A flat carborane with multiple aromaticity beyond Wade–Mingos’ rules

It is widely known that the skeletal structure of clusters reflects the number of skeletal bonding electron pairs involved, which is called the polyhedral skeletal electron pair theory (PSEPT) or Wade and Mingos rules. While recent computational studies propose that the increase of skeletal electrons of polyhedral clusters leads to the flat structure beyond the PSEPT, little experimental evidence has been demonstrated. Herein, we report the synthesis of a C2B4R4 carborane 2 featuring a flat ribbon-like structure. The C2B4 core of 2 bearing 16 skeletal electrons in the singlet-ground state defies both the [4n + 2] Hückel’s rule and Baird’s rule. Nevertheless, the delocalization of those electrons simultaneously induces two independent π- and two independent σ-aromatic ring currents, rendering quadruple aromaticity. The polyhedral skeletal electron pair theory (PESPT), also known as Wade-Mingos’ rules, defines a relationship between skeletal bonding electron pairs and structure of clusters. Here the authors report the synthesis, structure and computational studies of planar C2B4R4 carboranes that do not adhere to PESPT.

T he concept of aromaticity has been of paramount importance in myriad research fields of chemistry since the discovery in 1865 that the benzene molecule is cyclic 1 . Monocyclic conjugated hydrocarbons, namely annulenes, following the [4n + 2] Hückel's rule exhibit aromatic nature, whereas (singlet) annulenes featuring the 4n π electrons system are found to be antiaromatic [2][3][4] . Significantly, this concept is predicted to be reversed in the lowest triplet state on the basis of Baird's rule 5,6 . Thus, π-conjugated molecules with 4n π electrons in the triplet state may exhibit aromatic character 7,8 . Recently, the group of Wang and Boldyrev reported that despite the singlet ground state, the B 19 − cluster with 12 π electrons exhibits aromaticity 9 . This can be rationalized by the fact that the B 19 − cluster possesses two concentric π-aromatic networks, involving a 10 π-electron system and a 2 π-electron system, both of which satisfy the [4n + 2] Hückel's rule, independently. This study indicates that even π-conjugated molecules with 4n π electrons in the singlet state may be aromatic if the 4n π electrons are split into several [4n + 2] π-electron systems with delocalization. It is believed, however, that such a peculiar chemical bonding situation can only be found in atomic clusters.
The discovery of molecules of type C 2 B 4 H 6 RR' (R, R' = H, Me, C 3 H 7 ) by Onak, Williams and Weiss in 1962, is considered to be the beginning of the chemistry of carboranes, a class of boron clusters with the general formula of [(CH) a (BH) m H b ] c , mostly having polyhedral structures 10 . It has been recognized over the past several decades that the chemistry of carboranes can be ubiquitously applied to various research fields, ranging from medicinal chemistry, through catalysis, to materials science 11 . Particularly diagnostic of carboranes is the delocalization of the skeletal electrons through multi-center two-electron bonds, rendering the three-dimensional aromatic at the cage moiety [12][13][14][15] . The cage framework of carborane clusters can be rationalized by the polyhedral skeletal electron pair theory (PSEPT), also known as Wade-Mingos' rules, which provides the relationship with the skeletal bonding electron pairs (SEPs) [16][17][18] . The n-vertex carboranes with n, (n + 1), (n + 2) and (n + 3) SEPs prefer to adopt hypercloso-, closo-, nido-and arachno-structures, respectively. Afterward, the mno rules, as an extension of the PSEPT, have been reported to predict the structures of condensed polyhedral clusters with a shared triangle face, edge or single vertex 19 . Meanwhile, advanced computational studies propose that the increase of skeletal electrons of polyhedral clusters by reducing the number of substituents leads to considerable electron occupancy in the antibonding skeletal orbitals, which gives rise to flat structures beyond the PSEPT 20 . In this context, the group of Frenking and Hoffmann reported the theoretical studies on a C 2 B 4 H 4 cluster, and concluded that the favored structure is the hypercloso octahedron I involving two capped carbon atoms (Fig. 1a) 21 . By contrast, Ding and coworkers proposed that the global minima of the C 2 B 4 H 4 cluster is a ribbon-like isomer II, which lies 16.0 kcal mol −1 lower in energy than I 22 . Interestingly, II-despite bearing only two π-orbitals, thus a 4n π system-is predicted to be aromatic. Notwithstanding the fundamental significance of both PSEPT and aromaticity, however, an experimental proof regarding the nature of the C 2 B 4 H 4 cluster has never to our knowledge been reported, mainly because of the synthetic challenges of small carborane clusters (n vertex ≤ 12) bearing fewer substituents than their vertices 23 .
