Starting from the optimized anatase TiO₂ unit cell, we construct the TiOS model with the outermost and second layers terminated by twofold coordinated O atoms and fivefold coordinated Ti atoms, respectively. The doping concentration of TiOS doped with TM atoms is 1.37 at.% and six typical doping manners in Fig. 1b are considered. A TM atom can be vertically adsorbed on a twofold coordinated O atom (O1-Ad), threefold coordinated O atoms (O2-Ad, O3-Ad), a fivefold coordinated Ti atom (Ti1-Ad), and a sixfold coordinated Ti atom (Ti2-Ad). In addition, TM atoms are only allowed to enter the largest and outermost caves (Cav) because of their large atomic radii. Table 2 shows the impurity formation energies E_f for ten different 4d TM atom doped models of the TiOS in six different doping manners. We can see only Ag-Cav and Cd-Cav dopings have positive E_f , indicating these two doping processes correspond to endothermic reactions, and are difficult to occur. This should be reasonable since the structures with Ag or Cd atoms doped into the caves are unstable owing to the large atom radii of Ag and Cd. However, all the other doped cases studied here have negative E_f , which indicates the corresponding doping processes are exothermic reactions that can occur more easily. Furthermore, the optimal doping manners for all TM atoms can be readily found according to the lowest E_f , and listed in the following: O1-Ad doping for Ru, O2-Ad doping for Pd and Ag, O3-Ad doping for Y and Rh, Ti1-Ad doping for Tc and Cd, and Cav doping for Zr, Nb, and Mo. Obviously, different TM atoms have different optimal doping manners. In fact, even in the same doping manner, the impurity atoms may have various positions after being optimized. In particular, Tc, Pd, Ag, and Cd atoms, having stable full or half-full filling outermost orbitals, prefer the O2-Ad or Ti1-Ad doping, while Y, Zr, Nb, Mo, and Rh atoms with unstable outermost orbitals and spin multiplicity, prefer the O3-Ad or Cav doping. The different optimal doping manners are closely dependent on the 4d electron configuration, the atomic radius, and the electronegativity of the TM atom. Thus, the optimal doping manners of all 4d TM atoms have been determined.

Table 2 The formation energies (eV) of TiOS doped with 4d TM atoms.