Second hyperpolarizability (γ) of singlet diradical system: Dependence of γ on the diradical character

The dependence of the second hyperpolarizability (γ) on the diradical character (γ) for singlet diradical systems is investigated using a model compound, the p-quinodimethane (PQM) molecule with different both-end carbon-carbon (C-C) bond lengths, by several ab initio molecular orbital and density functional theory methods. The diradical character based on UHF calculations indicates that at equilibrium geometry PQM is in a singlet ground state and primarily exhibits a quinoid structure, whereas the diradical character increases when increasing both-end C-C bond lengths. At the highest level of approximation, that is, using the UCCSD(T) method with the 6-31G*+diffuse p (ζ = 0.0523) basis set, the longitudinal static γ of PQM presents a maximum value for intermediate diradical character (y ≈ 0.5) while the γ values are larger for intermediate and large diradical character (y ≈ 0.5-0.7) than for small diradical character (y < 0.2). This feature suggests that the γ values of singlet diradical systems in the intermediate and somewhat strong correlation regimes are significantly enhanced as compared to those in the weak correlation regime. These results are substantiated by a complementary study of the variation in γ upon twisted ethylene.