  Sodium (Na) vanadium (V) fluorophosphate $\mathrm{Na_xV_2(PO_4)_2F_3}$ (NVPF)
is a highly attractive intercalation electrode material due to its high
operation voltage, large capacity, and long cycle life. However, several issues
limit the full utilization of NVPF's energy density: 1) the high voltage
plateau associated with extracting the "third" Na ion in the reaction N$_1$VPF
$\rightarrow$ VPF (~4.9 V vs Na/Na$^+$) appears above the electrochemical
stability window of most practical electrolytes (~4.5 V); 2) a sudden drop in
Na-ion diffusivity is observed near composition $\mathrm{Na_1V_2(PO_4)_2F_3}$.
Therefore, it is important to investigate the potential substitution of V by
other transition metals in NVPF derivatives, which can access the extraction of
the third Na-ion. In this work, we investigate the partial substitution of V
with molybdenum (Mo), niobium (Nb), or tungsten (W) in NVPF to improve its
energy density. We examine the structural and electrochemical behaviors of
$\mathrm{Na_xV_{2-y}Mo_y(PO_4)_2F_3}$, $\mathrm{Na_xV_{2-y}Nb_y(PO_4)_2F_3}$,
and $\mathrm{Na_xW_{2}(PO_4)_2F_3}$ across the whole Na composition region of 0
$\leq$ x $\leq$ 4, and at various transition metal substitution levels, namely,
y=0.5, 1.0, 1.5, 2.0 for Mo, and y=1.0, 2.0 for Nb. We find that partial
substitution of 50% V by Mo in NVPF reduces the voltage plateau for extracting
the third Na ion by 0.6 Volts, which enables further Na extraction from
$\mathrm{Na_1Mo_{2}(PO_4)_2F_3}$ and increases the theoretical gravimetric
capacity from ~128 to ~174 mAh/g. Analysis of the migration barriers for
Na-ions in $\mathrm{Na_xVMo(PO_4)_2F_3}$ unveils improved kinetic properties
over NVPF. The proposed $\mathrm{Na_xVMo(PO_4)_2F_3}$ material provides an
optimal gravimetric energy density of ~577.3 Wh/kg versus ~507 Wh/kg for the
pristine NVPF, which amounts to an increase of ~13.9%.
