  We present electronic structure calculations on layered nickelate
oxyfluorides derived from the Ruddlesden-Popper arisotype structure in search
of unidentified materials that may host nickelate superconductivity. By
performing anion exchange of oxygen with fluorine, we create two heteroanionic
La$_2$NiO$_3$F polymorphs and stabilize Ni$^{1+}$ in 4-coordinate and
5-coordinate square planar and square pyramidal geometries, respectively. We
further predict chemical reactions with high thermodynamic driving forces to
guide their synthesis. These oxyfluorides are weakly correlated
antiferromagnetic insulators and their nonmagnetic phases exhibit quasi-2D
Fermi surfaces dominated by Ni $d_{x^2-y^2}$ states, which strikingly resemble
undoped cuprate superconductors. We discuss how the oxyfluoride anion chemistry
promotes Ni-O covalency and single-band character that is more similar to the
cuprates than homoanionic infinite-layer nickelates. We use our understanding
to propose doping strategies and layered LaSrNiO$_2$F$_2$ and
La$_3$Ni$_2$O$_4$F$_3$ nickelate oxyfluorides with tunable electronic and
magnetic structures for experimentation.
