We use density functional theory to study a free-standing 2D copper monolayer. We find that the Cu monolayer is stable in 15 ps ab initio molecular dynamics simulations up to 1200 K. Due to the smaller number of bonds per atom in the 2D layer compared to the 3D bulk, we observe a significantly enhanced energy per bond (0.92 versus 0.58 eV/bond). This is similar to the increase in bond strength going from 3D diamond to 2D graphene. We predict various properties of this material, including band

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... ructure and density of states. The free-standing 2D Cu monolayer is hexagonal close packed and is the global minimum structure. One valence electron from each atom is delocalized and is donated into a 2D nearly free electron gas.