  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$_{eff}=1/2$.
