A comparative study is presented, based on Density Functional Theory, of the influence that the different approximations of the exchange-correlation functional have on the structural and electronic properties of titanium dioxide in the anatase phase. In this work, the method of plane waves and pseudopotentials, as implemented in the Quantum Espresso package was used. The approximations to the correlation-exchange functional that were considered are the local density approximation, the generalized gradient approximation in the form of Perdew-Burke-Ernzerhof, the Perdew-Burke-Ernzerhof for solids, and the Perdew-Wang 91. For each case, the effects due to the inclusion of spin (spin polarization), and the correction of Hubbard (U=4.2 eV for Ti) were also studied. We found that the Perdew-Burke-Ernzerhof for solids functional offers the best results for the calculation of the lattice parameters and bond lengths, followed by the local density approximation with the Hubbard correction included. For the bond angles, the best description was obtained with the local density approximation. The inclusion of the U term increases the errors associated with the mentioned structural parameters when the following functionals are used: Perdew-Burke-Ernzerhof, Perdew-Burke-Ernzerhof for solids and Perdew-Wang 91. The Perdew-Burke-Ernzerhof and Perdew-Wang 91 functionals show the largest errors when the Hubbard correction is used; while the local density approximation shows significant improvement when the Hubbard correction is included. Regarding the energy gap, we found that the introduction of the U term improves the estimation of this property for all the approximations included in this work.

A comparative study is presented, based on density functional theory, of the influence that the different approximations of the exchange-correlation functional have on the structural and electronic properties of titanium dioxide in the rutile phase. In this work, the method of plane waves and pseudopotentials, as implemented in the Quantum Espresso package was used. The approximations to the exchange-correlation functional that were considered are the local density approximation, the generalized gradient approximation in the form of Perdew- Burke-Ernzerhof, the Perdew-Burke-Ernzerhof for solids, and the Perdew-Wang 91. For each case, the effects due to the inclusion of spin (spin polarization), and the correction of Hubbard (U = 4.2 eV for Ti) were also studied. We found that the Perdew-Burke-Ernzerhof for solids functional offers the best results for the calculation of the lattice parameters and bond lengths, followed by the Perdew-Burke-Ernzerhof and Perdew-Wang 91. For the bond angles, the best description was obtained with the Perdew-Burke-Ernzerhof and Perdew-Wang 91 approximations. The density analysis of states showed that the functional PW91 and PBE, better describe the band gap compared with the functional PBEsol and LDA when the Hubbard correction it is not been included, however, when this is included all the functional show the same deviation with respect to the experimental value (E gap = 3.0 eV). With and without the Hubbard correction (U = 4.2), all functionals underestimate the band gap.