Structural properties of energetically low-lying isomers of the isolated Al4O4 molecular system have been investigated by theoretical ab initio techniques within the Hartree-Fock (HF) and second-order Moller-Plesset (Mp2) frozen core level of approximation and density functional methods (DFT) employing the Becke-3-Pertlew-86 (B3P86) hybrid functional. In total, nine local minima representing six Al4O4 isomers of various spin multiplicities are completely characterised. The two energetically lowest of these stationary points, a singlet of planar D-2h and a triplet of cubic T-d symmetry, are furthermore sifted by considering other choices of exchange (B, B3) and correlation (LYP, PW91) functionals as well as higher levels of theory (G2/MP2, G2, and CCSD(T), D-2h only). We report energies, equilibrium geometric parameters, selected harmonic vibrational wavenumbers along with corresponding absorption coefficients and compare the different computational approaches.