  Magnetism in 2D networks of the acetylene-bridged transition metal porphyrins
M(P)-2(C-C)-2 (denoted P-TM), and oxo-TM-porphyrins OM(P)-2(C-C)-2 (denoted
P-TMO), is studied with the density functional theory (DFT) and the
self-interaction corrected pseudopotential scheme (pSIC). Addition of oxygen
lowers magnetism of P-TMO with respect to the corresponding P-TM for most of
the first-half $3d$-row TMs. In contrast, binding O with the second-half
$3d$-row TMs or Sc increases the magnetic moments. Ferrimagnetism is found for
the porphyrin networks with the TMs from V to Co and also for these cases with
oxygen. This is a long-range effect of the delocalized spin-polarization,
extended even to the acetylene bridges.
