With the rise of cluster-assembled materials, an index that is able to rank and identify stable clusters or molecules is of great interest in materials sciences and engineering. In the present work, we applied a stability ranking function (epsilon(3)) in nanoclusters formed by simple metals (Na, Mg), main group elements (Al), or transition metals (Ti, Cu). The epsilon(3) function parameters are molecular properties derived from the wave function. These parameters can be divided into kinetic and thermodynamic descriptors, in which the kinetic descriptors are the ionization potential and electronic excitation energy, while the atomization free Gibbs energy is the thermodynamic one. This simple epsilon(3) function was able to identify the possible magic numbers of the studied clusters across the periodic table in a good agreement with previous experimental and theoretical works.