Over the years, several studies have aimed to elucidate why certain molecules show more enhanced nonlinear optical (NLO) properties than others. This knowledge is particularly valuable in the design of new NLO switches, where the ON and OFF states of the switch display markedly different NLO behaviors. In the literature, orbital contributions, aromaticity, planarity, and intramolecular charge transfer have been put forward as key factors in this regard. Based on our previous work on functionalized hexaphyrin-based redox switches, we aim at identifying through explainable machine learning the driving forces of the first hyperpolarizability related to the hyper-Rayleigh scattering (β_HRS) of meso-substituted and/or core-modified [26]- and [30]hexaphyrins. The significant correlation between β_HRS and the HOMO–LUMO energy gap can be further improved by including other orbitals as well as charge-transfer features in a 6-fold cross-validated kernel-ridge-regression model. Our Shapley additive explanations (SHAP) analysis shows that the charge transfer excitation length is more important for 30R systems, whereas the transition dipole moment between the ground and first excited state is one of the main contributors for 26R systems. We also demonstrate that, besides various hexaphyrin-based redox states, the ML model can describe to a large degree the β_HRS response of other hexaphyrins, differing in substitution pattern and topology (26D and 28M).

中文翻译：

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通过可解释的机器学习破译功能化 hexaphyrins 中的非线性光学特性


多年来，一些研究旨在阐明为什么某些分子比其他分子表现出更强的非线性光学 （NLO） 特性。这些知识在新型 NLO 开关的设计中特别有价值，其中开关的 ON 和 OFF 状态显示明显不同的 NLO 行为。在文献中，轨道贡献、芳香性、平面性和分子内电荷转移被认为是这方面的关键因素。基于我们之前关于基于功能化六叶镉的氧化还原开关的工作，我们的目标是通过可解释的机器学习来确定与介旋取代和/或核心修饰 [26] 和 [30] 六叶镉的超瑞利散射 （β_HRS） 相关的第一超极化率的驱动力。通过在 6 倍交叉验证的核脊回归模型中包括其他轨道以及电荷转移特征，可以进一步改善 β_HRS 和 HOMO-LUMO 能隙之间的显着相关性。我们的 Shapley 加法解释 （SHAP） 分析表明，电荷转移激发长度对于 30R 系统更为重要，而基态和第一激发态之间的过渡偶极矩是 26R 系统的主要贡献者之一。我们还证明，除了各种基于六叶啉的氧化还原态外，ML 模型还可以在很大程度上描述其他六叶啉的 _{β HRS} 响应，在取代模式和拓扑 （26D 和 28M） 上有所不同。