Previous high-level theoretical calculations of aluminum clusters mostly relied on density functional theory (DFT) or theories less sophisticated than it. Here, we point out that a second-order Møller-Plesset perturbation (MP2) method is more appropriate and is the minimum level of theory in the predictions of property such as geometries, electronic structures, and IR and Raman spectra of Al4, Al4+, and Al4- clusters. The theoretical electron affinities and ionization potentials predicted with MP2 geometries are closer to experimental ones than those by DFT. The p-electron characters and single valence state of aluminum atoms and IR and Raman spectra of the aluminum clusters were also reliably predicted by MP2 and could be based on for further experimental and theoretical studies.