Validation of Theoretical Methods for the Structure and Energy of Aluminum Clusters

We calculated the atomization energy of aluminum clusters (Al2−Al7) with several multilevel methods, including MCG3/3 and G3X, that have been previously shown to provide high accuracy for atomization energies. We used the results to test a number of hybrid density functional theory (HDFT) methods and found that the PBE0 method is in best agreement with the accurate methods. We then used the PBE0/MG3 method to develop a more extensive data set for the energies of small aluminum clusters (Al2−Al13), and this was used to test a number of semiempirical methods, in particular Austin model 1 (AM1), modified neglect of differential overlap (MNDO), modified symmetric-orthogonalized intermediate neglect of differential overlap (MSINDO) with and without d-functions, parametrized model 3 (PM3), and the tight-binding total energy (TBTE) method, for geometries, energies, and multiplicities of Al clusters. The AM1 model and MSINDO model are the most accurate of the semiempirical methods for energetics, and PM3 is the most accurate method for geometries.