## 1 Introduction  
Many organic reagents were used in the froth flotation during the ore-dressing. Some of them discharged with the wastewater and are harmful to aquatic organisms and humans. The reported research indicated that some deformed cells of algae (_Scenedesmus obliquus_) were found in cultures exposed to 0145 for 48 h [1]: most of the fishes would die while the concentration of xanthate was over 5.0 mg.L\({}^{-1}\)[2]; Acrylonitrile, as the synthetic raw material of Ester-105, is possibly carcinogenic to humans (Group 2B) [3]. Besides, the residual beneficiation reagents might induce the release of heavy metals from the tailings pond, resulting in secondary pollution [4]. Many methods have been developed to treat organic beneficiation reagents or other organic compounds such as physical adsorption [5], biodegradation [6] and chemical oxidation [7, 8], and so on. For example, there needs to be 5 or more days to get to the removal efficiency of 85% for benzohydroxamic acid (BHA, the most widely-used collector in the flotation industry at present) with the method of biodegradation [9]. However, our previous studies indicated that La/TiO2 and Yb/TiO2 possessed high photodegradation activity to BHA (the removal efficiency was up to 90% in 2 h) [10]. TiO2 has been considered as the most promising photocatalyst among various semiconductor photocatalysts materials due to its benign physicochemical property and low cost [11]. In recent years,in order to improve the photocatalytic activity of TiO\({}_{2}\), the research topics have been aimed at resolving the problems of wide band gap (3.2 eV) and easy recombination of photogenerated electron-hole pairs. It is reported that doping with metal ions is an efficient way to enhance the photocatalytic activity of TiO\({}_{2}\)[12; 13]. Rare-earth elements have been proved to effectively promote the activity of TiO\({}_{2}\) because of the 4f electronic structure [14; 15; 16]. [PERSON] reported that the sample of 1 mol% of Yb\({}^{3+}\)-TiO\({}_{2}\) showed the highest photoactivity on the degradation of phenol under the visible light (\(\lambda>\) 450 nm) irradiation in the form of anatase of TiO\({}_{2}\)[15]. [PERSON]'s research results demonstrated that Nd doping inhibited the growth of TiO\({}_{2}\) crystallite and enhanced the thermal stability of anatase TiO\({}_{2}\)[16]. One suggested theory about the promoted photoactivity of rare-earth element doped compounds is that: The existence of the ground and excited states of rare-earth elements could reduce the recombination of electron-hole pairs by the transformation between RE\({}^{3+}\) and RE\({}^{2+}\)[17; 18]. Another proposed theory is that the added rare earth would change the surface composition of TiO\({}_{2}\) (more hydroxyl oxygen and adsorbed oxygen and some Ti\({}^{3+}\) species existed at the surface of the rare-earth modified TiO\({}_{2}\) (RE/TiO\({}_{2}\)) compared with pure TiO\({}_{2}\)) [19; 20]. Most of the published papers have focused on the discussion of RE/TiO\({}_{2}\) with one rare-earth element or two co-doped rare-earth elements [21; 22; 23]. [PERSON] and [PERSON] calculated lanthanide-doped anatase/rutile TiO\({}_{2}\) by density functional theory (DFT) respectively [24; 25], and the results indicated that most of the doped rare-earth ions could obviously reduce the band gap widths. To our knowledge, there is no systematic report of the combination of theoretical computation and practical experimentation. In this study, La, Ce, Gd, and Yb were chosen to prepare the rare-earth-doped TiO\({}_{2}\) due to their different 4f and 5d orbits. The 4f and 5d orbitals are 4f\({}^{9}\)5d\({}^{1}\), 4f\({}^{2}\)5d\({}^{0}\), 4f\({}^{7}\)5d\({}^{1}\), 4f\({}^{14}\)5d\({}^{0}\) for La, Ce, Gd and Yb, respectively. So, La, Ce, Gd, Yb present the non-4f orbitals, normal-4f orbitals, semi-4f orbitals, and full-4f orbitals. The synthesized RE/TiO\({}_{2}\) composites were characterized by XRD, XPS, UV-vis DRS, and N\({}_{2}\) adsorption.