Rh-hydride phases were believed to be key causes of the exceptional catalytic ability of Rh catalysts under H2 reductive conditions. Here, we utilize the large-scale machine-learning-based global optimization to explore millions of Rh bulk, surface, and nanoparticle structures in contact with H2, which rules out the presence of subsurface/interstitial H in Rh and Rh-hydride phases as thermodynamically stable phases under ambient conditions. Instead, an exceptional Rh-H affinity is identified for surface Rh atoms in Rh nanoparticles that can accommodate a high concentration of adsorbed H, with the surface Rh to H ratio reaching ∼2.5, featuring stable six-H-coordinated Rh, [RhH6]. Such [RhH6] species forming at edged Rh sites are found to be the key intermediates in the electrochemical hydrogen evolution reaction (HER) on Rh. Guided by theory, our synthesized Rh concave nanocubes with a high density of edged Rh sites achieve a Tafel slope of 28.4 mV dec-1 and a low overpotential of 36.1 mV at jECSA = 1 mA cm-2, which outperforms commercial Pt/C and other morphologies of Rh catalysts. Our results clarify the active phase in Rh-H nanosystems and guide the catalyst design by precise morphology control of nanocatalysts.