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Fully relativistic first-principles electronic structure calculations basedon a noncollinear local spin density approximation (LSDA) are performed forpyrochlore iridates Y$_2$Ir$_2$O$_7$ and Pr$_2$Ir$_2$O$_7$. The all-in, all-outantiferromagnetic (AF) order is stablized by the on-site Coulomb repulsion$U>U_c$ in the LSDA+$U$ scheme, with $U_c\sim1.1$~eV and 1.3~eV forY$_2$Ir$_2$O$_7$ and Pr$_2$Ir$_2$O$_7$, respectively. AF semimetals with andwithout Weyl points and then a topologically trivial AF insulator successivelyappear with further increasing $U$. For $U=1.3$~eV, Y$_2$Ir$_2$O$_7$ is atopologically trivial narrow-gap AF insulator having an ordered local magneticmoment $\sim0.5\mu_B$/Ir, while Pr$_2$Ir$_2$O$_7$ is barely a paramagneticsemimetal with electron and hole concentrations of $0.016$/Ir, in overallagreements with experiments. With decreasing oxygen position parameter $x$describing the trigonal compression of IrO$_6$ octahedra, Pr$_2$Ir$_2$O$_7$ isdriven through a non-Fermi-liquid semimetal having only an isolated Fermi pointof $\Gamma_8^+$, showing a quadratic band touching, to a $Z_2$ topologicalinsulator.

First-principles study on cubic pyrochlore iridates Y2Ir2O7 and Pr2Ir2O7