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[en] Highlights: • The ionic movement activation energies within lead iodide Perovskite materials depend on the monovalent cation dipole moment. • Energy cost for flipping a dipole next to a vacancy (>25 meV) depends on the iodine vacancy location (axial or equilateral). • The dipole vacancy interaction is rather complex and cannot be described by a simple monopole-dipole term. • We propose dipolar vacancy interactions are connected to higher degree of response to local fields for high dipolar A-cation. • Detailed local structural changes next to the vacancy have been reported for the first time for lead iodide perovskites. Ion migration has recently been suggested to play critical roles in the operation of lead halide perovskite solar cells. However, so far there has been no systematic investigation of how the monovalent cation affects the vacancy formation, ion migration and the associated hysteresis effect. Here, we present density functional theory calculations on all possible ion migration barriers in the perovskite materials with different cations i.e. CH3NH3PbI3, CH(NH2)2PbI3 and CsPbI3 in the tetragonal phase and investigate vacancy monovalent-cation interactions within the framework of the possible ion migrations. The most relevant ion movement (iodide) is investigated in greater detail and corresponding local structural changes, the relationships with the local ionic dielectric response, Stark effect and current-voltage hysteresis are discussed. We observe a correlation between the energy barrier for iodine migration and the magnitude of the dipole of the monovalent cation. From the data, we suggest a vacancy-dipole interaction mechanism by which the larger dipole of the monovalent cation can respond to and screen the local electric fields more effectively. The stronger response of the high dipolar monovalent cation to the vacancy electrostatic potential in turn leads to a lower local structural changes within the neighbouring octahedra. The presented data reveal a detailed picture of the ion movement, vacancy dipole interactions and the consequent local structural changes, which contain fundamental information about the photo-physics, and dielectric response of the material.