Employing first-principles density functional theory calculations and Wannierization of the low energy band structure, we analyze the electronic structure of undoped, infinite-layer nickelate compounds, NdNiO$_2$, PrNiO$_2$ and LaNiO$_2$. Our study reveals important role of non-zero $f$-ness of Nd and Pr atoms, as opposed to $f^{0}$ occupancy of La. The non-zero $f$-ness becomes effective in lowering the energy of the rare-earth 5$d$ hybridized axial orbital, thereby enhancing the electron pockets and influencing the Fermi surface topology. The Fermi surface topology of NdNiO$_2$ and PrNiO$_2$ is strikingly similar, while differences are observed for LaNiO$_2$. This difference shows up in computed doping dependent superconducting properties of the three compounds within a weak coupling theory. We find two gap superconductivity for NdNiO$_2$ and PrNiO$_2$, and possibility of a single gap superconductivity for LaNiO$_2$ with the strength of superconductivity suppressed by almost a factor of two, compared to Nd or Pr compound.
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