Using density-functional theory, we predict stable alloy configurations (ground states) for a 1 nm Pt–Pd cuboctahedral nanoparticle across the entire composition range and demonstrate their use as tunable alloy catalysts via hydrogen-adsorption studies. Unlike previous works, we use simulated annealing with a cluster expansion Hamiltonian to perform a rapid and comprehensive search that encompasses both high and low-symmetry configurations. The ground states show Pt(core)–Pd(shell) type configurations across all compositions but with specific Pd patterns. For catalysis studies at room temperatures, the ground states are more realistic structural models than the commonly assumed random alloy configurations. Using the ground states, we reveal that the hydrogen adsorption energy increases (decreases) monotonically with at. % Pt for the {111} hollow ({100} bridge) adsorption site. Such trends are useful for designing tunable Pd–Pt nanocatalysts for the hydrogen evolution reaction.