  Superconductivity in square BX$_2$-plane-based materials currently is only
found in $d^9$ configuration. This raises a question that whether other
configurations $d^{n}$ ($n\neq 9$) of transition metals in the prototype of
square BX$_2$ plane can also host superconductivity. We systematically explore
this question via analyzing the electronic structure of materials from $d^{8}$
to $d^5$ platforms using density-functional calculation, including existing
materials SrFeO$_2$ and SrFeO$_2$F, and proposed ones LaNiO$_2$F and
LaCoO$_2$F. Results show a good commonality between these materials and the
cuprate and nickelate superconductors in their high-energy electronic
structure, namely dominant low-energy states by ligand $p$ and $d_{x^2-y^2}$
orbitals. Other $d$ orbitals are all in the high-energy channel due to strong
intra-atomic repulsion resulting in similar low-energy effective Hamiltonian
except for the different number of local spins. These results hopefully suggest
the possible superconductivity besides the prototype of $d^9$. Superconducting
phases found in these sets of materials will be highly valuable to understand
the high-temperature superconductivity and even to find better superconducting
families than the cuprates.
