Flattened 1D fragments of fullerene C60 that exhibit robustness toward multi-electron reduction

Fullerenes are compelling molecular materials owing to their exceptional robustness toward multi-electron reduction. Although scientists have attempted to address this feature by synthesizing various fragment molecules, the origin of this electron affinity remains unclear. Several structural factors have been suggested, including high symmetry, pyramidalized carbon atoms, and five-membered ring substructures. To elucidate the role of the five-membered ring substructures without the influence of high symmetry and pyramidalized carbon atoms, we herein report the synthesis and electron-accepting properties of oligo(biindenylidene)s, a flattened one-dimensional fragment of fullerene C60. Electrochemical studies corroborated that oligo(biindenylidene)s can accept electrons up to equal to the number of five-membered rings in their main chains. Moreover, ultraviolet/visible/near-infrared absorption spectroscopy revealed that oligo(biindenylidene)s exhibit enhanced absorption covering the entire visible region relative to C60. These results highlight the significance of the pentagonal substructure for attaining stability toward multi-electron reduction and provide a strategy for the molecular design of electron-accepting π-conjugated hydrocarbons even without electron-withdrawing groups.

. In addition to the attractive spherical structure with high symmetry, their electron-accepting characteristic is notable among π-conjugated materials. Fullerenes have exceptional stability toward multi-electron reduction, unlike other electron-accepting π-conjugated systems 2, 3 . For example, C 60 reportedly undergoes 6-electron and 12-electron reductions in solution 2 and the solid state, respectively 3 . This robustness toward multi-electron reduction enables access to various alkaline metal salts, among which Cs 3 C 60 exhibits superconductivity with the transition temperature (T c ) of 38 K, which is the highest value among all the molecular materials 4-6 . Moreover, their moderately low-lying lowest unoccupied molecular orbital (LUMO) [7][8][9] and high electron mobility 10,11 have rendered them a central role as electron-transporting materials 12 . It is worth noting that this high electron affinity is realized based on the carbon-only framework. This is unlike the molecular design of most electron-accepting organic materials, which relies on introducing electron-withdrawing atoms or groups, such as fluorine [13][14][15] , chlorine 14 , cyano [16][17][18] , carbonyl [17][18][19] , and imine moieties 17,19 , into π-conjugated systems.
Hence, the minimum structural basis for the high electron affinity and exceptional stability toward the multi-electron reduction of fullerenes are of interest. Several structural factors have been proposed, including the degeneracy of LUMO and LUMO + 1 due to the highly symmetrical structure (Fig. 1a), the mitigation of bond angle strain around the carbon atoms upon reduction due to the inherently pyramidalized geometry (Fig. 1b), and the presence of fivemembered ring substructures that can acquire Hückel aromaticity in a reduced state ( Fig. 1c) 8,20,21 . Although π-conjugated hydrocarbons with fragment structures of fullerenes can be promising for understanding the effect of each factor, most fullerene fragment molecules reported to date, such as corannulene 22,23 , sumanene 24 , and larger molecules [25][26][27][28][29][30] , have bowl-shaped structures in which most of the carbon atoms adopt pyramidalized geometries ( Supplementary  Fig. 1). This fact indicates that the curved structure of the fullerenes is of significant interest. Although Brunetti and coworkers reported πextended 9,9′-bifluorenylidene derivatives composed of a C 60 substructure without having pyramidalized carbon atoms 31 , their highly twisted structures impede the effective extension of the π-conjugation, limiting the contribution of five-membered rings. A fragment molecule of C 60 with effective π-conjugation between the fivemembered ring substructures without pyramidalized carbon atoms is necessary to clarify the role of five-membered rings on the high electron affinity and robustness toward multi-electron reduction of fullerenes.
