A DFT+U calculations: Band structural and equation of states for anatase and rutile TiO<inf>2</inf>

Abstract

The band structure of anatase and rutile titanium dioxide has been calculated by using first-principles plane-wave pseudo-potential with CASTEP code, based on density functional and molecular dynamics theories, as incorporated in Accelrys Material studio. Studies presented in this work were performed using the generalized gradient approximation (GGA) method. For exchange-correlation function, we employed Perdow-Burke-Ernzerhof (PBE) by using both GGA and GGA with LDA+U. Localization of the excess electronic charge is encouraged by using +U term. For energy calculations the system is optimized for all values of U for rutile from 0 eV to 8.0 eV and for anatase from 0 eV to 9.5 eV. The optimum values of U for rutile TiO2 is 7.5 eV and for anatase TiO2 is 9.0 eV respectively. Our investigated results of band structure by using GGA-PBE are 2.140eV (fig. 1(a)) and 1.973eV (fig. 2(a)) for anatase and rutile respectively. The calculated band structures by using GGA-PBE with LDA+U term for both structures are 3.350 eV (anatase, fig.1 (b)) and 2.557 eV (rutile, fig. 2(b)). Obtained band gaps for both polymorphs are characterized as direct band gap for rutile (Figs. 2(a, b)) and indirect band gap for anatase (figs. 1(a, b)) TiO 2 by using both given methods. Our studies show that GGA underestimates the electronic structure but by introducing LDA+U term with GGA predict comparable to experimentally observed the electronic structure for anatase [1] and rutile [2] TiO 2 . In addition, to obtain the zero pressure equilibrium volume, bulk modulus and pressure derivative of bulk modulus, the energy volume equation of state calculations were performed. The calculated values for the parameters of equation of state (anatase (V 0 =141.7 A, B 0 =417.4 GPa and B′ 0 =3.97), rutile (V 0 =65.68 A, B 0 =153.24 GPa and B′ 0 =3.7)) have good agreement with experiment [3–5] and DFT [6] studies. Computed results have been compared with experimental and other theoretical predictions. A good agreement is obtained with the experimental measurements.