  The identification of alternatives to the Lithium-ion battery architecture
remains a crucial priority in the diversification of energy storage
technologies. Accompanied by the low reduction potential of
$\mathrm{Ca^{2+}/Ca}$, -2.87 V vs. SHE, metal-anode-based rechargeable Calcium
(Ca) batteries appear competitive in terms of energy densities. However, the
development of Ca-batteries lacks high-energy density intercalation cathode
materials. Using first-principles methodologies, we screen a large chemical
space for potential Ca-based cathode chemistries, with composition of
$\mathrm{Ca_iTM_jZ_k}$, where TM is a 1$^{st}$ or 2$^{nd}$ row transition metal
and $\mathrm{Z}$ is oxygen, sulfur, selenium or tellurium. 10 materials are
selected and their Ca intercalation properties are investigated. We identify
two previously unreported promising electrode compositions: the post-spinel
$\mathrm{CaV_2O_4}$ and the layered $\mathrm{CaNb_2O_4}$, with Ca migration
barriers of $\sim$654 meV and $\sim$785 meV, respectively. Finally, we analyse
the geometrical features of the Ca migration pathways across the 10 materials
studied and provide an updated set of design rules for the identification of
good ionic conductors, especially with large mobile cations.
