Experimental studies and theoretical calculations on the physical properties of ZnO with Cu/Ag/Au single doping have been reported, but reports on the magnetic and photocatalytic properties of ZnO by Zn vacancies and Cu/Ag/Au single doping and interstitial H coexistence are few. Moreover, locating the positions of the Zn vacancies is experimentally challenging. We used the GGA + U method within the framework of density functional theory to investigate the formation energy and magnetic and photocatalytic properties of Zn34MO36 (M = Cu/Ag/Au) and Zn34MHiO36 (M = Cu/Ag/Au) systems. Results show that the system is more stable under the O-rich condition. The Zn34CuO36, Zn34AgO36, and Zn34CuHiO36 systems all exhibit the magnetic properties of 2, −1 and 2 μB, and the O−-2p, Ag-4d, and Cu-3d states in the Zn34CuO36, Zn34AgO36 and Zn34CuHiO36 systems have local and itinerant electron properties. The Zn34AgHiO36 system has the longest electronic lifetime of 0.75 × 10−13 s and a longest hole lifetime of 0.70 × 10−13 s, with a relative maximum D value of 67.59, better carrier separation, and relatively high oxidation capacity. In the wavelength range of 400–800 nm, the Zn34AgHiO36 system has the strongest relative absorption spectrum intensity, the most pronounced red shift, the largest relative electric dipole moment of 109.19 × 10−30C·m and the largest relative activity. Therefore, the Zn34AgHiO36 system is the best photocatalyst for O production.
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