We have investigated electronic structures and magnetic properties of O$_{2}$$M$F$_{6}$ ($M$=Sb, Pt), which are composed of two building blocks of strongly correlated electrons: O$_{2}^{+}$ dioxygenyls and $M$F$_{6}^{-}$ octahedra, by employing the first-principles electronic structure band method. For O$_{2}$SbF$_{6}$, as a reference system of O$_{2}$PtF$_{6}$, we have shown that the Coulomb correlation of O(2$p$) electrons drives the Mott insulating state. For O$_{2}$PtF$_{6}$, we have demonstrated that the Mott insulating state is induced by the combined effects of the Coulomb correlation of O(2$p$) and Pt(5$d$) electrons and the spin-orbit (SO) interaction of Pt(5$d$) states. The role of the SO interaction in forming the Mott insulating state of O$_{2}$PtF$_{6}$ is similar to the case of Sr$_{2}$IrO$_{4}$ that is a prototype of a SO induced Mott system with J$_{eff}=1/2$.
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