Theoretical investigation on the second hyperpolarizabilities of open-shell singlet systems by spin-unrestricted density functional theory with long-range correction: Range separating parameter dependence

The long-range corrected spin-unrestricted density functional theory, LC-UBLYP, method has been used to determine the second hyperpolarizabilities (γ) of open-shell singlet π-conjugated diradical compounds, i.e., p-quinodimethane, 1,4-bis-(imidazole-2-ylidene)-cyclohexa-2,5-diene, pentalene and s-indacene. Analysis of the dependence of γ on the range separating parameter (μ) was carried out along with comparison to spin-unrestricted coupled cluster singles, doubles and perturbative triples [UCCSD(T)] calculations. Our investigation shows that the LC-UBLYP method with μ = 0.3–0.5 is adequate for calculating γ values for conjugated diradical systems and does not suffer from the catastrophic behavior found in conventional exchange–correlation functionals.