The amount of under-potential-deposited (UPD) H(ads), if it forms on Cu(111), is small compared to what forms on Pt(111). According to experimental literature, current density on polycrystalline copper increases slowly in the over-potential-deposited (OPD) potential range beginning at 0 V and rises rapidly at several hundred mV negative potential. Using a comprehensive density functional theory for the electrochemical interface, including Fermi level shifts, in this article we attribute this behavior to calculated weak H adsorption which requires the potential to be reduced to similar to 0.0 V(SHE) in order for H(ads) deposition to commence. A literature estimate, based on exchange current densities, of the activation energy for H-2 evolution at 0 V is similar to 0.32 eV. As the coverage increases with increasingly negative potentials, we calculate the H adsorption energy decreases at a rate 0.27 eV/V for Cu(111), and this will decrease the effective activation energy. We propose that the observed rapid increase in current density at approximately -0.4 V corresponds to similar to 0.5 ML coverage by H(ads) and reflects the decreasing activation energy at more negative potentials. We also relate our calculated findings to the literature for electroless copper deposition and to literature for palladium-doped copper as a heterogeneous hydrogenation catalyst. (C) The Author(s) 2017. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. All rights reserved.