“…The MTO has an inverse spinel structure, where half of the Mg 2+ occupies the 8 a sites; however, the other halves of Mg 2+ and Ti 4+ randomly occupy the 16 d sites, and O 2– occupies the 32 e sites. The direct coordinates of the Ti atoms ( x y z ) at the 16 d sites of the 56-atom Mg 16 Ti 8 O 32 model are (0.375 0.375 0.625), (0.875 0.625 0.875), (0.875 0.875 0.625), (0.125 0.625 0.125), (0.875 0.125 0.375), (0.125, 0.875, 0.375), (0.625, 0.125, 0.125), and (0.625, 0.875, 0.875), whereas those of the Mg atoms are (0.375 0.625 0.375), (0.625 0.375 0.375), (0.125 0.125 0.625), (0.625 0.625 0.625), (0.375 0.875 0.125), (0.125 0.375 0.875), (0.875 0.375 0.125), and (0.375 0.125 0.875). , For MTO:Mn, it has been experimentally demonstrated that the Mn dopant substitutes the Ti ions at the 16 d sites; thus, the atomistic model of MTO:Mn was built by substituting one of the eight Ti atoms in the 16 d sites after a systematical examination. Among the eight possible Ti 16 d sites, the most energetically favorable one for substitution was (0.375, 0.325, 0.675), as shown in Figure a.…”