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Recent discovery of superconductivity in the doped infinite-layer nickelateshas renewed interest in understanding the nature of high-temperaturesuperconductivity more generally. The low-energy electronic structure of theparent compound NdNiO$_{2}$, the role of electronic correlations in drivingsuperconductivity, and the possible relationship betweeen the cuprates and thenickelates are still open questions. Here, by comparing LaNiO$_2$ and NdNiO$_2$systematically within a parameter-free density functional framework,all-electron first-principles framework, we reveal the role Nd 4$f$ electronsin shaping the ground state of pristine NdNiO$_2$. Strong similarities arefound between the electronic structures of LaNiO$_2$ and NdNiO$_2$, except forthe effects of the 4$f$-electrons. Hybridization between the Nd 4$f$ and Ni3$d$ orbitals is shown to significantly modify the Fermi surfaces of variousmagnetic states. In contrast, the competition between the magnetically orderedphases depends mainly on the gaps in the Ni $d_{x2-y2}$ band, so that theground state in LaNiO$_2$ and NdNiO$_2$ turns out to be striking similarity tothat of the cuprates. The $d-p$ band-splitting is found to be much larger whilethe intralayer 3$d$ ion-exchange coupling is smaller in the nickelates comparedto the cuprates. Our estimated value of the on-site Hubbard $U$ is similar tothat in the cuprates, but the value of the Hund's coupling $J_H$ is found to besensitive to the Nd magnetic moment. The exchange coupling $J$ in NdNiO$_2$ isonly half as large as in the curpates, which may explain why $T_c$ in thenickelates is half as large as the cuprates.

$f$-electron and magnetic ordering effects in nickelates LaNiO$_2$ and NdNiO$_2$: remarkable role of the cuprate-like $3d_{x^2-y^2}$ band