  Common two-dimensional (2D) materials have a layered 3D structure with
covalently bonded, atomically thin layers held together by weak van der Waals
forces. However, in a recent transmission electron microscopy experiment,
atomically thin 2D patches of iron were discovered inside a graphene nanopore.
Motivated by this discovery, we perform a systematic density-functional study
on atomically thin elemental 2D metal films, using 45 metals in three lattice
structures. Cohesive energies, equilibrium distances, and bulk moduli in 2D are
found to be linearly correlated to the corresponding 3D bulk properties,
enabling the quick estimation of these values for a given 2D metal and lattice
structure. In-plane elastic constants show that most 2D metals are stable in
hexagonal and honeycomb, but unstable in square 2D structures. Many 2D metals
are surprisingly stable against bending.
