Direct evidence for a carbon–carbon one-electron σ-bond
碳-碳单电子σ键的直接证据

Unlocking the nature of covalent bonds is important to gain a deeper understanding of chemical phenomena. The concept of two atoms sharing an electron pair, which was initially proposed by Lewis in 1916 (ref. ⁸) and then termed ‘covalent bond’ in 1919 by Langmuir⁹, remains relevant in understanding chemical bonding.
揭示共价键的本质对于深入理解化学现象至关重要。1916 年，路易斯首次提出的两个原子共享一对电子的概念，随后在 1919 年被朗缪尔命名为“共价键”，这一概念至今在理解化学键合中仍具有重要意义。

Subsequently, Pauling proposed a concept of covalent bonds with one unpaired electron (‘one-electron σ-bonds’), which is shared between two atoms⁷. In 1931, Pauling postulated the existence of one-electron σ-bonds using the H₂^•+ radical cation as a simple model. Such one-electron σ-bonds are expected to be much weaker than typical two-electron σ-bonds and, therefore, their properties have been investigated primarily theoretically^10,11,12,13. Nevertheless, few studies on in situ generated radical anions^14,15,16,17 such as R₃B•BR₃⁻ and radical cations^10,18,19,20 such as R₃E•ER₃⁺ (E = C, Si and Ge) based on electron spin resonance measurements have been reported. Other reports have described the spectroscopic identification of chemical species with one-electron σ-bonds that were generated as single components; however, these compounds have not been isolated^21,22. X-ray crystallographic studies on species that contain one-electron σ-bonds are particularly scarce, that is, they are limited to P•P, B•B and Cu•M (M = B, Al and Ga) bonds^1,2,3,4. It is important to note here that, although species with C•C one-electron σ-bonds have been proposed as intermediates in chemical reactions such as the Cope rearrangement, there is no experimental evidence by, for example, X-ray crystallography for one-electron σ-bonds between carbon atoms^{23,24,25,26,27,28}.
随后，Pauling 提出了一种含有一个未成对电子的共价键概念（‘单电子σ键’），该电子在两个原子之间共享 ⁷ 。1931 年，Pauling 以 H ₂ ^•+ 自由基阳离子为简单模型，假设了单电子σ键的存在。这种单电子σ键预计比典型的双电子σ键弱得多，因此，其性质主要通过理论研究进行探讨 ^10,11,12,13 。然而，关于现场生成的自由基阴离子 ^14,15,16,17 如 R ₃ B•BR ₃ ⁻ 和自由基阳离子 ^10,18,19,20 如 R ₃ E•ER ₃ ⁺ （E = C, Si 和 Ge）的电子自旋共振测量研究报道甚少。其他报告描述了通过光谱识别生成的含单电子σ键的化学物种；然而，这些化合物尚未被分离 ^21,22 。包含单电子σ键的物种的 X 射线晶体学研究尤为稀缺，仅限于 P•P、B•B 和 Cu•M（M = B, Al 和 Ga）键 ^1,2,3,4 。 值得注意的是，尽管有人提出具有 C•C 单电子σ键的物种可能是如 Cope 重排等化学反应的中间体，但目前尚无通过 X 射线晶体学等实验证据来证实碳原子间存在单电子σ键 ^{23,24,25,26,27,28} 。

R₃C•CR₃⁺ radical cations are promising models with which to investigate C•C one-electron σ-bonds^18,20. However, reports on molecules that contain a C•C one-electron σ-bond remain elusive at present due to their intrinsically high reactivity, and stabilizing such compounds is as important a task as it is challenging. One approach to circumvent this obstacle is to use hexaphenylethane (HPE) derivatives, which can be expected to provide a suitable framework because their oxidation would lead to the formation of triarylmethyl cation and triarylmethyl radical units, which are well known, relatively stable, carbocations and radicals.
R ₃ C•CR ₃ ⁺ 自由基阳离子是研究 C•C 单电子σ键的有前景的模型。然而，目前关于含有 C•C 单电子σ键分子的报道仍然稀缺，这主要归因于其内在的高反应性，稳定这些化合物既是一项重要任务，也是一项挑战。一种绕过这一障碍的方法是使用六苯基乙烷（HPE）衍生物，因为它们的氧化会形成三芳基甲基阳离子和三芳基甲基自由基单元，这些单元是众所周知的、相对稳定的碳正离子和自由基，因此可以提供合适的框架。

An important issue in this context is that most redox-active HPEs undergo a process close to a one-step two-electron oxidation to produce two triarylmethyl cations because the oxidation potential for the bond-dissociated radical, which is generated readily by the C–C bond scission of the radical cation intermediate, is much less positive than that for neutral σ-bonded species (E₁^ox > E₂^ox) (Fig. 1, top). To obtain a radical cation with a C•C one-electron σ-bond, the oxidation of HPEs must proceed in a stepwise manner, that is, the level of the highest occupied molecular orbital (HOMO) for the neutral state must be higher than that of the singly occupied molecular orbital (SOMO) for the radical cation (E₁^ox < E₂^ox). Although raising the HOMO level is considered to be essential, the introduction of electron-donating heteroatoms into HPEs is not effective because it simultaneously raises the HOMO level of the neutral species and the SOMO level of the radical cations. Thus, alternative approaches for achieving a stepwise oxidation process are required.
在此背景下，一个重要问题是大多数氧化还原活性 HPEs 经历近乎一步两电子氧化过程，生成两个三芳基甲基阳离子，因为由自由基阳离子中间体的 C-C 键断裂易生成的键断裂自由基的氧化电位远低于中性σ键合物种的氧化电位（E ₁ ^ox > E ₂ ^ox ）（图 1，顶部）。要获得具有 C•C 单电子σ键的自由基阳离子，HPEs 的氧化必须分步进行，即中性态的最高占据分子轨道（HOMO）能级必须高于自由基阳离子的单占据分子轨道（SOMO）能级（E ₁ ^ox < E ₂ ^ox ）。尽管提高 HOMO 能级被认为是关键，但向 HPEs 中引入电子供体杂原子并不有效，因为它同时提高了中性物种的 HOMO 能级和自由基阳离子的 SOMO 能级。因此，需要寻找实现分步氧化过程的替代方法。

a, Typical oxidation processes in HPEs. b, Oxidation in the HPE derivative with an ultralong C–C single bond.
a, HPEs 中的典型氧化过程。b, 具有超长 C–C 单键的 HPE 衍生物中的氧化反应。

