  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.
