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 C(20), C(26), C(30), C(36), C(40), C(42), C(48), C(60), and C(70), 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 C(20), C(60), and C(70), whereas fullerenes C(26) and C(36) and C(30), C(40), C(42), and C(48) are pure and intermediate open-shell compounds, respectively. Interestingly, the γ(zzzz) enhancement ratios between C(30)/C(36) and C(40)/C(60) are 4.42 and 11.75, respectively, regardless of the smaller π-conjugation size in C(30) and C(40) than in C(36) and C(60). 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.