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We studied the electronic structure of $\beta$-Li$_2$IrO$_3$ insulator withinthe density-functional theory using the generalized gradient approximation withtaking into account strong Coulomb correlations in the framework of the fullyrelativistic spin-polarized Dirac linear muffin-tin orbital band-structuremethod. The $\beta$-Li$_2$IrO$_3$ undergoes a pressure-induced structural andmagnetic phase transitions at $P_c$ $\sim$4 GPa with symmetry lowering to themonoclinic $C2/c$. The structural phase transition is accompanied by theformation of Ir$_2$ dimers on the zigzag chains, with an Ir-Ir distance of$\sim$2.66~\AA, even shorter than that of metallic Ir. The strong dimerizationstabilizes the bonding molecular-orbital state, leads to the collapse of themagnetism and opens the energy gap with a concomitant electronic phasetransition from a Mott insulator to band insulator. The resonant inelasticx-ray scattering spectra (RIXS) at the Ir $L_3$ edge were investigatedtheoretically from first principles. The calculated results are in goodagreement with the experimental data. We show that the the drasticreconstruction of the RIXS spectral peak at 0.7 eV associated with thestructural $Fddd \rightarrow C2/c$ phase transition at $P_c$ can be related todisappearing of the Coulomb correlations in the high-pressure $C2/c$ phase

Resonant inelastic x-ray scattering spectra in the hyperhoneycomb iridate $\beta$-Li$_2$IrO$_3$: First principles calculations