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We tackled this issue by focusing on another notable feature of HPEs, which is that the central C–C single bond is elongated beyond 1.6 Å due to the steric hindrance imposed by the aryl groups surrounding the bond^{29,30,31,32,33}. This bond elongation causes an increase in the HOMO level by means of a through-bond interaction between the elongated C–C bond and the aryl groups. Thus, the bond elongation in HPEs provides an optimal approach to realize an energy reversal between the HOMO of the neutral state and the SOMO of the radical cation state without relying on the introduction of electron-donating heteroatoms (Fig. 1, bottom).
我们通过关注 HPEs 的另一个显著特征来解决这一问题，即由于围绕该键的芳基团所施加的空间位阻，中心 C–C 单键被拉长至超过 1.6 Å ^{29,30,31,32,33} 。这种键的拉长通过拉长的 C–C 键与芳基团之间的键间相互作用，导致 HOMO 能级的升高。因此，HPEs 中的键拉长提供了一种理想的方法，无需引入电子供体杂原子，即可实现中性态的 HOMO 与自由基阳离子态的 SOMO 之间的能量反转（图 1 底部）。

HPE 1 (refs. ^5,6) bears two spiro-dibenzocycloheptatriene (DBCHT) units and thus satisfies the aforementioned key factors, that is, it has an extremely elongated Csp³–Csp³ single bond (1.806(2) Å at 400 K), which is the highest value among hitherto reported HPEs. Such an extremely elongated C–C bond increases the HOMO level by means of a through-bond interaction, resulting in a stepwise oxidation process (E_1/2^ox1 = +0.57 V and E_1/2^ox2 = +0.69 V versus saturated calomel electrode) that was observed by cyclic voltammetry³⁴. Furthermore, the rigid acenaphthylene core causes a bond elongation in the neutral-state C…C distance required to form a one-electron bond. The naphthalene core, on the other hand, is not suitable to cause the stepwise oxidation in the corresponding hydrocarbon, although that worked well in the case of the B•B one-electron bond reported in ref. ²¹. We predicted that HPE 1 could potentially serve as a suitable platform to stabilize the C•C one-electron σ-bond through an intramolecular core–shell strategy.
HPE 1（参见文献 ^5,6 ）含有两个螺二苯并环庚三烯（DBCHT）单元，因此满足了上述关键条件，即其具有极长的 Csp ³ –Csp ³ 单键（400 K 时为 1.806(2) Å），这一数值在迄今报道的 HPEs 中是最高的。这种极长的 C–C 键通过键间相互作用提升了 HOMO 能级，导致阶梯式氧化过程（E _1/2 ^ox1 = +0.57 V 和 E _1/2 ^ox2 = +0.69 V，相对于饱和甘汞电极），这一过程通过循环伏安法得以观察 ³⁴ 。此外，刚性的苊烯核心导致中性状态下形成单电子键所需的 C…C 距离延长。而萘核心则不适合引发相应烃的阶梯式氧化，尽管在参考文献 ²¹ 中报道的 B•B 单电子键情况下表现良好。我们预测，HPE 1 有可能通过分子内核心–壳层策略成为稳定 C•C 单电子σ键的合适平台。

Figure 2a shows the redox reactions of 1. A two-electron oxidation was achieved by treating 1 with iodine (3.0 equiv.) to furnish dication salt 1²⁺(I₃⁻)₂, of which single crystals were obtained after recrystallization from CH₂Cl₂/diethyl ether. Meanwhile, the one-electron oxidation of 1 with iodine (1.5 equiv.) provided 1^•+I₃^– as a dark brown solid that is sparingly soluble in organic solvents such as CH₂Cl₂ and acetonitrile. The formation of paramagnetic species was confirmed by the absence of any ¹H nuclear magnetic resonance (NMR) signals and the presence of a characteristic doublet electron spin resonance signal in solution. Recrystallization of the radical cation salt 1^•+I₃⁻ from acetonitrile/diethyl ether afforded dark violet single crystals suitable for X-ray diffraction measurements. Upon reduction of the cationic species with zinc powder, the original compound 1 was restored.
图 2a 展示了 1 的氧化还原反应。通过用碘（3.0 当量）处理 1，实现了两电子氧化，得到了二阳离子盐 1 ²⁺ （I ₃ ⁻ ） ₂ ，其在 CH ₂ Cl ₂ /乙醚中重结晶后获得了单晶。同时，用碘（1.5 当量）对 1 进行单电子氧化，生成了深棕色固体 1 ^•+ I ₃ ^– ，该固体在有机溶剂如 CH ₂ Cl ₂ 和乙腈中难溶。通过缺乏任何 ¹ H 核磁共振（NMR）信号以及溶液中存在特征性的双峰电子自旋共振信号，确认了顺磁性物种的形成。将自由基阳离子盐 1 ^•+ I ₃ ⁻ 从乙腈/乙醚中重结晶，得到了适合 X 射线衍射测量的深紫色单晶。通过用锌粉还原阳离子物种，恢复了原始化合物 1。

a, Redox interconversion of 1. b–d, X-ray structures of 1 (b) and 1^•+I₃⁻ (d) at 100 K and 1²⁺(I₃⁻)₂ (c) at 110 K with thermal ellipsoids at 50% probability. e, Structural parameters determined at 100 K for 1 and 1²⁺(I₃⁻)₂ and at 110 K for 1^•+I₃⁻. Due to the phase transition occurring at around 100 K, the X-ray analysis of 1²⁺(I₃⁻)₂ was conducted at 110 K; disordered I₃⁻ is omitted for clarity in 1²⁺(I₃⁻)₂.
a, 1 的氧化还原互变。b–d, 1 在 100 K 下的 X 射线结构（b）和 1 ^•+ I ₃ ⁻ 在 100 K 下的 X 射线结构（d），以及 1 ²⁺ (I ₃ ⁻ ) ₂ 在 110 K 下的 X 射线结构（c），热椭球概率为 50%。e, 在 100 K 下测定的 1 和 1 ²⁺ (I ₃ ⁻ ) ₂ 的结构参数，以及在 110 K 下测定的 1 ^•+ I ₃ ⁻ 的结构参数。由于约 100 K 时发生的相变，1 ²⁺ (I ₃ ⁻ ) ₂ 的 X 射线分析在 110 K 下进行；为清晰起见，1 ²⁺ (I ₃ ⁻ ) ₂ 中无序的 I ₃ ⁻ 未显示。

