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To estimate the reaction free energies of the hydrogen evolution reaction (HER) on under-coordinated metallic sites, density function theory (DFT) calculations are usually employed to calculate the hydrogen adsorption energy with an "only-one-hydrogen-adsorption" model, assuming that adsorption with one hydrogen is the most thermodynamically favorable situation during catalysis. In this brief report, we show that on many single atom sites, adsorption of more than one hydrogen is sometimes even more thermodynamically favorable, with the presence of two or three hydrogens resulting in lower adsorption energies. These interesting non-monotonic trends indicate that modeling HER and other hydrogen-related reactions on under-coordinated sites should also consider the numbers of hydrogen being adsorbed at the same site, otherwise the results could deviate from real experimental situations. [ABSTRACT FROM AUTHOR]