  We present a theoretical study using density functional calculations of the
structural, electronic and magnetic properties of 3d transition metal, noble
metal and Zn atoms interacting with carbon monovacancies in graphene. We pay
special attention to the electronic and magnetic properties of these
substitutional impurities and found that they can be fully understood using a
simple model based on the hybridization between the states of the metal atom,
particularly the d shell, and the defect levels associated with an
unreconstructed D3h carbon vacancy. We identify three different regimes
associated with the occupation of different carbon-metal hybridized electronic
levels:
  (i) bonding states are completely filled for Sc and Ti, and these impurities
are non-magnetic;
  (ii) the non-bonding d shell is partially occupied for V, Cr and Mn and,
correspondingly, these impurties present large and localized spin moments;
  (iii) antibonding states with increasing carbon character are progressively
filled for Co, Ni, the noble metals and Zn. The spin moments of these
impurities oscillate between 0 and 1 Bohr magnetons and are increasingly
delocalized.
  The substitutional Zn suffers a Jahn-Teller-like distortion from the C3v
symmetry and, as a consequence, has a zero spin moment. Fe occupies a distinct
position at the border between regimes (ii) and (iii) and shows a more complex
behavior: while is non-magnetic at the level of GGA calculations, its spin
moment can be switched on using GGA+U calculations with moderate values of the
U parameter.
