Theoretical study on diradical characters and nonlinear optical properties of 1,3-diradical compounds.

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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 structure-property relationship are clarified for several 1,3-diphenylcyclopentane-1,3-diyl derivatives, which are known as the systems with weak or intermediate π-single-bonding characters. The parent 1,3-diphenylcyclopentane-1,3-diyl (1a: X = H) is found to be almost pure diradical (y ∼ 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 (γ) of 1b and 1c are found to be enhanced by a factor of ∼4.5 and ∼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 γ from the corresponding nonsubstituted analogues. The present results have revealed strong correlation between the π-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.