Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University Toyonaka, Osaka 560-8531, Japan.
Chemistry. 2013 Jan 28;19(5):1677-85. doi: 10.1002/chem.201203463. Epub 2012 Dec 18.
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.
为了揭示与富勒烯开壳特性相关的非线性光学（NLO）性质中的新结构-性质关系，我们使用broken-symmetry 密度泛函理论（DFT；LC-UBLYP（μ=0.33）/6-31G*//UB3LYP/6-31G*）研究了几个富勒烯（包括 C（20）、C（26）、C（30）、C（36）、C（40）、C（42）、C（48）、C（60）和 C（70））中自由基特性（y(i)）和二阶超极化率（纵向分量，γ(zzzz)）之间的相互作用。我们发现，富勒烯的几何形状和拓扑结构的巨大差异对每个富勒烯的自由基特性有显著影响。基于它们不同的自由基特性，这些富勒烯被分为三组，即闭壳（y(i)=0）、中间开壳（0<y(i)<1）和几乎纯开壳化合物（y(i)=/~1），这源于它们的拓扑特征，如奇电子密度和自旋密度图所示。例如，我们发现闭壳富勒烯包括 C（20）、C（60）和 C（70），而富勒烯 C（26）和 C（36）以及 C（30）、C（40）、C（42）和 C（48）分别为纯和中间开壳化合物。有趣的是，C（30）/C（36）和 C（40）/C（60）之间的 γ(zzzz)增强比分别为 4.42 和 11.75，尽管 C（30）和 C（40）中的 π 共轭大小小于 C（36）和 C（60）。其他具有中间自由基特性的富勒烯的 γ(zzzz)值较大，这与我们之前对双位点自由基模型的价层组态相互作用（VCI）结果一致。γ(zzzz)密度分析表明，大的正贡献源于富勒烯右扩展边缘和左扩展边缘之间的大γ(zzzz)密度分布，在无限制的 DFT 理论水平内，其中出现了显著的自旋极化（与它们的中间自由基特性有关）。
