Periodic ab initio QM calculations are applied to study the structure and acidity of Mg, Ca, Cr, Mn, Fe, Co, Ni, Zn, and Sr divalent metal ions in the AlPO-34 framework, charge compensated by an acid proton on a neighboring oxygen. Our results show that the local environment of the divalent dopants is a distorted tetrahedron, in which the Me-OH bond of the dopant to the protonated oxygen is similar to0.15 Angstrom longer than the other three Me-O bonds. The nature of bonding between the Me2+ dopants and the neighboring oxygens is ionic in nature, explaining the Lewis acidity of the Me2+ ions. However, for Ni2+, the Lewis active orbitals are oriented within the framework, where they are screened from an effective Lewis-type interaction with adsorbed molecules. The attack of Lewis bases is favored from the side of the framework opposite to the Bronsted acid proton. The replacement energy of a framework Al3+ with a Me2+ ion increases linearly as a function of the ionic size of Me2+. Finally, we show that the acid strength is attributable to a complex combination of the structural and electronic features of the dopant ion and does not show appreciable correlation with the local environment or electronic distribution of the Me2+ dopant in the framework.