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The single crystals obtained were subjected to an X-ray diffraction analysis to explain redox-state-dependent differences in the molecular structures. The X-ray structure of dication 1²⁺ in 1²⁺(I₃⁻)₂ exhibits a twisted conformation with a twisting C1–C3–C4–C2 angle (θ) of 20.8(6)°, while both DBCHT moieties are planar (Fig. 2c). As in the case of 1²⁺(I₃⁻)₂, typical dibenzocycloheptatrienylium (cation) and dibenzocycloheptatrienyl (radical) derivatives would be expected to exhibit a preference for planarity, which is more conducive to π-stacking and electron delocalization^35,36,37. In contrast, an eclipsed conformation with a small θ value of 2.19(19)° was observed in the X-ray structure of 1^•+ in 1^•+I₃⁻ (Fig. 2d,e). One of the DBCHT moieties in 1^•+, that is, the one containing C1, adopts a bent geometry with larger dihedral angles between the a–e planes (Fig. 2). The concave surface of the bent seven-membered ring faces the other DBCHT unit, that is, the one containing C2, which exhibits an almost planar geometry. The estimated s.d. of the structural parameters (bond length: 0.004 Å; bond angle: 0.3°) and R indices (R1 = 0.0220; wR2 = 0.0569) for 1^•+I₃⁻ were sufficiently small to confirm the unsymmetrical bent-planar structure, and the nearly perfect round shape of the thermal ellipsoids of C1 and C2 excludes the possibility of a disordering copresence of 1 or 1²⁺ at the site of 1^•+. Crystals of 1^•+I₃⁻ can be stored under ambient conditions for at least two weeks without appreciable decomposition and remained intact even during high-temperature X-ray measurements at 400 K (Supplementary Fig. 4). The observed geometrical difference between 1^•+ and 1²⁺ is intrinsic and reproducible, which was confirmed by analysing several single crystals of 1^•+I₃⁻ and 1²⁺(I₃⁻)₂.
所得单晶经 X 射线衍射分析，以阐明氧化还原状态依赖的分子结构差异。二价阳离子 1 ²⁺ 在 1 ²⁺ （I ₃ ⁻ ） ₂ 的 X 射线结构显示扭曲构象，其扭曲的 C1–C3–C4–C2 角度（θ）为 20.8(6)°，而两个 DBCHT 部分均为平面（图 2c）。如同 1 ²⁺ （I ₃ ⁻ ） ₂ 的情况，典型的二苯并环庚三烯正离子（阳离子）和二苯并环庚三烯基（自由基）衍生物预期会偏好平面性，这更有利于π堆积和电子离域 ^35,36,37 。相反，在 1 ^•+ 在 1 ^•+ I ₃ ⁻ 的 X 射线结构中观察到重叠构象，其θ值较小，为 2.19(19)°（图 2d,e）。1 ^•+ 中的一个 DBCHT 部分，即包含 C1 的部分，采用弯曲几何结构，a–e 平面间的二面角较大（图 2）。弯曲的七元环凹面朝向另一个 DBCHT 单元，即包含 C2 的单元，该单元几乎呈平面几何结构。结构参数（键长：0.004 Å；键角：0.3°）的标准偏差和 R 指数（R1 = 0.0220；wR2 = 0.0569) 对于 1 ^•+ I ₃ ⁻ ，其值足够小以证实非对称弯曲平面结构，而 C1 和 C2 的热椭球近乎完美的圆形排除了 1 或 1 ²⁺ 在 1 ^•+ 位点上无序共存的可能性。1 ^•+ I ₃ ⁻ 的晶体在常温条件下至少可保存两周而未见明显分解，甚至在 400 K 高温下的 X 射线测量中仍保持完整（补充图 4）。观察到的 1 ^•+ 与 1 ²⁺ 之间的几何差异是内在且可重复的，这一点通过分析多个 1 ^•+ I ₃ ⁻ 和 1 ²⁺ (I ₃ ⁻ ) ₂ 的单晶得以确认。

