The chemical conversion of small molecules such as H$_2$, H$_2$O, O$_2$, N$_2$, CO$_2$, and CH$_4$ to energy and chemicals is critical for a sustainable energy future. Theoretical approaches have suggested various potential catalysts and enhanced our understanding. However, current theoretical model, which neglects surface charging and kinetics, does not sufficiently describe the electrode-electrolyte interface. In this dissertation, we employed advanced interface model which describes more realistic interface and investigated the electrochemical conversion of small molecule. We mainly focus on the quantitative explanation for the potential-dependent experimental measurements such as potential-dependent competition with side reaction, active site coverage changes and catalytic activity which have not been theoretically investigated by conventional methods. Two reactions (N$_2$ reduction and CO$_2$ reduction) are mainly discussed here. In Chapter 3, we investigated the origin of premature decrease of NRR activity based on the potential-dependent competition with hydrogen evolution reaction and suggested potential directions for overcoming the premature decrease. In Chapter 4, we investigated CO$_2$ reduction on Ni single atom catalyst and suggested design strategy for enhancing catalytic activity of Ni single atom catalyst.