  The HfV$_2$Ga$_4$ compound was recently reported to exhibit unusual bulk
superconducting properties, with the possibility of multiband behavior. To gain
insight into its properties, we performed ab-initio electronic structure
calculations based on the Density Functional Theory (DFT). Our results show
that the density of states at the Fermi energy is mainly composed by V--$d$
states. The McMillan formula predicts a superconducting critical temperature
($T_{c}$) of approximately $3.9\,$K, in excellent agreement with the
experimental value at $4.1\,$K, indicating that superconductivity in this new
compound may be explained by the electron-phonon mechanism. Calculated valence
charge density maps clearly show directional bonding between Hf and V atoms
with 1D highly populated V-chains, and some ionic character between Hf--Ga and
V--Ga bonds. Finally, we have shown that there are electrons occupying two
distinct bands at the Fermi level, with different characters, which supports
experimental indications of possible multiband superconductivity. Based on the
results, we propose the study of a related compound, ScV$_2$Ga$_4$, showing
that it has similar electronic properties, but probably with a higher $T_c$
than HfV$_2$Ga$_4$.

Superconductivity;Materials Science