This distinctive geometry deviates from the typical planar conformation of a pimer composed of cationic and radical moieties/molecules^38,39,40. Contrary to the unsymmetric structure of 1^•+I₃⁻, the bond lengths in the two different DBCHT moieties are almost identical (Supplementary Tables 1 and 2), which indicates that the spin and positive charge are delocalized over the two DBCHT moieties in 1^•+I₃⁻, that is, spin and charge-separated states are not favoured. Other effects between the two DBCHT moieties stem most probably from the stabilization of the unique and unsymmetric bent conformation. At present, we consider that the molecular structure of 1^•+ with an unsymmetric bent-planar geometry is similar to that of 1, which implies an inheritance from the covalent bond nature between the C1 and C2 atoms. In fact, the short contact between the C1 and C2 atoms (2.921(3) Å at 100 K) was confirmed in the X-ray structure of 1^•+I₃⁻ (Fig. 2e). The sum of the three bond angles around the C1 (359.3°) and C2 (359.6°) atoms indicates that each atom is sp² hybridized despite the unsymmetrical bent-planar geometry. This finding is consistent with previous examples of weak C…C bondings, in which the carbon atoms involved exhibit a preference for sp² hybridization^41,42. Focusing on the intramolecular C…C distance between the two DBCHT units, although some interatomic distances (2.92–3.32 Å) closer to the naphthalene skeleton were found to be less than the sum of the van der Waals radii of carbon atoms (3.40 Å), most are greater (3.44–3.79 Å), indicating an unfavourable conformation for stabilization by π–π interactions (Supplementary Fig. 10 and Supplementary Table 1). This behaviour contrasts with the usual planar π-systems, indicating that stabilizing interactions other than π–π stacking are occurring between the DBCHT units. In the crystal, short intermolecular contacts between one DBCHT unit and I₃⁻ (approximately 3.5 Å; sum of the van der Waals radii: 3.8 Å) were observed. However, they correspond to the proximity of the σ-hole—a positively polarized site—in the I₃⁻ ion and the cationic π-surface of DBCHT and, accordingly, this intermolecular interaction has little effect on the geometrical features of 1^•+ in crystal. It is also worth noting here that residual electron density between the C1 and C2 atoms is present in the Fo–Fc map that was obtained from the X-ray analysis of 1^•+I₃⁻ (Fig. 3a–c), which proves electron sharing between the C1 and C2 atoms. This electron sharing contributes to the molecular stability, which predestines radical cation 1^•+ to serve as a host for a C•C one-electron σ-bond with a bond length of 2.921(3) Å. In the case of the B•B one-electron bond, which is based on the naphthalene core, a similar interatomic distance was predicted²¹, whereas a smaller value was determined in the corresponding molecule with a biphenyl core. This difference should most probably be interpreted in terms of the rigidity of the π-framework.
这种独特的几何结构偏离了由阳离子和自由基部分/分子组成的典型平面构象 ^38,39,40 。与 1 ^•+ I ₃ ⁻ 的不对称结构不同，两种不同 DBCHT 部分的键长几乎相同（补充表 1 和 2），这表明在 1 ^•+ I ₃ ⁻ 中，自旋和正电荷在两个 DBCHT 部分上离域化，即自旋和电荷分离状态并不受青睐。两个 DBCHT 部分之间的其他效应很可能源于这种独特且不对称的弯曲构象的稳定作用。目前我们认为，具有不对称弯曲-平面几何结构的 1 ^•+ 分子结构与 1 相似，这暗示了 C1 和 C2 原子间共价键性质的继承。实际上，在 1 ^•+ I ₃ ⁻ 的 X 射线结构中确认了 C1 和 C2 原子间的短接触（100 K 时为 2.921(3) Å）（图 2e）。围绕 C1（359.3°）和 C2（359.6°）原子的三个键角之和表明，尽管几何结构不对称且弯曲-平面，但每个原子均为 sp ² 杂化。 这一发现与先前弱 C…C 键合的例子相符，其中涉及的碳原子表现出对 sp ² 杂化 ^41,42 的偏好。聚焦于两个 DBCHT 单元间的分子内 C…C 距离，尽管发现一些靠近萘骨架的原子间距离（2.92–3.32 Å）小于碳原子的范德华半径之和（3.40 Å），但大多数距离更大（3.44–3.79 Å），表明不利于通过π–π相互作用稳定构象（补充图 10 和补充表 1）。这种行为与通常的平面π系统形成对比，表明在 DBCHT 单元间存在除π–π堆积以外的稳定相互作用。在晶体中，观察到 DBCHT 单元与 I ₃ ⁻ 之间存在短的分子间接触（约 3.5 Å；范德华半径之和：3.8 Å）。然而，这些接触对应于 I ₃ ⁻ 离子中的σ-孔——一个正极化位点——与 DBCHT 的阳离子π表面之间的接近，因此，这种分子间相互作用对晶体中 1 ^•+ 的几何特征影响甚微。 值得注意的是，在通过 X 射线分析 1 ^•+ I ₃ ⁻ 获得的 Fo–Fc 图中，C1 和 C2 原子之间存在剩余电子密度（图 3a–c），这证明了 C1 和 C2 原子间的电子共享。这种电子共享有助于分子稳定，从而使自由基阳离子 1 ^•+ 成为 C•C 单电子σ键的宿主，键长为 2.921(3) Å。对于基于萘核的 B•B 单电子键，预测了类似的原子间距离 ²¹ ，而在具有联苯核的相应分子中测得的值较小。这种差异很可能应从π骨架的刚性角度来解释。

a–c, Experimentally obtained Fo–Fc maps of 1^•+I₃⁻ at 100 K on the C1–C3–C4–C2 plane (a,b) and on its orthogonal plane (c) through the midpoint between the C1 and C2 atoms (C2 → C1 direction). Residual electron density is shown in green (a) and blue (b,c). d, Raman spectrum measured at 298 K using a single crystal of 1^•+I₃⁻. e, Simulated Raman spectrum for 1^•+ obtained from DFT calculations at the UM06-2X/6-311+G** level.
a–c，在 100 K 下，1 ^•+ I ₃ ⁻ 在 C1–C3–C4–C2 平面（a,b）及其正交平面（c）上通过 C1 和 C2 原子中点（C2 → C1 方向）获得的实验性 Fo–Fc 图。剩余电子密度以绿色（a）和蓝色（b,c）显示。d，使用 1 ^•+ I ₃ ⁻ 的单晶在 298 K 下测得的拉曼光谱。e，通过 UM06-2X/6-311+G**水平 DFT 计算得到的 1 ^•+ 模拟拉曼光谱。

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To verify whether this electron sharing corresponds to the bond, a single crystal of 1^•+I₃⁻ was subjected to Raman spectroscopy at 298 K to obtain direct information about the force constant of the bond. The experimentally obtained and simulated Raman spectra of 1^•+ are shown in Fig. 3d,e. The simulated spectrum obtained from density functional theory (DFT) calculations at the UM06-2X/6-311+G** level accurately reproduced the experimental results. The observed Raman shift (1^•+I₃⁻: 379 cm⁻¹) attributed to the symmetric C1–C2 stretching vibration is significantly lower than that for neutral 1, which contains an ultralong C–C single bond (589 cm⁻¹)^5,6. However, this Raman shift is higher than that observed in molecules that contain C…C bonding interactions beyond 2.0 Å (refs. ^41,42). This contrasts with the common absence of Raman shifts for weak interactions in π-stacked molecules such as pimers.
为验证这种电子共享是否对应于键合，对单晶 1 ^•+ I ₃ ⁻ 在 298 K 下进行了拉曼光谱分析，以获取有关键力常数的直接信息。实验所得及模拟的 1 ^•+ 拉曼光谱如图 3d,e 所示。通过密度泛函理论（DFT）在 UM06-2X/6-311+G**水平上的计算所得模拟光谱准确再现了实验结果。观察到的拉曼位移（1 ^•+ I ₃ ⁻ ：379 cm ⁻¹ ）归因于对称 C1–C2 伸缩振动，显著低于中性 1 的值，后者含有超长 C–C 单键（589 cm ⁻¹ ） ^5,6 。然而，此拉曼位移高于含有超过 2.0 Å的 C…C 键合相互作用的分子所观察到的值（参考文献 ^41,42 ）。这与通常π堆积分子如 pimers 中弱相互作用缺乏拉曼位移的现象形成对比。

