  We investigate the details of the electronic structure in the neighborhoods
of a carbon atom vacancy in graphene by employing magnetization-constrained
density-functional theory on periodic slabs, and spin-exact, multi-reference,
second-order perturbation theory on a finite cluster. The picture that emerges
is that of two local magnetic moments (one \pi-like and one \sigma-like)
decoupled from the \pi- band and coupled to each other. We find that the ground
state is a triplet with a planar equilibrium geometry where an apical C atom
opposes a pentagonal ring. This state lies ~0.2 eV lower in energy than the
open-shell singlet with one spin flipped, which is a bistable system with two
equivalent equilibrium lattice configurations (for the apical C atom above or
below the lattice plane) and a barrier ~0.1 eV high separating them.
Accordingly, a bare carbon-atom vacancy is predicted to be a spin-one
paramagnetic species, but spin-half paramagnetism can be accommodated if
binding to foreign species, ripples, coupling to a substrate, or doping are
taken into account.
