Combining concepts of semiconductor physics and corrosion science, we develop a novel approach that allows us to perform ab initio calculations under controlled potentiostat conditions for electrochemical systems. The proposed approach can be straightforwardly applied in standard density functional theory codes. To demonstrate the performance and the opportunities opened by this approach, we study the chemical reactions that take place during initial corrosion at the water-Mg interface under anodic polarization. Based on this insight, we derive an atomistic model that explains the origin of the anodic hydrogen evolution.