First Principle Ab-initio Study of TiO$_2$*

We report results from first principle computations of electronic properties of rutile TiO${_2}$ within the local density functional approximation (LDA). Our first principle, non-relativistic and ground state calculations employed a local density functional approximation (LDA) potential and the linear combination of atomic orbitals (LCAO) -- utilizing a self-consistently obtained, optimized basis set. We solved self-consistently both the Kohn-Sham equation and the equation giving the ground state charge density in terms of the wave functions of the occupied states. Our calculated band structure shows that there is significant O$_2p$-Ti$_3d$ hybridization in the valence bands. These bands are well separated from the conduction bands by an indirect band gap of 2.95 eV, from $\Gamma$ to R. Consequently, this work predicts that rutile TiO$_2$ is an indirect band gap material, as all other gaps from our calculations are larger than 2.95 eV. A slightly larger, direct band gap of 3.05 eV is found at the $\Gamma$ point, in excellent agreement with experiment. Our structural optimization led to lattice parameters of 4.65 {\AA} and 2.97 {\AA} for $a_o$ and c$_o$, respectively, with a u parameter of 0.3051, and a bulk modulus of 215 GPa.