The recent discovery of superconductivity in oxygen-reduced monovalent nickelates has raised a new platform for the study of unconventional superconductivity, with similarities and differences with the cuprate high temperature superconductors. In this paper we investigate the family of infinite-layer nickelates $R$NiO$_2$ with rare-earth $R$ spanning across the lanthanide series, introducing a new and non-trivial knob with which to tune nickelate superconductivity. When traversing from La to Lu, the out-of-plane lattice constant decreases dramatically with an accompanying increase of Ni $ d_{x^2-y^2}$ bandwidth; however, surprisingly, the role of oxygen charge transfer diminishes. In contrast, the magnetic exchange grows across the lanthanides which may be favorable to superconductivity. Moreover, compensation effects from the itinerant $5d$ electrons present a closer analogy to Kondo lattices, indicating a stronger interplay between charge transfer, bandwidth renormalization, compensation, and magnetic exchange. We also obtain the microscopic Hamiltonian using Wannier downfolding technique, which will provide the starting point for further many-body theoretical studies.
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