  Charge density functional plus $U$ calculations are carried out to examine
the validity of molecular $J_\text{eff}$=1/2 and 3/2 state in lacunar spinel
GaM$_4$X$_8$ (M = Nb, Mo, Ta, and W). With LDA (spin-unpolarized local density
approximation)$+U$, which has recently been suggested as the more desirable
choice than LSDA (local spin density approximation)$+U$, we examine the band
structure in comparison with the previous prediction based on the
spin-polarized version of functional and with the prototypical
$J_\text{eff}$=1/2 material Sr$_2$IrO$_4$. It is found that the previously
suggested $J_\text{eff}$=1/2 and 3/2 band characters remain valid still in
LDA$+U$ calculations while the use of charge-only density causes some minor
differences. Our result provides the further support for the novel molecular
$J_\text{eff}$ state in this series of materials, which can hopefully motivate
the future exploration toward its verification and the further search for new
functionalities.
