Doped IrTe₂ is considered a platform for topological superconductivity and therefore receives currently a lot of interest. In addition, the superconductivity in these materials exists in close vicinity to electronic order and the formation of molecular orbital crystals, which we explore here by means of high-pressure single crystal x-ray diffraction in combination with density functional theory. Our crystallographic refinements provide detailed information about the structural evolution as a function of applied pressure up to 42 GPa. Using this structural information for density functional theory calculations, we show that the local multicenter bonding in IrTe₂ is driven by changes in the Ir-Te-Ir bond angle. When the electronic order sets in, this bond angle decreases drastically, leading to a stabilization of a multicenter molecular orbital bond. This unusual local mechanism of bond formation in an itinerant material provides a natural explanation for the different electronic orders in IrTe₂. It further illustrates the strong coupling of the electrons with the lattice and is most likely relevant for the superconductivity in this material.