Next, DFT calculations were carried out to obtain more information on the strength of the C•C one-electron σ-bond. The estimated force constant for 1^•+ (56.8 N m⁻¹), which was obtained as a second derivative of the energy with respect to the bond length at the (U)M06-2X/6-31+G** level based on the Lennard–Jones potential, is much smaller than that for 1 (113.7 N m⁻¹) or ethane (445.9 N m⁻¹). The estimated force constant is in good agreement with the calculated value (50.8 N m⁻¹) obtained from the relationship between the force constant and the vibrational frequency using the value of the observed Raman shift of the symmetric C1–C2 stretching vibration (for details, see Supplementary Information). These results indicate a covalent nature of the electron sharing between the C1 and C2 atoms in 1^•+I₃⁻.
接下来，进行了 DFT 计算以获取有关 C•C 单电子σ键强度的更多信息。基于 Lennard-Jones 势能，在(U)M06-2X/6-31+G**水平上，通过能量对键长的二阶导数得到的 1 ^•+ 的力常数估计值（56.8 N m ⁻¹ ），远小于 1（113.7 N m ⁻¹ ）或乙烷（445.9 N m ⁻¹ ）的力常数。该估计的力常数与通过力常数与振动频率关系计算得到的值（50.8 N m ⁻¹ ）非常吻合，计算中使用了对称 C1–C2 伸缩振动的观测拉曼位移值（详见补充信息）。这些结果表明，在 1 ^•+ I ₃ ⁻ 中，C1 和 C2 原子间的电子共享具有共价性质。

Le Floch et al. reported that the radical anion of the calixarene exhibits a short C…C distance (3.323(3) Å)⁴³. From a theoretical point of view, the coefficients of the SOMO indicate that a bonding orbital between the carbon atoms in close proximity was not formed since they reside on the nodal plane. Thus, a detailed investigation is needed to verify whether this short contact represents a bond or is due merely to physical proximity. To gain further insight into the electronic structure, DFT calculations for 1^•+ were performed at the UM06-2X/6-311+G** level based on the X-ray coordinates. The results indicate that the SOMO, the lowest unoccupied molecular orbital (LUMO) and the spin density are located mainly on the C1 and C2 atoms (Fig. 4a–c). According to the shape of the orbitals, the α-SOMO and α-LUMO of 1^•+ represent the σ-type bonding and σ*-type antibonding orbitals, respectively. In the natural bond orbital (NBO) analysis of 1^•+, both orbitals were confirmed for the C1 and C2 atoms as well. The C1–C2 bond exhibits 0.3–0.4% 2s character and 99.6–99.7% 2p character, with 0.76 electrons involved in the bond. Equal values of a positive charge for both C1 (0.05) and C2 (0.05) atoms in 1^•+ were estimated using natural population analysis methods, indicating a delocalized charge distribution in the DBCHT moieties. The natural population analysis also predicted a relatively large spin-density distribution on the C1 (0.26) and C2 (0.24) atoms. A localized molecular orbital analysis using the Foster–Boys method showed that the contribution of the C1 (28.0%) and C2 (27.5%) atoms in the α-SOMO is dominant and that the contributions of the other atoms is less than 5%. The shape of the localized α-SOMO clearly reflects the formation of the σ-orbital (Supplementary Fig. 21). Considering these results and the comparable bond lengths in each DBCHT moiety, the contribution of a coordinating-type bonding interaction can be excluded, that is, these results indicate that a σ-bond between carbon atoms could be maintained even if fewer than one electron is involved. Furthermore, we carried out bond topological analyses including quantum theory of atom in molecules and electron localized functions for the whole series. Each parameter for 1^•+ exhibits an intermediate value between those of bonded 1 and non-bonded 1²⁺, which indicates that 1^•+ possesses an intermediary nature. This finding is consistent with the notion of the presence of a one-electron bond, which would be expected to fall between a two-electron bond and a non-bonded state.
Le Floch 等人报道，杯芳烃的阴离子表现出较短的 C…C 距离（3.323(3) Å）。从理论角度来看，SOMO 的系数表明，由于碳原子位于节面上，因此并未形成相邻碳原子间的成键轨道。因此，需要进行详细研究以确认这种短接触是否代表化学键，还是仅由物理接近造成。为进一步了解其电子结构，基于 X 射线坐标，在 UM06-2X/6-311+G**水平上对 1 进行了 DFT 计算。结果显示，SOMO、最低未占据分子轨道（LUMO）及自旋密度主要分布在 C1 和 C2 原子上（图 4a–c）。根据轨道形状，1 的α-SOMO 和α-LUMO 分别代表σ型成键轨道和σ*型反键轨道。在 1 的自然键轨道（NBO）分析中，C1 和 C2 原子上的这两种轨道也得到了确认。C1–C2 键具有 0.3–0.4%的 2s 特征和 99.6–99.7%的 2p 特征，成键电子数为 0.76。C1 和 C2 均带有相等的正电荷值。05)和 C2 (0.05)原子的自然布居分析结果表明，DBCHT 部分呈现出电荷离域分布。自然布居分析还预测 C1 (0.26)和 C2 (0.24)原子上有较大的自旋密度分布。采用 Foster-Boys 方法进行的局域分子轨道分析显示，C1 (28.0%)和 C2 (27.5%)原子对α-SOMO 的贡献占主导地位，而其他原子的贡献均小于 5%。局域化的α-SOMO 形状清晰反映了σ轨道的形成（见补充图 21）。结合这些结果及各 DBCHT 部分中相近的键长，可排除配位型键合相互作用的可能性，即这些结果表明，即使涉及的电子数少于一个，碳原子间的σ键仍可能得以维持。此外，我们对整个系列进行了包括量子分子中的原子理论和电子局域化函数在内的键拓扑分析。 每个参数在 1 ^•+ 中表现出介于键合 1 和非键合 1 ²⁺ 之间的中间值，这表明 1 ^•+ 具有中间性质。这一发现与存在单电子键的概念相符，该键应介于双电子键和非键合状态之间。

