We present an extensive and systematic study on the regioselectivity of Diels–Alder (DA) cycloadditions to empty fullerenes, covering the whole range of cage sizes from C₆₀ to C₁₈₀. Reaction energies obtained from DFT calculations, which correlate with activation barriers, can be well reproduced by using a simple Hückel model, indicating that π electronic effect is the key factor determining the relative stability of DA adducts. Based on these results, we propose a couple of simple rules of thumb, in terms of a set of bond patterns, as a visual guide for approximate prediction of DA reactive sites. Moreover, we suggest two quantitative descriptors for the stability of DA regioadducts of empty fullerenes; one combines the π free valences and bond orders involved in the DA addition, and the other characterizes the local π aromaticity around the addition site. The latter criterion allows us to easily rationalize the proposed rules.

中文翻译：

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简单的键合模式可预测空富勒烯的Diels–Alder加合物的稳定性†

我们对Diels-Alder（DA）环加成化合物对空富勒烯的区域选择性进行了广泛而系统的研究，涵盖了从C ₆₀到C ₁₈₀的整个笼尺寸范围。通过使用简单的Hückel模型可以很好地重现从DFT计算获得的与活化能垒相关的反应能，表明π电子效应是决定DA加合物相对稳定性的关键因素。基于这些结果，我们针对一组键模式提出了一些简单的经验法则，作为近似预测DA反应位的视觉指南。此外，我们提出了两个定量的描述符来描述空富勒烯的DA区域加合物的稳定性。一种结合了DA加成中涉及的π自由价和键序，另一种表征了加成位点附近的局部π芳香性。后一个标准使我们可以轻松地合理化建议的规则。