  Na-ion batteries (NIBs) are increasingly looked at as a viable alternative to
Li-ion batteries due to the abundance, low cost, and thermal stability of
Na-based systems. To improve the practical utilization of NIBs in applications,
it is important to boost the energy and power densities of the electrodes being
used, via discovery of novel candidate materials. Thus, we explore the chemical
space of transition metal containing oxyfluorides (TMOFs) that adopt the
perovskite structure as possible NIB electrodes. Our choice of the perovskite
structure is motivated by the `large' cationic tunnels that can accommodate
Na$^+$, while the chemistry of TMOFs is motivated by the high electronegativity
and inductive effect of F$^-$, which can possibly lead to higher voltages. We
use density functional theory based calculations to estimate the ground state
polymorphs, average Na (de)intercalation voltages, thermodynamic stabilities
and Na$^+$ mobility on two distinct sets of compositions: the F-rich
Na$_{x}$MOF$_{2}$, and the O-rich Na$_{1+x}$MO$_{2}$F where $x$ = 0--1 and
M~=~Ti, V, Cr, Mn, Fe, Co, or Ni. Upon identifying the ground state polymorphs
in the charged compositions (i.e., MOF$_2$ and NaMO$_2$F), we show that F-rich
perovskites exhibit higher average voltages compared to O-rich perovskites.
Also, we find six stable/metastable perovskites in the F-rich space, while all
O-rich perovskites (except NaTiO$_2$F) are unstable. Finally, our Na-ion
mobility calculations indicate that TiOF$_{2}$-NaTiOF$_2$, VOF$_{2}$-NaVOF$_2$,
CrOF$_{2}$, and NaMnOF$_{2}$ can be promising compositions for experimental
exploration as NIB cathodes, primarily if used in a strained electrode
configuration and/or thin film batteries. Our computational approach and
findings provide insights into developing practical NIBs involving
fluorine-containing intercalation frameworks.
