From Macrocycles to Quantum Rings: Does Aromaticity Have a Size Limit?

ConspectusThe ring currents of aromatic and antiaromatic
molecules are remarkable
emergent phenomena. A ring current is a quantum-mechanical feature
of the whole system, and its existence cannot be inferred from the
properties of the individual components of the ring. Hückel’s
rule states that when an aromatic molecule with a circuit of [4n + 2] π electrons is placed in a magnetic field,
the field induces a ring current that creates a magnetic field opposing
the external field inside the ring. In contrast, antiaromatic rings
with 4n π electrons exhibit ring currents in
the opposite direction. This rule bears the name of Erich Hückel,
and it grew from his molecular orbital theory, but modern formulations
of Hückel’s rule incorporate contributions from others,
particularly William Doering and Ronald Breslow. It is often assumed
that aromaticity is restricted to small molecular rings with up to
about 22 π electrons. This Account outlines the discovery of
global ring currents in large macrocycles with circuits of up to 162
π electrons. The largest aromatic rings yet investigated are
cyclic porphyrin oligomers, which exhibit global ring currents after
oxidation, reduction or optical excitation but not in the neutral
ground state. The global aromaticity in these porphyrin nanorings
leads to experimentally measurable aromatic stabilization energies
in addition to magnetic effects that can be studied by NMR spectroscopy.
Wheel-like templates can be bound inside these nanorings, providing
excellent control over the molecular geometry and allowing the magnetic
shielding to be probed inside the nanoring. The ring currents in these
systems are well-reproduced by density functional theory (DFT), although
the choice of DFT functional often turns out to be critical. Here
we review recent contributions to this field and present a simple
method for determining the ring current susceptibility (in nA/T) in
any aromatic or antiaromatic ring from experimental NMR data by classical
Biot–Savart calculations. We use this method to quantify the
ring currents in a variety of aromatic rings. This survey confirms
that Hückel’s rule reliably predicts the direction of
the ring current, and it reveals that the ring current susceptibility
is surprisingly insensitive to the size of the ring. The investigation
of aromaticity in even larger molecular rings is interesting because
ring currents are also observed when mesoscopic metal rings are placed
in a magnetic field at low temperatures. The striking similarity between
the ring currents in molecules and mesoscopic metal rings arises because
the effects have a common origin: a field-dependent phase shift in
the electronic wave function. The main difference is that the magnetic
flux through mesoscopic rings is much greater because of their larger
areas, so their persistent currents are nonlinear and oscillatory
with the applied field, whereas the flux through aromatic molecules
is so small that their response is approximately linear in the applied
field. We discuss how nonlinearity is expected to emerge in large
molecular nanorings at high magnetic fields. The insights from this
work are fundamentally important for understanding aromaticity and
for bridging the gap between chemistry and mesoscopic physics, potentially
leading to new functions in molecular electronics.

研究概要
芳香性与反芳香性分子的环电流是一类显著的涌现现象。环电流是整个体系的量子力学特征，其存在性无法通过环的单个组成部分的性质推导得出。休克尔规则（Hückel’s rule）指出：当含有[4n+2]个π电子回路的芳香性分子处于磁场中时，外部磁场会诱导产生环电流，该环电流会生成一个与环内部外磁场方向相反的磁场。与之相反，拥有4n个π电子的反芳香性环则会产生方向相反的环电流。该规则以埃里希·休克尔（Erich Hückel）的名字命名，其起源于他的分子轨道理论，但现代版本的休克尔规则吸纳了其他学者的贡献，尤其是威廉·多林（William Doering）与罗纳德·布雷斯洛（Ronald Breslow）的工作。

学界通常认为芳香性仅局限于π电子数至多约22个的小型分子环。本综述概述了针对π电子回路多达162个的大型大环化合物中全局环电流的发现历程。目前已被研究的最大芳香性环为环状卟啉低聚物，这类低聚物在经过氧化、还原或光激发后会表现出全局环电流，但在中性基态下则不会。这类卟啉纳米环的全局芳香性不仅可通过核磁共振（NMR）波谱学研究其磁效应，还能产生可实验测量的芳香稳定化能。

轮状模板可结合在这些纳米环内部，从而实现对分子几何构型的精准调控，并可探测纳米环内部的磁屏蔽效应。尽管DFT泛函的选择往往至关重要，但密度泛函理论（DFT）能够很好地复现这些体系中的环电流。本文综述了该领域的近期研究进展，并提出了一种简便方法：通过经典毕奥-萨伐尔（Biot–Savart）计算，基于实验NMR数据确定任意芳香性或反芳香性环的环电流磁化率（单位为纳安每特斯拉，nA/T）。我们利用该方法量化了多种芳香性环的环电流。

本次调研证实，休克尔规则能够可靠预测环电流的方向，同时发现环电流磁化率对环的尺寸出人意料地不敏感。对更大尺寸分子环的芳香性研究颇具意义，因为在低温下将介观金属环置于磁场中时，同样会观测到环电流。分子环与介观金属环的环电流存在惊人的相似性，这是因为二者的效应具有共同起源：电子波函数的场相关相移。二者的主要区别在于：介观环的面积更大，因此穿过其的磁通量要大得多，其持久电流呈现非线性且随外磁场呈振荡变化；而穿过芳香性分子的磁通量极小，因此其响应近似于随外磁场线性变化。我们讨论了在强磁场下大型分子纳米环中非线性效应的预期表现。本研究的相关发现对于理解芳香性、弥合化学与介观物理学之间的鸿沟具有根本重要性，有望为分子电子学领域带来新的功能应用。