  The entanglement of the spin and orbital degrees of freedom through the
spin-orbit coupling has been actively studied in condensed matter physics. In
several iridium-oxide systems, the spin-orbital entangled state, identified by
the effective angular momentum $j_{\rm eff}$, can host novel quantum phases
with the help of electron correlations. Here, we show that a series of lacunar
spinel compounds, Ga$M_4X_8$ ($M$ = Nb, Mo, Ta, and W and $X$ = S, Se, and Te),
gives rise to a $\textit{molecular}$ $j_{\rm eff}$ state as a new spin-orbital
composite on which the low energy effective Hamiltonian is based. A wide range
of electron correlations is accessible by tuning the bandwidth under external
and/or chemical pressure, enabling us to investigate the interesting
cooperation between spin-orbit coupling and electron correlations. As
illustrative examples, a two-dimensional topological insulating phase and an
anisotropic spin Hamiltonian are investigated in the weak and strong coupling
regimes, respectively. Our finding can provide an ideal platform for exploring
$j_{\rm eff}$ physics and the resulting emergent phenomena.
