To theoretically study the structures of metal clusters on oxides is very important and becomes one of the most challenging works in computational heterogeneous catalysis since many factors affect their structures and lead to various possibilities. In this work, it is very interesting to find that the stable structures and stability evolution of Au-x clusters on ceria are varied with different index surfaces of CeO2. The corresponding reasons in chemical, geometric and electronic properties are systematically explored. Au-x (x=1-4) clusters prefer to separately disperse at the O-O bridge sites on CeO2(100) due to the low coordination number of surface O; while aggregate due to the strong Au-Au attractions when x is larger than 4. Owing to the uniform distribution of O-O bridge sites on CeO2(111) and (100), the most stable configurations of Au-x are 3D structures with bottom atoms more than top ones when xis larger than 4. However, 2D configurations of Au-x/CeO2(110) (x<10) are more stable than the corresponding 3D structures due to the particular O-O arrangement on CeO2(110). 3D Au-x clusters across O-O-Y lines are suggested as the most stable configurations for Au-x/CeO2(110) (x >= 10). The present work gives a detailed example for the theoretical study of metal clusters on oxide, and will shed light into the design for controllable synthesis of ceria-based catalysts with metal nanoparticles supported on CeO2. (C) 2016 Elsevier B.V. All rights reserved.