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We investigate the magnetic phase diagram of the newly discovered iron-basedhigh temperature oxypnictide superconductors of the type RO$_{1-x}$F$_x $FeAs,with rare earths R=La, Sm, Nd, Pr and Ce by means of {\it ab initio} SGGA andSGGA+U density functional computations. We find undoped LaOFeAs to be a Mottinsulator when incorporating electronic correlations via SGGA+U for anyphysically relevant value of $U$. The doped compounds are according to SGGAconductors with a transition from an antiferromagnetic to a non-magnetic stateat a hole doping of concentration $x_c$=0.075 for R=Nd, Pr and at electrondoping $x_c$=0.25 for Ce and 0.6 for Sm. Superconductivity in these rare-earthoxypnictides thus appears in the vicinity of a magnetic quantum critical pointwhere electronic correlations are expected to play an important role because ofthe vicinity of a Mott insulating state at zero doping.

Mott State and Quantum Critical Points in Rare-Earth Oxypnictides $RO_{1-x}F_xFeAs$ ($R=La, Sm, Nd, Pr, Ce$)