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We study the Be–C doped MgB2 system by the first principles method based on density functional theory. The compensation effect between electron type doping and hole type doping is shown in the total density of states on the Fermi level, the real part of optical conductivity, and the number of effective carriers. The compensation mechanisms are discussed. The critical temperatures for different systems are calculated.

Using the first-principles approach based upon the density functional theory (DFT), we have studied the electronic structure of wurtzite ZnO systems doped with C at different sites. When Zn is substituted by C, the system turns from a direct band gap semiconductor into an indirect band gap semiconductor, and donor levels are formed. When O is substituted by C, acceptor levels are formed near the top of the valence band, and thus a p-type transformation of the system is achieved. When the two kinds of substitution coexist, the acceptor levels are compensated for all cases, which is unfavorable for the p-type transformation of the system.

The band structure and the optical properties of Ba0.5Sr0.5TiO3 are studied by the first principles method. The results show that the conduction band and the valence band are derived from the hybridization between titanium 3d orbitals and oxygen 2p orbitals. In the conduction band, titanium 3d orbitals play a primary role, while in the valence band, oxygen 2p orbitals play a primary role. The absorption coefficient is as targe as 105cm-1, and the absorption is mainly localised in the low energy region. The refractive index n（0） equals 2.1. Our results are in good agreement with the experimental results.