Theoretical band energetics of $Ba(M0.5Sn0.5)O3$ for solar photoactive applications

We report here a comparative study of the theoretically calculated electronic structures of cubic $BaSnO3$ and cubic $Ba(M0.5Sn0.5)O3$ with $M=Ti$⁠, V, Cr, Zr, Ce, and Pb, the tetravalent metal ions, to explore their possible efficacy for the visible light photocatalysis and solar energy conversion. We performed the calculations within the framework of density functional theory by using WIEN97 code. The $3d$ orbitals of Ti, V, and Cr, $4d$ of Zr, and the $4f$ and $6s$ orbitals of Ce and Pb, respectively, contributed to the bottom of the conduction band for narrowing of the band gap of cubic $BaSnO3$⁠. Calculation of the frequency dependent absorption coefficient $I(ω)$ of $Ba(M0.5Sn0.5)O3$ indicated that among the transition metal (Ti, V, Cr, and Zr) doped systems, Cr has comparatively higher visible absorption efficiency, whereas among other metal (Pb and Ce) systems, Pb showed significant absorption coefficient in low energy range $(E⩽2eV)$⁠. The comparison of the computed optical absorption coefficients shows that the $Ba(M0.5Sn0.5)O3$ systems can be arranged with respect to $M$ as (i) $Cr>V>Ti$ among first row transition metals and (ii) $Pb>Ce>Zr$ among rest of tetravalent metals, in decreasing order of photoresponse towards low energy photons $(E⩽2.5eV)$⁠.