The first binuclear sandwich-like complexes based on the aromatic tetraatomic species with formula M2(η4-E4)2 (M = Al, Ga; E = N, P, As) have been studied by density functional theory (DFT). The stable conformer for each M2(η4-E4)2 is the staggered one with D4d symmetry except for Ga2(η2-N4)2 with C2v symmetry. Natural bonding orbital (NBO) analysis indicates that the metal–metal bonds of Al2(η4-E4)2 (E = N, P, As) and Ga2(η4-E4)2 (E = P, As) are all σ single bonds, which are derived mostly from the s and pz orbitals of the metal atoms by molecular orbital (MO) analysis. For M2(η4-E4)2 (M = Al, Ga; E = P, As), the metal–ligand interactions are covalent, while for Al2(η4-N4)2 the interactions between the Al atoms and the N42− ligands are ionic. According to the calculated dissociation energies for breaking metal–metal bonds, the Al–Al and Ga–Ga bonds are very strong indicating that these stable sandwich-like compounds Al2(η4-E4)2 (E = N, P, As) and Ga2(η4-E4)2 (E = P, As) may be synthesized in future experiments. The nitrogen-rich compounds Al2(η4-N4)2 and Ga2(η2-N4)2 may be used as potential candidates of high energy density materials (HEDMs). Nucleus-independent chemical shifts (NICS) values reveal that the E42− rings in the Al2(η4-E4)2 (E = N, P, As) and Ga2(η4-E4)2 (E = P, As) species possess conflicting aromaticity (σ antiaromaticity and π aromaticity) and with the same ligands, the E42− ligands in Ga2(η4-E4)2 have more aromaticity than those in Al2(η4-E4)2.