We investigate the relationships between the diradical character (y) and nonlinear optical (NLO) properties of open-shell 1,3-diradical compounds using the broken-symmetry density functional theory method. The 2,2-substituent effects on the structureproperty relationship are clarified for several 1,3-diphenylcyclopentane-1,3-diyl derivatives, which are known as the systems with weak or intermediate p-single-bonding characters. The parent 1,3-diphenylcyclopentane-1,3-diyl (1a: X = H) is found to be almost pure diradical (y similar to 1) owing to the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). The energy gap is determined by the balance of the through-space coupling with the through bond coupling effect. On the other hand, the introduction of the electron-withdrawing substituents X at the C2 position of cyclopentane-1,3-diyls (1b: X = OH, 1c: X = F) is found to decrease the y-value owing to the effects of additional through-bond interactions. As a result, 1b and 1c are found to have intermediate y. Static second hyperpolarizabilities (gamma) of 1b and 1c are found to be enhanced by a factor of similar to 4.5 and similar to 6.4, respectively, compared with those of the pure singlet diradical 1a and those of the triplet 1a-1c. From the analysis of the third-order responses of electron density, the introduction of the 2,2-substituents is found to enhance the field-induced third-order polarizations over the whole system. We also investigate the effects of asymmetric donor/acceptor substitutions at the para positions of phenyl rings on the response properties. Although the asymmetric donor/acceptor substitutions have no significant impact on y in the present systems, they are found to provide the increase of gamma from the corresponding nonsubstituted analogues. The present results have revealed strong correlation between the p-bonding character (diradical character) and third-order NLO properties in the real 1,3-diradical compounds. On the basis of the theoretically predicted correlation in the real systems, NLO measurements are speculated to be utilized as a new probe of the unique chemical bonding nature in such localized diradical compounds, which is one of the fundamental subjects in chemistry.