The structures and energies of low-lying electronic states of AlN3, Al3N, and Al2N2 have been evaluated at the HF, MP2, QCISD(T), CCSD, and CCSD(T) levels of theory, using the several basis sets of 6-31G* (for HF), cc-pVDZ (for MP2 and QCISD(T)), and cc-pVTZ (for CCSD and CCSD(T)). The ground state of AlN3 is predicted to be a (1)Sigma(+) state with a linear Al-N-N-N structure. The most stable species of Al3N is found, however, to have D-3h symmetry and (1)A(1)＇ ground state. For Al2N2, various isomers are found to be energetically favorable. A rhombic isomer with the nitrogen atoms along the short diagonal and with a (1)A(g) electronic state is the lowest in energy at the MP2/cc-pVDZ, QCISD(T)/cc-pVDZ, CCSD/cc-pVTZ, and CCSD(T)/cc-pVTZ levels. A linear structure Al-N-N-Al with a (3)Sigma(g)(-) electronic state is the second lowest. The third stable isomer with the aluminum atoms bonded directly to the N-2 pi orbital seems to be one of the model species for the sake of the nitrogen fixation. Our results suggest that the formation of a variety of the configuration of Al2N2 is energetically plausible under the reaction conditions employed since the energy differences in the Al2N2 species are relatively small.