  The electronic structure and physical properties of the pnictide compound
families $RE$OFeAs ($RE$ = La, Ce, Pr, Nd, Sm), $A$Fe$_{2}$As$_{2}$ ($A$ = Ca,
Sr, Ba, Eu), LiFeAs and FeSe are quite similar. Here, we focus on the members
of the $A$Fe$_{2}$As$_{2}$ family whose sample composition, quality and single
crystal growth are better controllable compared to the other systems. Using
first principles band structure calculations we focus on understanding the
relationship between the crystal structure, charge doping and magnetism in
$A$Fe$_{2}$As$_{2}$ systems. We will elaborate on the tetragonal to
orthorhombic structural distortion along with the associated magnetic order and
anisotropy, influence of doping on the $A$ site as well as on the Fe site, and
the changes in the electronic structure as a function of pressure.
Experimentally, we investigate the substitution of Fe in
SrFe$_{2-x}TM_{x}$As$_{2}$ by other 3$d$ transition metals, $TM$ = Mn, Co, Ni.
In contrast to a partial substitution of Fe by Co or Ni (electron doping) a
corresponding Mn partial substitution does not lead to the supression of the
antiferromagnetic order or the appearance of superconductivity. Most calculated
properties agree well with the measured properties, but several of them are
sensitive to the As $z$ position. For a microscopic understanding of the
electronic structure of this new family of superconductors this structural
feature related to the Fe-As interplay is crucial, but its correct ab initio
treatment still remains an open question.
