Interplay between the Diradical Character and Third‐Order Nonlinear Optical Properties in Fullerene Systems

To reveal new structure–property relationships in the nonlinear optical (NLO) properties of fullerenes that are associated with their open‐shell character, we investigated the interplay between the diradical character (y_i) and second hyperpolarizability (longitudinal component, γ_zzzz) in several fullerenes, including C₂₀ , C₂₆ , C₃₀ , C₃₆ , C₄₀ , C₄₂ , C₄₈ , C₆₀ , and C₇₀ , by using the broken‐symmetry density functional theory (DFT; LC‐UBLYP (μ=0.33)/6‐31G*//UB3LYP/6‐31G*). We found that the large differences between the geometry and topology of fullerenes have a significant effect on the diradical character of each fullerene. On the basis of their different diradical character, these fullerenes were categorized into three groups, that is, closed‐shell (y_i=0), intermediate open‐shell (0<y_i<1), and almost pure open‐shell compounds (y_i?1), which originated from their diverse topological features, as explained by odd‐electron‐density and spin‐density diagrams. For example, we found that closed‐shell fullerenes include C₂₀ , C₆₀ , and C₇₀ , whereas fullerenes C₂₆ and C₃₆ and C₃₀ , C₄₀ , C₄₂ , and C₄₈ are pure and intermediate open‐shell compounds, respectively. Interestingly, the γ_zzzz enhancement ratios between C₃₀ / C₃₆ and C₄₀ / C₆₀ are 4.42 and 11.75, respectively, regardless of the smaller π‐conjugation size in C₃₀ and C₄₀ than in C₃₆ and C₆₀ . Larger γ_zzzz values were obtained for other fullerenes that had intermediate diradical character, in accordance with our previous valence configuration interaction (VCI) results for the two‐site diradical model. The γ_zzzz density analysis shows that the large positive contributions originate from the large γ_zzzz density distributions on the right‐ and left‐extended edges of the fullerenes, between which significant spin polarizations (related to their intermediate diradical character) appear within the spin‐unrestricted DFT level of theory.