  Systematic ab initio LDA calculations were performed for all the typical
representatives of recently discovered class of iron based high-temperature
superconductors: REOFe(As,P) (RE=La,Ce,Nd,Sm,Tb), Ba2Fe2As, (Sr,Ca)FFeAs,
Sr4Sc2O6Fe2P2, LiFeAs and Fe(Se,Te). Non-monotonic behavior of total density of
states at the Fermi level is observed as a function of anion height relative to
Fe layer with maximum at about Dz_a~1.37A, attributed to changing Fe - As
(P,Se,Te) hybridization. This leads to a similar dependence of superconducting
transition temperature Tc as observed in the experiments. The fit of this
dependence to elementary BCS theory produces semiquantitative agreement with
experimental data for Tc for the whole class of iron based superconductors. The
similar fit to Allen - Dynes formula underestimates Tc in the vicinity of the
maximum, signifying the possible importance of non - phonon pairing in this
region. These results unambiguously demonstrate that the main effect of Tc
variation between different types of iron based superconductors is due to the
corresponding variation of the density of states at the Fermi level.
