  Recent experimental discoveries of graphene-stabilized patches of
two-dimensional (2D) metals have motivated also their computational studies.
However, so far the studies have been restricted to ideal and infinite 2D
metallic monolayers, which is insufficient because in reality the properties of
such metallic patches are governed by microstructures pervaded by edges,
defects, and several types of perturbations. Here we use density-functional
theory to calculate edge and vacancy formation energies of hexagonal and square
lattices of 45 elemental 2D metals. We find that the edge and vacancy formation
energies are strongly correlated and decrease with increasing Wigner-Seitz
radii, analogously to surface energies. Despite a radical reduction in atomic
coordination numbers, the 2D and 3D vacancy formation energies and work
functions are nearly the same for each metal. Finally, static polarizabilities
reveal a clear cubic dependence on bond length. These trends provide useful
insights when moving towards reality with elemental 2D metals.