a–c, Kohn–Sham orbitals of the α-SOMO (a), the α-LUMO (isovalue = 0.05) (b), and spin density (isovalue = 0.004) (c) obtained from DFT calculations at the UM06-2X/6-311+G** level. The atomic coordinates of the X-ray structure of 1^•+I₃⁻ at 100 K were used for the calculations. d,e,g, UV/Vis/NIR absorption spectra in CH₂Cl₂ (d, 16.7 μM; e, 417 μM) and for a single crystal of 1^•+I₃⁻ (g). f, Photograph of a single crystal of 1^•+I₃⁻. h,i, Changes (black arrows) in UV/Vis/NIR spectra upon constant-current electrochemical oxidation of 1 (11.1 μM, 30 μA, every 2 min) in CH₂Cl₂ containing 0.05 M Bu₄NBF₄ as a supporting electrolyte: first step (0–28 min, 1 to 1^•+) (h); second step (28–90 min, 1^•+ to 1²⁺) (i).
a–c，由 UM06-2X/6-311+G**水平 DFT 计算得到的α-SOMO（a）、α-LUMO（等值面=0.05）（b）和自旋密度（等值面=0.004）（c）的 Kohn-Sham 轨道。计算中使用了 1 ^•+ I ₃ ⁻ 在 100 K 下的 X 射线结构的原子坐标。d,e,g，在 CH ₂ Cl ₂ 中的 UV/Vis/NIR 吸收光谱（d，16.7 μM；e，417 μM）以及单晶 1 ^•+ I ₃ ⁻ 的吸收光谱（g）。f，单晶 1 ^•+ I ₃ ⁻ 的照片。h,i，在含有 0.05 M Bu ₄ NBF ₄ 作为支持电解质的 CH ₂ Cl ₂ 中，对 1 进行恒电流电化学氧化时 UV/Vis/NIR 光谱的变化（黑色箭头）：第一步（0–28 min，1 至 1 ^•+ ）（h）；第二步（28–90 min，1 ^•+ 至 1 ²⁺ ）（i）。

Full size image 全尺寸图像

In their entirety, the experimental and theoretical results indicate that the short C1…C2 contact with a value of 2.921(3) Å in 1^•+I₃⁻ is, although weak, an example of a C•C one-electron σ-bond.
实验和理论结果整体表明，1 ^•+ I ₃ ⁻ 中 C1…C2 间距为 2.921(3) Å 的短接触尽管较弱，但仍是一个 C•C 单电子 σ 键的实例。

To investigate the properties of the compound from the photochemical point of view, we recorded the ultra-violet/visible/near-infrared (UV/Vis/NIR) spectrum of 1^•+I₃⁻ in CH₂Cl₂. An NIR absorption band was observed at around 2,000 nm (λ_max ≃ 1,405 nm) (Fig. 4d,e), which cannot be explained by disproportionation (2 × 1^•+ ⇄ 1 + 1²⁺) because neither 1 nor 1²⁺ exhibits such an NIR absorption (Fig. 4h,i and Supplementary Fig. 15). In solution, 1^•+ could exist in an equilibrium between the σ-bonded form and the pimer-like form predicted by DFT calculations (for details, see Supplementary Information). To confirm that the pimer-like form is not responsible for the NIR absorption, a solid-state absorption spectrum was recorded using a single crystal of 1^•+I₃⁻, which showed an NIR absorption in the same region as that in solution (Fig. 4f,g). Thus, the NIR absorption for 1^•+I₃⁻ can be attributed to the σ–σ* transition of the weak C•C one-electron bond.
为了从光化学角度研究该化合物的性质，我们记录了 1 ^•+ I ₃ ⁻ 在 CH ₂ Cl ₂ 中的紫外/可见/近红外（UV/Vis/NIR）光谱。在约 2,000 nm 处（λ _max ≃ 1,405 nm）观察到一个 NIR 吸收带（图 4d,e），这无法用歧化反应（2 × 1 ^•+ ⇄ 1 + 1 ²⁺ ）解释，因为 1 和 1 ²⁺ 均不显示此类 NIR 吸收（图 4h,i 及补充图 15）。在溶液中，1 ^•+ 可能存在于σ键合形式与 DFT 计算预测的类聚合物形式之间的平衡中（详见补充信息）。为确认类聚合物形式并非 NIR 吸收的原因，我们使用 1 ^•+ I ₃ ⁻ 的单晶记录了固态吸收光谱，结果显示其 NIR 吸收与溶液中相同区域（图 4f,g）。因此，1 ^•+ I ₃ ⁻ 的 NIR 吸收可归因于弱 C•C 单电子键的σ–σ*跃迁。

