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

Charge density functional plus $U$ calculation of lacunar spinel GaM$_4$Se$_8$ (M = Nb, Mo, Ta, and W)