Rappaport Shay M, Rzepa Henry S
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
J Am Chem Soc. 2008 Jun 18;130(24):7613-9. doi: 10.1021/ja710438j. Epub 2008 May 28.
The geometries of coiled annulenes belonging to the chiral C2 and D(n) (n = 2,7) point groups are defined by two chiral indices, W(r) and T(w), respectively (writhe and twist), which sum to give an overall integer linking number, L(k) (the Cãlugãreanu-White-Fuller theorem). While the value of L(k) can been equated with single-twist (L(k) = 1pi), double-twist (L(k) = 2), and higher-order (L(k) > 2) twisted (Möbius-Listing) annulenes, we suggest that the correct Huckel molecular-orbital treatment is to use T(w) specifically in the 2p(pi)-2p(pi) overlap correction first suggested by Heilbronner, rather than L(k). Quantitatively, because many of these systems project much of the finite value of T(w) into W(r), a simple mechanism exists to increase the pi-electron resonance stabilization beyond what simple Heilbronner theory predicts. Examples of a diverse set of such chiral annulenes are dissected into W(r) and T(w) contributions, which reveals that those with the minimum value of T(w) are associated with the greater delocalized stability.
属于手性C2和D(n)（n = 2,7）点群的螺旋状轮烯的几何结构分别由两个手性指数W(r)和T(w)（分别为扭曲数和扭转数）定义，它们的总和给出一个整体整数环绕数L(k)（卡卢加雷亚努 - 怀特 - 富勒定理）。虽然L(k)的值可以等同于单扭转（L(k) = 1π）、双扭转（L(k) = 2）和高阶（L(k) > 2）扭曲（莫比乌斯 - 利斯廷）轮烯，但我们认为正确的休克尔分子轨道处理方法是在海布伦纳首先提出的2p(π)-2p(π)重叠校正中专门使用T(w)，而不是L(k)。从定量角度来看，由于这些体系中的许多将T(w)的很大一部分有限值投影到了W(r)中，所以存在一种简单机制来增加π电子共振稳定性，使其超出简单的海布伦纳理论预测。一组多样的此类手性轮烯的例子被剖析为W(r)和T(w)的贡献，这表明T(w)值最小的那些与更大的离域稳定性相关。
