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It has been well established experimentally that the interplay of electroniccorrelations and spin-orbit interactions in Ir$^{4+}$ and Ir$^{5+}$ oxidesresults in insulating J$_{\rm eff}$=1/2 and J$_{\rm eff}$=0 ground states,respectively. However, in compounds where the structural dimerization of iridumions is favourable, the direct Ir $d$--$d$ hybridisation can be significant andtakes a key role. Here, we investigate the effects of direct Ir $d$--$d$hybridisation in comparison with electronic correlations and spin-orbitcoupling in Ba$_5$AlIr$_2$O$_{11}$, a compound with Ir dimers. Using acombination of $ab$ $initio$ many-body wave function quantum chemistrycalculations and resonant inelastic X-ray scattering (RIXS) experiments, weelucidate the electronic structure of Ba$_5$AlIr$_2$O$_{11}$. We find excellentagreement between the calculated and the measured spin-orbit excitations.Contrary to the expectations, the analysis of the many-body wave function showsthat the two Ir (Ir$^{4+}$ and Ir$^{5+}$) ions in the Ir$_2$O$_9$ dimer unit inthis compound preserve their local J$_{\rm eff}$ character close to 1/2 and 0,respectively. The local point group symmetry at each of the Ir sites assumes animportant role, significantly limiting the direct $d$--$d$ hybridisation. Ourresults emphasize that minute details in the local crystal field (CF)environment can lead to dramatic differences in electronic states in iridatesand 5$d$ oxides in general.

Charge ordering in Ir dimers in the ground state of Ba$_5$AlIr$_2$O$_{11}$