Relevance of Dispersion and the Electronic Spin in the DFT + U Approach for the Description of Pristine and Defective TiO₂ Anatase

Abstract

A density functional theory + U systematic theoretical study was performed on the geometry, electronic structure, and energies of properties relevant for the chemical reactivity of TiO 2 anatase. The effects of D3(BJ) dispersion correction and the Hubbard U value over the energies corresponding to the TiO 2 /Ti 2 O 3 reduction reaction, the oxygen vacancy formation, and transition-metal doping were analyzed to attain an accurate and well-balanced description of these properties. It is suggested to fit the Hubbard correction for the metal dopant atom by taking as reference the observed low spin–high spin (HS) energy difference for the metal atom. PBEsol-D3 calculations revealed a distinct electronic ground state for the yttrium-doped TiO 2 anatase surface depending upon the type of doping and interstitial or substitutional defects. Based on the calculations, it was found that a HS state explains the observed ferromagnetism in cobalt-substituted TiO 2 anatase. The results presented herein might be relevant for further catalytic studies on TiO 2 anatase using a large surface model that would be worthwhile for heterogeneous catalysis simulations.

Highly active Ru/TiO2 nanostructures for total catalytic oxidation of propane

“…DFT + U calculations were performed by using the Perdew-Burke-Ernzerhof for solids (PBEsol) functional in conjunction with the Hubbard ( U ) correction in the Dudarev formalism (Dudarev et al 1998 ). A value of U = 3 was applied to the 3d states of titanium (Torres et al 2021 ) as previously reported. The D3 (BJ) Grimme dispersion correction was included (Grimme et al 2011 ).…”

“…The calculations were converged to 10 −6 eV in the total energy and 0.01 eV/Å on atomic forces. This method has proven to be effective for the description of TiO 2 anatase (Torres et al 2021 ). DFT calculations were carried out using Vienna Ab-initio Simulation Package VASP code (version 5.4.4) (Kresse and Hafner 1993 ; Kresse and Hafner 1994 ; Kresse and Furthmüller 1996a , b ).…”

“…A titania (001) surface was modeled through a 4 × 4 × 1 supercell with vacuum > 15 Å. The lattice parameters were fixed at the optimized values of bulk anatase as reported in Torres et al ( 2021 ). The four bottom layers of the TiO 2 surface were only fixed, while the positions of the remaining atoms were relaxed.…”