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 (Cu 2 S) surfaces. The considered H-donors are OH − /H 2 O and HS − /H 2 S 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 − /H 2 S have lower reaction barriers than H 2 O, our kinetic analysis suggest that H 2 O is expected to be the main H-source for the cathodic reaction under SNF repository conditions as results of the low sulfide concentrations ( 10 μM) expected in SNF repositories in Sweden, Finland and Canada.