Herein, we report the synthesis, single-crystal X-ray diffraction, and computational studies of a flat C 2 B 4 R 4 carborane 2, the latter of which suggest simultaneous electronic delocalization in both πand σ-orbitals of the C 2 B 4 scaffold. In addition, a 6-vertex, 7-SEP carborane 3, which displays an unusual spiral triangle-strip geometry, is also structurally characterized; both compounds thus defy the PSEPT-based structural prediction.

Results
Synthesis and structural elucidation of flat carborane 2. Treatment of tetraatomic boron(0) species 1 24 with two equivalents of 2,6-diisopropylphenyl isonitrile (DipNC) in benzene at ambient temperature yielded a brown solution, and after workup compound 2 was gained as orange crystals in 23% yield (Fig. 2a). The 11 B NMR spectrum of 2 exhibits two characteristic broad singlets at 16.5 ppm and 11.3 ppm, which are in line with the computationally estimated 11 B NMR chemical shifts (the central non-substituted boron: 14.4 ppm, the substituted boron: 9.8 ppm, respectively). The corresponding 1 H NMR spectrum shows two downfield singlets at δ = 5.7 ppm (CH BNC3-ring ) and δ = 3.2 ppm (NH), indicative of the hydrogen migration from the BNC 3 five-membered ring of 1 to the nitrogen atom of isonitrile during the reaction.
An X-ray diffraction analysis revealed that 2 adopts a C 2 symmetry with the central B 4 C 2 moiety assuming the twodimensional ribbon-like structure (Fig. 1b). Two BNC 3 fivemembered ring substituents bounded to the B2 (B2') atoms are in trans fashion, which are slightly twisted with respect to the central  26,29 . 2 represents a rare example of a molecule involving planar tetracoordinate boron centers [30][31][32] . Taking these metrics into account, it can be envisaged that the skeletal electrons are delocalized within the C 2 B 4 core. It is salient to highlight that compound 2 with the 6-vertex and 8-SEP system does not show a nido cage structure predicted by the Wade-Mingos' rules but instead adopts a planar geometry 20,22 .
Theoretical studies of 2. The electronic structure of 2 was further examined by DFT calculations using the optimized structure of the slightly modified model compound opt-2'. The singlet ground state is found to be thermodynamically more stable by 26.7 kcal mol −1 than the triplet ground state opt-2'T, which shows the distorted C 2 B 4 plane. The two most characteristic molecular orbitals are illustrated in Fig. 3a. The highest occupied molecular orbital (HOMO) of opt-2' mainly corresponds to the π-type orbitals over the C1B1B2 (C1'B1'B2') three-membered rings, which exhibits anti-bonding relationship with the C2-C3 (C2'-C3') π-orbitals and the lone pairs of nitrogen atoms. The HOMO−3 comprises the π-type orbitals of the central B 4 moiety with contribution from the 2,6-diisopropyl phenyl rings. The B-C and B-B bonding interactions within the σ-frameworks of the C 2 B 4 core are well found in the MOs (Supplementary Fig. 13). The 4-electron π-system and 12-electron σ-system indicate that the skeletal electrons are delocalized in both πand σ-frameworks of the C 2 B 4 core 22 . The respective Wiberg bond index (WBI) values of 1.3091 for B1-C1 (B1'-C1') and 1.1069 for B2-C1 (B2'-C1') are in line with their bond distances. Interestingly, despite the short B1-B1' distance (1.601(4) Å), a relatively small WBI value of 0.8041 is found for B1-B1', indicating the weak covalent bond character. Thus, the observed short B1-B1' distance is likely due to the strained ribbon-like structure rather than the strong π/σ-bonding interaction.
