The novel insights gained along these lines will contribute to establish general and reliable guidelines towards the rational design of molecules featuring ST inversion. As an additional bonus, we show that information easily obtained at the Hartree-Fock (HF) level (including the HOMO-LUMO gap and exchange energy) offers safe guidance to recognize molecular structures with negative ∆E ST . An easy-to-use computational tool is made available for a quick screening of interesting structures.