  We perform combined density functional and dynamical mean-field calculations
to study the pyrochlore iridates Lu$_2$Ir$_2$O$_7$, Y$_2$Ir$_2$O$_7$ and
Eu$_2$Ir$_2$O$_7$. Both single-site and cluster dynamical mean-field
calculations are performed and spin-orbit coupling is included. Paramagnetic
metallic phases, antiferromagnetic metallic phases with tilted Weyl cones and
antiferromagnetic insulating phases are found. The magnetic phases display
all-in/all-out magnetic ordering, consistent with previous studies. Unusually
for electronically three dimensional materials, the single-site dynamical
mean-field approximation fails to reproduce qualitative material trends,
predicting in particular that the paramagnetic phase properties of
Y$_2$Ir$_2$O$_7$ and Eu$_2$Ir$_2$O$_7$ are almost identical, although in
experiments the Y compound has a much higher resistance than the Eu compound.
This qualitative failure is attributed to the importance of intersite magnetic
correlations in the physics of these materials.