General information 基本信息

All commercially available compounds were used without further purification unless otherwise indicated. Acetonitrile was dried before use by distillation from CaH₂. Column chromatography was performed on silica gel (Wakogel 60N; neutral; particle size: 38–100 μm). ¹H and ¹³C NMR spectra were recorded on a BRUKER AscendTM 400 (¹H/400 MHz and ¹³C/100 MHz) spectrometer. Mass spectra were recorded on a JEOL JMS-T100GCV spectrometer in FD mode (GC-MS&NMR Laboratory, Research Faculty of Agriculture, Hokkaido University). Melting points were measured on a Stanford Research Systems MPA100 Optimelt for powder samples and on a YANACO MP-J3 for single crystals; all values are uncorrected. The Raman spectroscopy using a 785 nm laser was carried out on a RENISHAW inVia Reflex at the OPEN FACILITY, Hokkaido University Sousei Hall. Infrared (IR) spectra were measured on a Shimadzu IRAffinity-1S spectrophotometer (attenuated total reflection (ATR) mode) for powder samples and on a JASCO IRT-5200FT/IR-6600 spectrophotometer for single crystals (Transmission Mode). X-band CW-EPR measurements were conducted using a Bruker BioSpin EMX Plus. Solid-state UV/Vis/NIR spectra were measured on a microscopic spectrometer (MSV 5200, JASCO; Transmission Mode), while solution-state UV/Vis/NIR spectra were recorded on a JASCO V-770 spectrophotometer.
除非另有说明，所有市售化合物均未经进一步纯化直接使用。使用前，乙腈通过从 CaH ₂ 蒸馏进行干燥。柱层析在硅胶（Wakogel 60N；中性；粒径：38–100 μm）上进行。 ¹ H 和 ¹³ C NMR 谱图由 BRUKER AscendTM 400（ ¹ H/400 MHz 和 ¹³ C/100 MHz）光谱仪记录。质谱在 JEOL JMS-T100GCV 光谱仪上以 FD 模式记录（GC-MS&NMR 实验室，北海道大学农学研究科）。熔点测定采用 Stanford Research Systems MPA100 Optimelt 对粉末样品进行，单晶样品则使用 YANACO MP-J3；所有数值均未经校正。拉曼光谱使用 785 nm 激光在 RENISHAW inVia Reflex 上进行，地点为北海道大学创成馆开放设施。红外（IR）光谱对粉末样品在 Shimadzu IRAffinity-1S 分光光度计（衰减全反射（ATR）模式）上测量，单晶样品则在 JASCO IRT-5200FT/IR-6600 分光光度计（透射模式）上进行。X 波段连续波电子顺磁共振（CW-EPR）测量使用 Bruker BioSpin EMX Plus 进行。 固态紫外/可见/近红外光谱使用显微光谱仪（MSV 5200，JASCO；透射模式）进行测量，而溶液态紫外/可见/近红外光谱则通过 JASCO V-770 分光光度计记录。

DFT calculations were performed using the Gaussian 16W⁴⁴ program package. Parts of the DFT calculations for 1^•+ were performed with the atomic coordinates obtained from the X-ray diffraction analysis of sample 1 of 1^•+I₃⁻ at 100 K. Multiwfn software⁴⁵ (v.3.8) was used for localized molecular orbital (Foster–Boys method) and topological analysis (quantum theory of atom in molecules and electron localized functions) of the electron density that was obtained from the DFT calculations. The NBO analyses were performed using v.3.1 of the NBO⁴⁶ function in the Gaussian 16W program package.
使用 Gaussian 16W ⁴⁴ 程序包进行了 DFT 计算。部分针对 1 ^•+ 的 DFT 计算采用了从 1 ^•+ I ₃ ⁻ 样品 1 在 100 K 下 X 射线衍射分析获得的原子坐标。利用 Multiwfn 软件 ⁴⁵ （v.3.8）对从 DFT 计算中获得的电子密度进行了局域分子轨道（Foster-Boys 方法）和拓扑分析（分子中原子的量子理论及电子局域函数）。NBO 分析则通过 Gaussian 16W 程序包中的 NBO ⁴⁶ 功能 v.3.1 版本完成。

A suitable crystal was selected and used for the measurement on a Rigaku XtaLAB Synergy (Cu-Kα radiation, λ = 1.54184 Å) with HyPix diffractometer. Using Olex2 (ref. ⁴⁷), the structure was solved with the SHELXT⁴⁸ structure solution program using Intrinsic Phasing and refined with the SHELXL⁴⁹ refinement package using least squares minimization.
选择了一颗合适的晶体，用于在 Rigaku XtaLAB Synergy（Cu-Kα辐射，λ = 1.54184 Å）上配备 HyPix 衍射仪进行测量。利用 Olex2（参考文献 ⁴⁷ ），结构通过 SHELXT ⁴⁸ 结构解析程序采用本征相位法求解，并使用 SHELXL ⁴⁹ 精修包通过最小二乘法最小化进行精修。

Starting material 起始材料

HPE 1 was prepared according to literature procedures⁵.
HPE 1 按照文献程序制备 ⁵ 。

Synthesis of radical cation salt 1^•+I₃ ^–
自由基阳离子盐 1 的合成

1 (4.74 mg, 8.93 μmol) was added to a solution of iodine (1.70 mg, 13.4 μmol) in dry CH₂Cl₂ (5 ml) at 26 °C. After stirring at 26 °C for 1 h, the resulting suspension was dried under reduced pressure to give a dark brown solid (6.4 mg). Mp: 157–163 °C (decomp.); ¹H NMR (CD₃CN): silent; IR (ATR): ν cm⁻¹ 3,046; 3,023; 1,607; 1,485; 1,465; 1,418; 1,310; 1,229; 1,164; 1,130; 1,111; 1077; 1,043; 952; 877; 863; 841; 825; 795; 767; 739; 723; 686; 672; 646; 627; 608; 587; 517; 485; 470; 430; 422; 420; LR-MS (FD) m/z (%): 532.26 (12), 531.26 (46), 530.25 (M⁺, bp); HR-MS (FD) calculated for C₄₂H₂₆: 530.20345; Found: 530.20552.
将 1 (4.74 mg, 8.93 μmol) 加入到碘 (1.70 mg, 13.4 μmol) 的干燥 CH ₂ Cl ₂ (5 ml) 溶液中，温度为 26 °C。在 26 °C 下搅拌 1 小时后，所得悬浮液在减压下干燥，得到深棕色固体 (6.4 mg)。熔点：157–163 °C (分解)； ¹ H NMR (CD ₃ CN): 无信号；IR (ATR): ν cm ⁻¹ 3,046; 3,023; 1,607; 1,485; 1,465; 1,418; 1,310; 1,229; 1,164; 1,130; 1,111; 1077; 1,043; 952; 877; 863; 841; 825; 795; 767; 739; 723; 686; 672; 646; 627; 608; 587; 517; 485; 470; 430; 422; 420; LR-MS (FD) m/z (%): 532.26 (12), 531.26 (46), 530.25 (M ⁺ , bp)；HR-MS (FD) 计算值为 C ₄₂ H ₂₆ : 530.20345；实测值：530.20552。

