmetry of the removed oxygen atoms in the supercells with vacancies allows us to obtain all the possible atomic and magnetic polaron configurations, and predict which vacancy positions correspond to the lowest formation energies associated with small polarons. We give a simple symmetry based explanation for the existence of controversies in the literature on the nature of the oxygen vacancies in CeO. In particular, the experimentally observed small polaron formation could arise for oxygen vacancies with the lowest C site symmetry, which exist in 3 × 3 × 3 and larger supercells. The results of first principles calculations using a linear combination of atomic orbitals and hybrid exchange-correlation functionals are compared with those from previous studies, obtained using a widely used DFT+U approach.

In this article, we study the competing oxygen evolution and hydrogen peroxide (H 2 O 2 ) formation reactions for periodic models of graphene with different active-site concentrations by means of density functional theory (DFT) calculations. Linking the DFT calculations to ab-initio thermodynamic considerations in conjunction with microkinetic modeling enables gaining deep insights into the activity and selectivity trends of graphene-based electrodes as a function of applied bias. We illustrate that both the coverage of intermediates on the electrode surface and the applied electrode potential have a significant effect on the Faradaic efficiency for the electrocatalytic production of H 2 O 2 . The presented approach to study overpotential-dependent selectivity trends allows deriving design criteria for peroxide formation, which may serve as a guideline for further studies to realize selective formation of H 2 O 2 using carbon-based materials.

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In this paper we present the results of quantum chemical modeling for energetically stable anatase (001) TiO 2 nanotubes, undoped, doped, and codoped with N O and S O atoms. We calculate the electronic structure of one-dimensional (1D) nanotubes and zero-dimensional (0D) atomic fragments cut out from these nanotubes, employing hybrid density functional theory with a partial incorporation of an exact, nonlocal Hartree-Fock exchange within the formalism of the linear combination of atomic orbitals, as implemented in both CRYSTAL and NWChem total energy codes. Structural optimization of 1D nanotubes has been performed using CRYSTAL09 code, while the cutout 0D fragments have been modelled using the NWChem code. The electronic properties of the studied systems prove that the band structure of the pristine TiO 2 nanotube can be substantially modified by introducing substitutional impurity defects. The Ndoped nanotube creates a midgap state that largely has a nitrogen p 2 character. The S-doped nanotube has a defect state that almost coincides with the top of the valence bond for the pristine material. For nanotubes codoped with both S and N, we observe a downward shift of the gap state of nitrogen relative to the purely N-doped state by about 0.3 eV. This results in a system with a filled gap state about 0.3 eV below the O 2 /H 2 O oxidation level, making it a very promising candidate for photocatalytic hydrogen generation under visible light, because due to the presence of sulfur, the bottom of the conduction band is only about 2.2 eV above the occupied midgap state, and also, clearly above the standard hydrogen electrode level.

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