Recently, Au-based nanostructures have attracted extensive interest due to their excellent activities in heterogeneous catalysis. The reaction mechanisms have been interpreted qualitatively by the quantum confinement effect due to the low-coordination of Au atoms in nanostructures. In this work, systematic first-principles calculations were carried out to obtain an in-depth understanding of the origin of C-H bond activations with Au-based catalysts in on-surface synthesis. Combining density functional theory (DFT) calculations and scanning tunneling microscopy (STM) studies, we reveal that the d-band centre and the d-band width of the Au-5dz2 orbital in an energy window of -6.80 to 0.00 eV may serve as theoretical descriptors for the prediction of the activity of Au catalysts in C-H bond activations. This work may therefore inspire further investigations on the design of new catalysts.