Sulfide-induced corrosion is expected to be the dominating long-term corrosion process for copper containers in technical concepts for deep geological disposal of spent nuclear fuel (SNF), adapted in several waste management programs around the world. The present study investigates the atomic-scale mechanism of the cathode side of the corrosion reaction using Density Functional Theory (DFT) calculations. Despite the central role of the reaction, neither the site of reaction nor the active species has been previously established. Here we compare the cathodic reaction leading to H-2-evolution on pure copper and on chalcocite (Cu2S) surfaces. The considered H-donors are OH-/H2O and HS-/H2S which are all available at the neutral to alkaline conditions anticipated at the SNF disposal sites. Assuming Volmer-Tafel-Heyrovsky kinetics, we find that the cathodic reactions are many orders of magnitude faster on copper compared to copper sulfide. Although we find that HS-/H2S have lower reaction barriers than H2O, our kinetic analysis suggest that H2O is expected to be the main H-source for the cathodic reaction under SNF repository conditions as results of the low sulfide concentrations (less than or similar to 10 mu M) expected in SNF repositories in Sweden, Finland and Canada. (c) 2019 The Electrochemical Society.