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Iridium oxides with d⁵ configuration have attracted considerable interest in the last decade due to the realisation of spin-orbit coupled (SOC) j_eff = 1/2 insulating ground states. Recently, a new class of 5d⁴ iridates with a singlet (j_eff = 0) ground state has been proposed and realized in Sr₂YIrO₆ and Ba₂YIrO₆. Although their ground state is non-magnetic, the existence of excitonic magnetism in these materials is intensely debated. Here, we propose a new honeycomb lattice compound Ba₃CaIr₂O₉ in the j_eff = 0 class of materials. Using a combination of ab initio methods including many-body wavefunction calculations we characterise the SOC ground and excited states and show that the compound realises a j_eff = 0 singlet state. We use a microscopic model inferred from the low energy spin-orbital states to analyse the magnetic excitations and find the system to be non-magnetic and far from being an excitonic magnetic insulator. However, we find a non-trivial electronic band structure with a well defined Z₂ topological invariant. We analyse the effect of electronic correlations on the non-trivial bands using the Gutzwiller wavefunction approach.