The frontier molecular orbital (MO) topology of linear carbon molecules, such as polyynes, can be visually identified as helices. However, there is no clear way to quantify the helical curvature of these π-MOs, and it is thus challenging to quantify correlations between the helical curvature and molecular properties. In this paper, we develop a method that enables us to compute the helical curvature of MOs based on their nodal planes. Using this method, we define a robust way of quantifying the helical nature of MOs (helicality) by their deviation from a perfect helix. We explore several limiting cases, including polyynes, metallacumulenes, cyclic allenes, and spiroconjugated systems, where the change in helical curvature is subtle yet clearly highlighted with this method. For example, we show that strain only has a minor effect on the helicality of the frontier orbitals of cycloallenes and that the MOs of spiroconjugated systems are close to perfect helices around the spiro-carbon. Our work provides a well-defined method for assessing orbital helicality beyond visual inspection of MO isosurfaces, thus paving the way for future studies of how the helicality of π-MOs affects molecular properties.

中文翻译：

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螺旋分子轨道螺旋度的量化

线性碳分子（如聚炔）的前沿分子轨道 (MO) 拓扑结构可以在视觉上识别为螺旋。然而，没有明确的方法来量化这些 π-MO 的螺旋曲率，因此量化螺旋曲率和分子特性之间的相关性具有挑战性。在本文中，我们开发了一种方法，使我们能够根据节点平面计算 MO 的螺旋曲率。使用这种方法，我们定义了一种稳健的方法，通过它们与完美螺旋的偏差来量化 MO 的螺旋性质（螺旋性）。我们探索了几种极限情况，包括聚炔、金属柱烯、环状丙二烯和螺共轭系统，其中螺旋曲率的变化很微妙，但使用这种方法可以清楚地突出显示。例如，我们表明应变只对环丙二烯的前线轨道的螺旋性产生很小的影响，并且螺共轭系统的 MO 接近螺碳周围的完美螺旋。我们的工作提供了一种定义明确的方法来评估轨道螺旋性，而不是对 MO 等值面进行目视检查，从而为未来研究 π-MO 的螺旋性如何影响分子特性铺平了道路。