Abstract
To explore quasiparticle (QP) energy gaps and photoabsorption spectra of rutile TiO2 with nonmagnetic transition metal (Zr, Mo, Zn, Cd) impurities, we conducted a Γ-point only GW ＋ Bethe–Salpeter equation (BSE) calculation on a 72 (or 71) atom supercell. Our findings reveal that Zn and Cd impurities must coexist, at least partly, with oxygen vacancies to maintain charge neutrality. Among the systems considered, Mo, Zn, or Cd doped rutile TiO2 may exhibit optical absorption and catalytic activity under visible light. The resulting QP energy gaps (ΔɛQP) and photoabsorption energies (PAEs) are fairly in good agreement with both experimental and theoretical data currently available. The necessary conditions for the applicability of the Γ-point only approach in the GW ＋ BSE framework were found to be: (1) The Γ-point only GW calculation should reproduce a reasonable band gap. (2) The “superficial” exciton binding energy (the diagonal element of Wvc;vc−2Xvc;vc between v= VBM and c= CBM, where W and X are the direct and exchange terms of the BSE matrix elements, respectively) must be positive or marginally negative. (3) The “real” exciton binding energy (ΔɛQP− the lowest PAE) should be positive, even if it is exceptionally small.
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