Recrystallization of the obtained material from dry acetonitrile/dry tetrahydrofuran/dry diethyl ether gave dark violet crystals of 1^•+I₃⁻ (at least 0.06 mg, more than 1%), which were picked up with a needle and characterized by X-ray crystallography. The isolated yield was calculated based on the separated crystals from the as-prepared crystals, which might also contain 1, 1^•+I₅^– (determined by preliminary X-ray analysis), and other forms of cationic species. Mp: 191–196 °C (decomp.); IR (a single crystal, transmission mode): ν cm⁻¹ 3,094; 3,045; 2,979; 2,925; 1,955; 1,929; 1,907; 1,819; 1,614; 1,587; 1,530; 1,455; 1,436; 1,345; 1,260; 1,207; 1,166; 1,149; 1,124; 1,084; 1,047; 947; 859; 839; 809; 777; 752; 725; 670; 611.
将所得材料从干燥的乙腈/干燥的四氢呋喃/干燥的乙醚中重结晶，得到深紫色的 1 ^•+ I ₃ ⁻ 晶体（至少 0.06 mg，超过 1%），用针尖挑取并进行 X 射线晶体学表征。分离产率根据从制备的晶体中分离出的晶体计算，这些晶体可能还含有 1, 1 ^•+ I ₅ ^– （通过初步 X 射线分析确定），以及其他阳离子形式。熔点：191–196 °C（分解）；红外光谱（单晶，透射模式）：ν cm ⁻¹ 3,094；3,045；2,979；2,925；1,955；1,929；1,907；1,819；1,614；1,587；1,530；1,455；1,436；1,345；1,260；1,207；1,166；1,149；1,124；1,084；1,047；947；859；839；809；777；752；725；670；611。

Synthesis of dication salt 1²⁺(I₃ ⁻)₂
二阳离子盐 1 ²⁺ （I ₃ ⁻ ） ₂ 的合成

1 (3.00 mg, 5.65 μmol) was added to a solution of iodine (2.15 mg, 16.9 μmol) in dry CH₂Cl₂ (5 ml) at 26 °C. After stirring at 26 °C for 1 h, the resulting suspension was dried under reduced pressure to give a dark violet solid (5.1 mg). Mp: 177–182 °C (decomp.); ¹H NMR (CD₃CN): silent (given that the reduction potential of iodine was not sufficient to oxidize radical cation 1^•+ completely, the silent NMR spectrum was attributed to a partial contribution of radical cation 1^•+.); IR (ATR): ν cm⁻¹ 3,042; 1,606; 1,529; 1,513; 1,476; 1,430; 1,419; 1,342; 1,318; 1,229; 1,189; 1,163; 1,128; 1,115; 1,088; 1,040; 990; 952; 941; 874; 859; 840; 811; 796; 774; 768; 751; 721; 711; 693; 676; 657; 627; 610; 551; 517; 469; LR-MS (FD) m/z (%): 532.18 (13), 531.18 (47), 530.17 (M⁺, bp); HR-MS (FD) calculated for C₄₂H₂₆: 530.20345; Found: 530.20499.
将 1 (3.00 mg, 5.65 μmol) 加入到碘 (2.15 mg, 16.9 μmol) 的干燥 CH ₂ Cl ₂ (5 ml) 溶液中，温度为 26 °C。在 26 °C 下搅拌 1 小时后，所得悬浮液在减压下干燥，得到深紫色固体 (5.1 mg)。熔点：177–182 °C（分解）； ¹ H NMR (CD ₃ CN)：无信号（鉴于碘的还原电位不足以完全氧化自由基阳离子 1 ^•+ ，NMR 谱的无信号归因于自由基阳离子 1 ^•+ 的部分贡献）；IR (ATR)：ν cm ⁻¹ 3,042；1,606；1,529；1,513；1,476；1,430；1,419；1,342；1,318；1,229；1,189；1,163；1,128；1,115；1,088；1,040；990；952；941；874；859；840；811；796；774；768；751；721；711；693；676；657；627；610；551；517；469；LR-MS (FD) m/z (%): 532.18 (13), 531.18 (47), 530.17 (M ⁺ , bp)；HR-MS (FD) 计算值为 C ₄₂ H ₂₆ : 530.20345；实测值：530.20499。

Recrystallization of the obtained material from dry CH₂Cl₂/dry diethyl ether gave dark violet crystals of 1²⁺(I₃⁻)₂ (at least 0.10 mg, more than 2%), which were picked up with a needle and characterized by X-ray crystallography. The isolation yield was calculated based on the separated single crystals from the as-prepared crystals, which might contain 1^•+I₅⁻ (determined by preliminary X-ray analysis) or other cationic species.
将所得材料从干燥的 CH ₂ Cl ₂ /干燥的乙醚中重结晶，得到深紫色的 1 ²⁺ (I ₃ ⁻ ) ₂ 晶体（至少 0.10 mg，超过 2%），用针尖挑取并经 X 射线晶体学表征。分离产率根据从制备的晶体中分离出的单晶计算，这些晶体可能含有 1 ^•+ I ₅ ⁻ （通过初步 X 射线分析确定）或其他阳离子物种。

Mp: 147–153 °C (decomp.); IR (a single crystal, transmission): ν cm⁻¹ 3,187; 3,078; 3,038; 2,928; 2,855; 1,907; 1,724; 1,646; 1,605; 1,514; 1,471; 1,440; 1,386; 1,358; 1,327; 1,256; 1,198; 1,121; 1,096; 991; 976; 941; 890; 866; 841; 793; 727; 661; 638.
熔点：147–153 °C（分解）；红外光谱（单晶，透射）：ν cm ⁻¹ 3,187；3,078；3,038；2,928；2,855；1,907；1,724；1,646；1,605；1,514；1,471；1,440；1,386；1,358；1,327；1,256；1,198；1,121；1,096；991；976；941；890；866；841；793；727；661；638。