Is there a proximate antiferromagnetic insulating phase in infinite-layer nickelates?

We provide a set of computational experiments based on \textit{ab initio} calculations to elucidate whether a cuprate-like antiferromagnetic insulating state can be present in the phase diagram of the infinite-layer nickelate family (RNiO$_2$, R= rare-earth). We show that metallicity in the parent phase is produced by an R-d band that requires hybridization with the Ni-d bands to become largely dispersive. If this off-plane R-Ni coupling is suppressed, the system is an antiferromagnetic insulator since that largely dispersive band is no longer able to cross the Fermi level. As such, the reduction of the strong out-of-plane Ni-d hopping leads to an electronic structure closer to the nominal Ni-d$^9$ occupation as the self-doping effect -- understood as charge transfer from the Ni-d to the R-d orbitals -- disappears. This can be achieved if a structural element that suppresses the c-axis dispersion is introduced (i.e. vacuum in a monolayer of NdNiO$_2$, or a blocking layer in multilayers formed by (NdNiO$_2$)$_1$/(NdNaO$_2$)$_1$). We also show how the reduced Ruddlesden-Popper counterparts (R$_4$Ni$_3$O$_8$) are able to produce the same effect due to the presence of fluorite RO$_2$ blocking slabs.