Ab initio (MP2) and density functional theory (DFT) methods are used to examine a series of MN4 compounds, where M is an alkaline-earth cation (Mg2+, Ca2+, Sr2+, Ba2+), and N-4(2-) is a six-pi-electron ring. All pyramidal structures except MgN4 are the most energetically favored for all singlet MN4 systems considered here. For MgN4, the C-S structure with dicoordinated Mg out of the N-4 ring plane is the most stable of all. Among these systems, the pyramidal CaN4, SrN4, BaN4 and the planar C-S structure containing dicoordinated Ba are stable as singlet molecules due to their significant isomerization or dissociation barriers (21.3-94.1 kcal/mol). Structural, natural bond orbital (NBO), and molecular orbital (MO) analyses indicate that the bonding in the BaN4 system has a larger covalent character as compared with other MN4 systems. In addition, substantial d character is found in the bonding of the MN4 (M = Ca2+, Sr2+, Ba2+) species.