莫比乌斯碳纳米带的简单休克尔分子轨道理论
Simple Hückel Molecular Orbital Theory for Möbius Carbon Nanobelts
AI总结：
针对双链莫比乌斯碳纳米带（CNBs）π共轭拓扑扩展理解的不确定性，本研究深入考察简单休克尔分子轨道（SHMO）理论，证明其邻接矩阵特征值和特征向量在符号反转位置变化时的稳定性，且与DFT结果高度一致，为莫比乌斯CNBs电子结构研究提供可靠模型。
摘要：
近期合成的莫比乌斯碳纳米带（CNBs）因其独特的π共轭拓扑结构而受到关注，该结构产生了具有基础和实际意义的独特电子性质。尽管在原子轨道（AO）基组中具有相位反转的莫比乌斯共轭在单环体系中已得到充分证实，但将这种理解扩展到双链莫比乌斯CNBs仍不确定。本研究深入考察了用于描述莫比乌斯CNBsπ电子结构的简单休克尔分子轨道（SHMO）理论。我们证明，任何莫比乌斯CNB的邻接矩阵在不同符号反转位置下都能保留其特征值和特征向量（方向可能翻转），确保无论AO相位反转位置如何，SHMO结果都相同。包括实验合成的莫比乌斯CNBs在内的代表性例子表明，休克尔分子轨道（MOs）与DFT计算的π MOs极为相似，后者是通过本文提出的基于DFT正则MOs的局域化和再离域化技术获得的。有趣的是，低能π MOs表现出奇数个节面，并且由于莫比乌斯大环中的相位反转而呈双重准简并，这与大环休克尔体系形成对比。从SHMO理论推导的库尔森键级与测试莫比乌斯CNBs中所有C-C键的DFT计算维伯格键指数相关性良好。此外，在大量莫比乌斯CNBs拓扑异构体的SHMO和GFN2-xTB计算得到的HOMO-LUMO间隙之间观察到显著相关性。因此，SHMO模型不仅捕捉了莫比乌斯CNBsπ电子结构的本质，还提供了可与DFT结果媲美的可靠定量预测。
英文摘要：
The recently synthesized Möbius carbon nanobelts (CNBs) have gained attention owing to their unique $π$-conjugation topology, which results in distinctive electronic properties with both fundamental and practical implications. Although Möbius conjugation with phase inversion in atomic orbital (AO) basis is well-established for monocyclic systems, the extension of this understanding to double-stranded Möbius CNBs remains uncertain. This study thoroughly examines the simple Hückel molecular orbital (SHMO) theory for describing the $π$ electronic structures of Möbius CNBs. We demonstrate that the adjacency matrix for any Möbius CNB can preserve its eigenvalues and eigenvectors (with possibly flipped directions) under different placements of the sign inversion, ensuring identical SHMO results regardless of AO phase inversion location. Representative examples of Möbius CNBs, including the experimentally synthesized one, show that the Hückel molecular orbitals (MOs) strikingly resemble the DFT-computed $π$ MOs, which were obtained using a herein proposed technique based on the localization and re-delocalization of DFT canonical MOs. Interestingly, the lower-lying $π$ MOs exhibit an odd number of nodal planes and are doubly quasidegenerate as a consequence of the phase inversion in Möbius macrocycles, contrasting with macrocyclic Hückel systems. Coulson bond orders derived from SHMO theory correlate well with DFT-calculated Wiberg bond indices for all C-C bonds in tested Möbius CNBs. Additionally, a remarkable correlation is observed between HOMO-LUMO gaps obtained from the SHMO and GFN2-xTB calculations for a large number of topoisomers of Möbius CNBs. Thus, the SHMO model not only captures the essence of $π$ electronic structure of Möbius CNBs, but also provides reliable quantitative predictions comparable to DFT results.
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