Lithium-oxygen batteries are considered as promising energy storage technique because of high specific energy. However, their applications face a large challenge such as high overpotential, poor cycle and rate performance. Developing active catalysts to enhance electrochemical reactions is important to improve their electrochemical performance. Herein, I will focus on unraveling the descriptor of catalytic activity related to physical properties of catalyst. The first-principles calculations based on interfacial model were performed to study the oxygen reduction and evolution reaction mechanisms of Li2O2 supported on active surfaces of transition metal compounds. The O2 evolution and Li+ desorption energies show linear and volcano relationship with surface acidity of catalysts, respectively. Therefore, the charging voltage and desorption energies of Li+ and O2 over TMC could correlate with their corresponding surface acidity. According to this correlation, some highly active catalysts such as Co3O4, Mo2C, TiC, and TiN are predicted by calculations and confirmed by experiments.