Abstract
Abstract Calculations have been performed by using ab-initio pseudo-potentials with plane-wave basis set within the local-density approximation for three phases of titanium dioxide. The band structure, density of states, structure optimization and optical properties of three phases of titanium dioxide have been studied. The general features of the band structure for rutile and anatase are quite similar and both in agreement with experimental data and other calculations. The band structure of brookite is also close to other calculations. Rutile has the smallest band gap among these phases and brookite has the largest one. Rutile and brookite have direct band gap at Γ but anatase has an indirect one. The general features of three phases of TiO2 are quite similar. From the analysis of partial density of states, we find the hybridization of 2p states of O and 3d states of Ti. We minimize the total energy of the three phases of TiO2 with respect to the structure parameters a, c/a and u. Our calculated lattice constant a, lattice constant ratio c/a and the internal coordinate u are in good agreement with experi-mental results and close to other theoretical calculations. Bulk modulus is also obtained by fitting the data with Murnaghan’s equation of states. Our data of bulk modulus of rutile and anatase are consistent with experimental values. Brookite has the smallest value of these polymorphs this may be attributed to its structure. We also studied the optical properties of TiO2 by calculating the dielectric functions. All three phases of TiO2 show anisotropic structures in the dielectric functions. Static dielectric constants are obtained from the real part of the dielectric function. Our calculations show subtle differences in the optical properties of three phases of TiO2.