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The structural and electronic properties of the doubly charged diatomic dications Be X2+ ( X = Na, K) have been systematically investigated. The ab initio calculations method is based on the use of non-empirical pseudopotentials for the Be2+, Na+, and K+ cores, Gaussian basis sets, and parameterized l-dependent polarization potentials. The potential energy curves and their spectroscopic properties for the low-lying electronic states of 2Σ+, 2Π, and 2Δ symmetries have been determined for the species BeNa2+ and BeK2+ for the first time. Results show, for each diatomic dication, that the ground and the first excited electronic states are repulsive. For both systems, for which no experimental and theoretical data are available, we discuss our results by comparing their potential energies with similar systems. Numerous avoided crossings between electronic states of 2Σ+ and 2Π symmetries have been localized and analyzed. Their existence is related to the interaction between the electronic states and to the charge transfer process between the two ionic structures Be(2+) X and Be(+) X(+). Furthermore, the transition dipole functions from the ground state to the 2-102Σ+ and between neighbor electronic states of 2Σ+ symmetry, revealed many abrupt changes, which are localized at particular distances corresponding to the positions of the avoided crossings. [ABSTRACT FROM AUTHOR]