We have carried out a detailed first-principles study of a d 4.5 quaternary iridate Ba 3 YIr 2 O 9 both in its 6H-perovskite-type ambient pressure (AP) phase and also for the high pressure (HP) cubic phase. Our analysis reveals that the AP phase belongs to the intermediate spin-orbit coupling (SOC) regime. This is further supported by the identification of the spin moment as the primary order parameter (POP) obtained from a magnetic multipolar analysis. The large t 2g bandwidth renormalizes the strength of SOC and the Ir intersite exchange interaction dominates resulting in long-range magnetic order in the AP phase. In addition to SOC and Hubbard U , strong intradimer coupling is found to be crucial for the realization of the insulating state. At high pressure (HP) the system undergoes a structural transformation to the disordered cubic phase. In sharp contrast to the AP phase, the calculated exchange interactions in the HP phase are found to be much weaker and SOC dominates leading to a quantum spin-orbital liquid (SOL) state. picture the insulating state of Ba 3 YIr 2 O 9 is not obvious as Ir with 4.5 electrons is a quarter-filled system as opposed to half-filled d 5 iridates. The origin of pressure induced magnetic transition in this system has also remained unexplored. Furthermore, there could be a possibility of a temperature dependent structural transformation to a charge ordered (CO) state, as seen in Ba 3 NaRu 2 O 9 [13].Earlier experimental studies on Ba 3 YIr 2 O 9 [14] at ambient pressure (AP) reported a sharp anomaly at 4 K in the heat capacity data although no such feature was seen in the susceptibility data. Later, Dey et al. [15] found that the variation of the susceptibility with temperature shows a weak * Presently at Uppsala University, Uppsala, Sweden. † sspid@iacs.res.in anomaly at about 4 K in agreement with previous heat capacity measurements reflecting the presence of long-range ordering. The susceptibility data [15] follows a Curie-Weiss (CW) behavior with θ CW ∼ 0 and effective moment 0.3 μ B much less than the spin-only value expected for a d 4.5 system. On the other hand, the high-pressure (HP) synthesized sample undergoes a structural phase transition and does not order down to 2 K as evidenced from susceptibility, heat capacity, and nuclear magnetic resonance (NMR) measurements and is suggested to be a 5d-based, gapless QSL [12].In view of the above, and also due to the fact that iridates, where Ir ions are in a fractional charge state and form structural dimers, have not been explored before, we have performed density functional theory (DFT) electronic structure calculations within the local density approximation (LDA) as well as LDA + U + SOC that includes the Hubbard U and SOC using the augmented plane waves plus local orbitals (APW + lo) method as implemented in the ELK code [16][17][18]. The SOC was treated through the second variational method. In this approach, given a value of U using a screened Coulomb potential (Yukawa potential), the corresponding on-site exchange energy J...