  Some important aspects of the electronic structure of the iron oxypnictides
depend very sensitively on small changes in interatomic distances and bond
angles within the iron-pnictogen subunit. Using first-principles full-potential
electronic structure calculations, we investigate this sensitive dependence,
contrasting in particular LaOFeAs and LaOFeP. The width of the Fe-bands is
significantly larger for LaOFeP, indicating a better metal and weaker
electronic correlations. When calculated at their experimental crystal
structure these two materials have significantly different low-energy band
structure. The topology of the Fermi surface changes when going from LaOFeP to
LaOFeAs, with a three-dimensional hole pocket present in the former case
transforming into a tube with two-dimensional dispersion. We show that the
low-energy band structure of LaOFeAs evolves towards that of LaOFeP as the As
atom is lowered closer to the Fe plane with respect to its experimental
position. The physical origin of this sensitivity to the iron-pnictogen
distance is the covalency of the iron-pnictogen bond, leading to strong
hybridization effects. To illustrate this, we construct Wannier functions,
which are found to have a large spatial extension when the energy window is
restricted to the bands with dominant iron character. Finally, we show that the
Fe bandwidth slightly increases as one moves along the rare-earth series in
ReOFeAs and discuss the physical origin of this effect.
