DFT+U calculations of crystal lattice, electronic structure, and phase stability under pressure of TiO2 polymorphs

Abstract

This work investigates crystal lattice, electronic structure, relative stability, and high pressure behavior of TiO(2) polymorphs (anatase, rutile, and columbite) using the density functional theory (DFT) improved by an on-site Coulomb self-interaction potential (DFT+U). For the latter the effect of the U parameter value (0 < U < 10 eV) is analyzed within the local density approximation (LDA+U) and the generalized gradient approximation (GGA+U). Results are compared to those of conventional DFT and Heyd-Scuseria-Ernzehorf screened hybrid functional (HSE06). For the investigation of the individual polymorphs (crystal and electronic structures), the GGA+U/LDA+U method and the HSE06 functional are in better agreement with experiments compared to the conventional GGA or LDA. Within the DFT+U the reproduction of the experimental band-gap of rutile/anatase is achieved with a U value of 10/8 eV, whereas a better description of the crystal and electronic structures is obtained for U < 5 eV. Conventional GGA∕LDA and HSE06 fail to reproduce phase stability at ambient pressure, rendering the anatase form lower in energy than the rutile phase. The LDA+U excessively stabilizes the columbite form. The GGA+U method corrects these deficiencies; U values between 5 and 8 eV are required to get an energetic sequence consistent with experiments (E(rutile) < E(anatase) < E(columbite)). The computed phase stability under pressure within the GGA+U is also consistent with experimental results. The best agreement between experimental and computed transition pressures is reached for U ≈ 5 eV.

Hubbard-Ucorrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS,TiO2, and NiO

“…The O-2s states lie far (17 eV) below the VBM. These electronic structure features have been observed and discussed in numerous other works [67][68][69][70][71][72].…”

“…The latter phenomenon leads to a strong dependence of the fundamental gap on U [72,73], illustrated in Fig. 3(c).…”

The DFT+U: Approaches, Accuracy, and Applications

“…However, upon applying the localization of the excess electronic charge using +U correction, the predicted bandgaps are accurate and in a good agreement with the experimental and the computationally expensive hybrid functional (HSE06) results [43], Figure 2. In another study, for rutile TiO2, the prediction of the experimental bandgap is achieved with a U value of 10 eV, whereas the crystal and electronic structures were better described with U < 5 eV [19].…”

“…This semiempirical trend in practical implementation of U is present because of the significant computational cost of ab initio calculation of U, and in the cases of studying static physical properties, the results of computed U are not necessarily found to be better than the empirical ones. Within this practice, however, caution should be taken while pursuing the semiempirical method [19]. If it will be possible to describe all the relevant aspects of a system, except the bandgap, with a reasonable U, one might then look into using a scissor operator or rigid shift to the bandgap [20,21].…”

“…Dompablo et al [19] compared the effect of the U parameter value (0 < U < 10 eV) within the LDA+U and the GGA+U on the calculated properties of anatase TiO 2 . Both LDA+U and GGA+U required a small value of U (3 and 6 eV, respectively) to reproduce the experimental measurements, Figure 3.…”