Measures of unpaired electrons for large conjugated systems

It is shown that the numerical measure of effectively unpaired electrons N (eff), proposed by Head-Gordon in 2003, is a particle-hole index: N (eff) is reduced to the average occupation of virtual particle-hole pairs. Specific pi calculations of the N (eff) index provide a reasonable interpretation of the radicaloid character of the singlet ground state in complex conjugated systems. The results of the accurate pi model (based on the total configuration interaction) and approximate approaches are compared. The coupled cluster method and various Hartree-Fock schemes (UHF and Lowdin EHF scheme) demonstrate an acceptable quantitative description of unpairing effects, UHF being favorable in simplicity of obtaining the measure of unpairing in megamolecules, such as graphene structures. The application of the known Yamaguchi index results in a rougher representation of the radical character of a system.