Relationship between singlet-triplet excitation energies and the Kohn-Sham orbitals obtained with potentials that exhibit a wrong asymptotic behavior

A linear relationship was found between the singlet-triplet excitation energy and the energy difference presented by the Kohn-Sham frontier molecular orbitals, independently of the used exchange-correlation functional and of the basis set functions quality. The relationship was explored in three different situations: (a) when the number of carbons is increased in an all-trans acetylene family; (b) rotation of the trans-butadiene around the single bond; (c) dissociation process of the molecules H2 and FH. Additionally, it was found a strong relationship between the vertical singlet-triplet excitation energy obtained with the B3LYP and the multiconfiguration-self consistent methods.