How to determine an optimal multiplicity of a metal oxide cluster?

Dear All,I struggle with determining the most optimal multiplicity of small metal oxide nanoclusters, e.g. Fe2O3 or Al2O3. For instance, here they say https://pubs.rsc.org/en/content/articlepdf/2014/cp/c4cp02099e that singlet state is the most stable one as there are formaly Fe3+ and Fe2+ cations with total spin number of S=-5/2 and S=2, respectively. However, I don't really understand how this sign is determined. Is it plausible to do it a priori, i.e. not through trials and errors? In case of Al2O3, the triplet state, i.e. with two unpaired electron is somehow more stable than singlet one. I don't really understand how it is possible for the Al3+ cations. Al belongs to block p, so after the valence electrons transfer to oxygen atoms all molecular should be closed as far as I'm concered. However, I checked and in fact the triplet state is more stable.I would like to understand how I can determine the optimal multiplicity because I have a whole series of metal oxides and I'm not happy with doing it by trials and errors.Thank you for all suggestions.