The transition level diagrams and self-consistent Fermi level were calculated using the PY-SC-FERMI package. The EFFMASS package was used to analyse the transport effective mass. Due to their long-range nature, quadrupolar interactions must be taken into account for an accurate description of the scattering potential and mobilities. SOC also plays an important role in the transport properties of CuI and must also be taken in account. In this plot, SOC+Q * mobilities obtained with SOC phonons, SOC+noQ* mobilities with SOC phonons, SOC+Q * mobilities obtained with noSOC phonons and noSOC+Q * mobilities obtained with noSOC phonons are represented in blue, orange, green and red, respectively. The absence of SOC in the phonons calculations do not affect the mobility results, as the blue and green curves overlap.