To assess the delocalization of electrons within the C 2 B 4 core of 2, the nucleus-independent chemical shifts (NICS) calculation was performed on opt-2' and the relevant compounds III-V for comparison ( Fig. 3b) 33 . The calculated NICS(1) values of the BBB and CBB rings in opt-2' (−8.80 ppm and −11.76 ppm) are less negative compared with those (III: −14.13 ppm, IV: −16.14 ppm, V: −15.34 ppm) of 2π-aromatic molecules III-V, indicating that the π-aromatic nature of 2, in particular at the BBB rings, is relatively weak (Tables 1 and 2). This can be rationalized by the fact that there are only 4π electrons formally spreading over the C 2 B 4 plane (Fig. 3a). By contrast, the corresponding NICS  could be attributed to the substituent effect ( Supplementary  Fig. 14, Supplementary Table 14) 34 (Table 3). It is noteworthy that both the π-system with four electrons and σ-system with 12 electrons are usually considered as antiaromatic.
The property of electron delocalization was further evaluated by the anisotropy of the current-induced density (ACID) analysis using another structurally simplified model compound C 2 B 4 H 2 (NH 2 ) 2 opt-2" 35 . The clockwise current density vectors were plotted on the π-component of ACID isosurface at the two CBB rings (Fig. 3c), which confirms the distinct ring current over the CBB rings, and suggests the presence of the two local aromaticity of the 2π CBB three-membered rings (Fig. 3d, left), each of which satisfies the [4n + 2] electron Hückel's rule independently. This observation agrees with the more negative NICS(1) values of the CBB rings than those of BBB rings (Tables 1 and 2). Indeed, Natural Bond Orbital (NBO) analysis confirms the three-center two-electron (3c-2e) π-bonding over the two CBB rings (Supplementary Tables 15 and 16). We also performed bonding analysis using the adaptive natural density partitioning (AdNDP) method (Fig. 3e), which presents two 3c-2e π-bonding over the two CBB rings 36 . In the σ framework, all C-B bonds are found to be 2c-2e peripheral bonds (Fig. 3d, middle), whereas the delocalized 3c-2e bonding character is seen at the two BBB three-membered rings, each of which-fulfilling the Hückel's rule with n = 0-could be responsible for the local σ-aromaticity (Fig. 3d, right). Collectively, the experimental structural analysis and theoretical calculation results suggest that the C 2 B 4 moiety of 2, albeit the globally antiaromatic species in general, features two πand two σ-aromatic distinct frameworks, manifesting the multiple local aromaticity 32,[37][38][39][40][41] . It is most likely that the presence of consecutive 3c-2e π and 3c-2e σ bonding plays a pivotal role in the stabilization of the flat ribbonlike geometry [42][43][44][45] .
Synthesis and structural analysis of spiral carborane 3. Interestingly, when compound 1 was reacted with four equivalents of tert-Butyl isonitrile ( t BuNC) in benzene at ambient temperature, a deltahedron carborane derivative 3 was obtained in 26% isolated yield (Fig. 2a). The 11 B NMR spectrum of 3 shows broad singlets at δ = −12.2 ppm for B-C≡N and at δ = 12.2 ppm for BBNC3-ring, respectively. Orange single crystals of 3 were obtained by recrystallization from a saturated toluene solution, and the solid-state structure determined by X-ray diffraction analysis shows that 3 with the 7-SEP system features a spiral triangle-strip structure (Fig. 2c), rather than octahedron predicted for the 6-vertex and 7-SEP closo-carboranes according to Wade-Mingos' rules. The solid-state structure of 3 also differs from trigonal bipyramidal and butterfly shapes corresponding to the global minima of the substituted dicarboranes (C 2 B 4 R 6 ) 46 25,26 . The observed structural change from 2 to 3 confirms that the removal of two electrons from the C 2 B 4 skeleton may decrease the electron delocalization and therefore the stability of the flat core, which leads to distortion from the planar ribbon-like geometry, consistent with Jemmis' prediction 20 . We have also investigated the reaction of 1 and CO, which however gave a complex mixture and no identifiable product was obtained from the mixture.

