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Nonelectrochemical hydrogen peroxide direct synthesis (HPDS) under ambient conditions is an environmentally benign and energy-efficient process that produces a green oxidizer. Despite its industrial importance, the reaction mechanism of HPDS is still controversial, even for the prototypical catalyst Pd. Density functional theory (DFT) calculations with a comprehensive consideration of entropic and solvation effects reveal that the conventionally accepted Langmuir-Hinshelwood mechanism fails to explain why H2O2 production dominates over H2O production, which was experimentally reported. Inspired by the recently suggested heterolytic mechanism that involves electron and proton transfer at Pd catalysts, we propose a new electrochemical DFT model that is applicable for nonelectrochemical systems where a protonation intrinsically occurs. Our model is based on combining the Butler-Volmer equation and constant potential DFT with hybrid explicit-implicit solvent treatments. Application of this model to Pd(111) surfaces produces accurate descriptions of the activation barriers of both H2O2 and H2O production (within only ~0.1 eV of experimentally measured values). The heterolytic mechanism has a lower barrier for the protonation steps for H2O2 production than the nonelectrochemical hydrogenation steps, leading to advantageous kinetics for H2O2 production over H2O production. This work is the first theoretical and computational study supporting the heterolytic H2O2 production mechanism, and it resolves the unanswered discrepancies between previous experimental and DFT results. We expect that these results will readily help the systematic development of improved catalysts for H2O2 synthesis.