Quantum chemical calculations using ab initio methods at the MRCI+Q(8,9)/def2-QZVPPD and CCSD(T)/def2-QZVPPD levels as well as density functional theory are reported for the diatomic molecules AeN- (Ae = Ca, Sr, Ba). The nature of the bonds is analyzed with a variety of methods. The anions CaN- and SrN- have electronic triplet (3Π) ground states with nearly identical bond dissociation energies De ~57 kcal/mol calculated at the MRCI+Q(8,9)/def2-QZVPPD level of theory. In contrast, the heavier homologue BaN- has a singlet (1Σ+) ground state, which is only 1.1 kcal/mol below the triplet (3Σ-) state. The computed bond dissociation energy of (1Σ+) BaN- is 68.4 kcal/mol. The calculations at the CCSD(T)-full/def2-QZVPPD and BP86-D3(BJ)/def2-QZVPPD levels of theory are in reasonable agreement with the MRCI+Q(8,9)/def2-QZVPPD data except for the singlet (1Σ+) state, which has a large multireference character. The calculated atomic partial charges given by the CM5, Voronoi and Hirshfeld methods suggest small to medium-sized charge donation toward Ae atom Ae←N- for most electronic states. In contrast, the NBO method predicts for all species medium to large electronic charge donation toward nitrogen Ae→N-, which is due to the neglect of the (n)p AOs of Ae atoms as genuine valence orbitals.