Discussion
Almost five decades after the establishment of the polyhedral skeletal electron pair theory, this work shows that a flat carborane featuring a ribbon-like architecture 2 based on the 6-vertex and 8-SEP system can be isolated. Theoretical studies manifest the delocalization of the skeletal electrons in both πand σ-orbitals of the C 2 B 4 core in 2, inducing the simultaneous πand σ-ring currents. The synthesis of a relevant carborane 3 with 6 vertices and 7 SEPs is also feasible, which is found to exhibit a spiral triangle-strip geometry. Both compounds 2 and 3 represent the first C 2 B 4 carboranes disobeying the structural prediction by PSEPT, which may contribute to extending Wade-Mingos' rules and rationalizing the electronic structure of other E n R x (n ≥ x) carborane isomers.

Methods
Materials. For details of spectroscopic analyses of compounds in this paper, see General synthetic procedure. All reactions were performed under an atmosphere of dry nitrogen or argon by using standard Schlenk or dry box techniques; solvents were dried over Na metal, K metal or CaH 2 . 1 H, 11 B and 13 C NMR spectra were obtained with Bruker AVIII 400 MHz BBFO and JEOL ECA400 spectrometer at 298 K unless otherwise stated. NMR multiplicities are abbreviated as follows: s = singlet, d = doublet, t = triplet, sep = septet, m = multiplet, br = broad signal. Coupling constants J are given in Hz. HRMS spectra were obtained at the Mass Spectrometry Laboratory at the Division of Chemistry and Biological Chemistry, Nanyang Technological University. Melting point was measured with an OpticMelt Stanford Research System. Fourier transform infrared (FT-IR) spectra were recorded on a Bruker ALPHA-Transmittance FT-IR Spectrometer. Cyclic voltammetry (CV) was performed on a Biologic SP-50 electrochemical analyzer in anhydrous THF containing recrystallized tetra-n-butyl-ammoniumhexafluorophosphate (TBAPF 6 , 0.1 M) as supporting electrolyte at 298 K under an inert atmosphere of argon. A conventional three electrode cell was used with a glassy carbon electrode as the auxiliary electrode, silver/silver nitrate as the reference electrode, and a platinum wire as the working electrode. Compound 1 was synthesized according to the literature method 24 .
Synthesis of compound 2. At ambient temperature, benzene-d 6 (2 ml) was added to 1 (0.20 g, 0.20 mmol) to give a red solution, followed by 2 equivalents of 2,6diisopropyl isonitrile (0.075 g, 0.40 mmol). The reaction mixture was stirred at room temperature for 24 h to give a brown solution. After completion of the reaction, all volatiles were removed under reduced pressure to afford a brown mixture. Slow evaporation of a pentane solution of this mixture in glove box yielded 2 as orange crystals (0.056 g, 23%).  Synthesis of compound 3. At ambient temperature, benzene-d 6 (2 ml) was added to 1 (0.10 g, 0.10 mmol) to give a red mixture, followed by 4 equivalents of tertbutyl isonitrile (0.033 g, 0.40 mmol). The reaction mixture was stirred at room temperature for 24 h to give a brown solution. After completion of the reaction, all volatiles were removed under reduced pressure to afford a brown mixture. Slow evaporation of a toluene solution of the mixture in glove box afforded 3 as orange crystals (0.032 g, 26%). M.p.: 223°C (Dec.); 1 H NMR (400 MHz, C 6 D 6 , 25°C)