Electronic structure of rutile (TiO₂)

The energy band, band gap and density-of-states (DOS) have been calculated for rutile (TiO₂) using the embedded-cluster numerical discrete variational method. The chemically complete cluster TiO₄O₂ is embedded in the periodic crystal lattice of rutile and the entire system is treated iteratively by one-electron local-density theory. The interaction of the cluster with the crystal environment is represented by an effective potential with boundary conditions which contain cluster-host Coulomb and exchange interactions as well as intracluster interactions. A comparison with rutile valence-band X-ray photoelectron spectra (XPS) and optical absorption data shows that the results are generally in reasonable agreement with the experiment; the agreement being particularly good for the band gap. We also plot the map of charge-density distribution of valence-electrons, from which the interaction between Ti and O atoms and the degree of Ti_3dO_2p covalency are indicated.