We examine one of the simplest cyclic rotaxanes—a molecule made from three rods with variable length between 0 and L. This [3]rotaxane, unlike a traditional molecule, shows significant size and shape fluctuations. We quantify these using a number of different measures. In particular, we show that the average angles are 100∘,52∘, and 28∘ and the most populated lengths lie at L,2L/3, and L/3. The triangles are usually obtuse. We discuss the area allowed within the triangle for inclusion compounds. Inspired by the linear rotaxane switches, we also consider the statistical mechanics of switching when stations with attractive interactions promote small-cycle areas.

我们研究了一种最简单的环状轮烷，这是一种由长度在0到L之间的三根棒组成的分子。与传统分子不同，这种[3]轮烷显示出明显的尺寸和形状波动。我们使用多种不同的方法对这些结果进行量化。特别地，我们表明平均角度为100∘，52∘， 和 28岁∘ 而人口最多的长度是 大号，2个大号/3， 和 大号/3。三角形通常是钝的。我们讨论了三角形内允许包含化合物的面积。受到线性轮烷开关的启发，我们还考虑了具有吸引力相互作用的工位促进小循环区域时的开关统计机制。