  We report $\textit{ab-initio}$ density functional theory calculation and
Raman scattering results to explore the electronic structure of
Ba$_5$CuIr$_3$O$_{12}$ single crystals. This insulating iridate, consisting of
face-sharing IrO$_6$ octahedra forming quasi-one-dimensional chains, cannot be
described by the local $j_{\rm eff}$=1/2 moment picture commonly adopted for
discussing electronic and magnetic properties of iridate compounds with IrO$_6$
octahedra. The shorter Ir-Ir distance in the face-sharing geometry, compared to
corner- or edge-sharing structures, leads to strong covalency between
neighboring Ir. Then this strong covalency results in the formation of
molecular orbitals (MO) at each Ir trimers as the low-energy electronic degree
of freedom. The theoretically predicted three-peak structure in the joint
density of states, a distinct indication of deviation from the $j_{\rm
eff}$=1/2 picture, is verified by observing the three-peak structure in the
electronic excitation spectrum by Raman scattering.
