The dependence of the second hyperpolarizability (gamma) on the diradical character (gamma) 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 (zeta = 0.0523) basis set, the longitudinal static gamma of PQM presents a maximum value for intermediate diradical character (gamma approximate to 0.5) while the gamma values are larger for intermediate and large diradical character (y approximate to 0.5-0.7) than for small diradical character (y < 0.2). This feature suggests that the y 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 y upon twisted ethylene.