Therefore, to elucidate the role of the five-membered ring substructures in the exceptional electron affinity of fullerenes without the influence of high symmetry and pyramidalized geometries of carbon atoms, we conceived a molecular design of π-conjugated oligomers 3 and 4 composed of a one-dimensional fragment of C 60 in their main chains ( Fig. 1e) based on the following idea. First, we focused on the hoop-shaped substructure of C 60 wherein 6 five-membered rings were linearly connected, that is, cyclic ter(1,1′-biindenylidene) 1 (Fig. 1d). Next, based on the similarity of the π-conjugated hoops and corresponding linear π-conjugated polymers, excluding their symmetry and structural distortion 32,33 , we designed linear π-conjugated polymer 2 with an identical repeating unit to eliminate the pyramidalization effect. We also anticipated that it could be an excellent platform for demonstrating the effect of five-membered rings on the stability toward the multi-electron reduction as the number of five-membered rings per molecule can be increased by elongating the chain length. Poly(pentafulvalene)s, including 2, have previously been studied as candidate structures for narrow-or zero-bandgap polymers by quantum chemical calculations [34][35][36][37] , although their electron-accepting characteristics have not yet been discussed. Moreover, the synthesis of π-conjugated oligomers or polymers of pentafulvalenes has not yet been reported. In this study, to clarify the molecular structures and chain-length dependence of the properties, we designed 3 and 4, wherein both ends of the one-dimensional C 60 fragment 2 were endcapped with phenyl and 4-silylphenyl groups, respectively (Fig. 1e). a high symmetry that results in the triply degenerated LUMO and LUMO + 1, b pyramidalized carbon atoms that mitigate bond angle strain around the carbon atoms upon reduction, and c five-membered ring substructures that can acquire aromatic character in a reduced state. d Our molecular design of π-conjugated polymer 2 based on the hoop-shaped substructure 1 of C 60 . e End-capped oligo(biindenylidene)s 3 and 4 examined in this study.
Herein, we report the syntheses and properties of 3 and 4 up to n = 3. X-ray crystallographic analyses showed that the C 60 fragment structures in 3 and 4 were unaffected by the pyramidalization of carbon atoms. Electrochemical and photophysical studies revealed the role of five-membered rings in the exceptional electron-accepting characteristic of C 60 without electron-withdrawing groups. Moreover, comparison of the electronic structures of 3 and 4 with those of C 60 revealed the characteristics of oligo(biindenylidene)s, reflecting onedimensional π-conjugation between the five-membered rings.
The molecular structures of oligo(biindenylidene)s 3a-c and 4a-c obtained were verified by nuclear magnetic resonance (NMR) spectroscopy and mass spectrometry, and those of the monomers (3a and 4a) and dimers (3b and 4b) were confirmed by single-crystal X-ray diffraction analyses ( Fig. 3 and Supplementary Fig. 3, vide infra).
Notably, 3a-c and 4a-c were stable under ambient conditions and could be handled without any precautions. Furthermore, a series of oligo(biindenylidene)s exhibited moderate solubility in common organic solvents. For example, the solubilities of 3b and 3c in CH 2 Cl 2 were 5 and 2 g L -1 , respectively, which are one order of magnitude higher than that of C 60 (0.26 g L -1 ) 40 .
Single-crystal X-ray diffraction analyses of 3b and 4b revealed one-dimensional π-conjugated frameworks wherein the biindenylidene units were directly bonded with the same connectivity as those in C 60 (Fig. 3a, b). Each biindenylidene unit had an E configuration, and all the adjacent units adopted s-trans conformation. The C-C bond lengths in the biindenylidene units of 3b and 4b were comparable to those of the corresponding 3a and 4a without any noticeable dimerization effect (Supplementary Table 2). Although their π-conjugated frameworks deviated from coplanarity, the conformation differed depending on the terminal substituents. In particular, the biindenylidene skeletons in phenyl-capped 3b and trialkylsilylphenyl-capped 4b   were slightly twisted to comparable extents, with intra-unit torsion angles (C2-C1-C10-C11) of 160.6°and -166.4°, respectively, because of the steric repulsion between peripheral hydrogen atoms. Conversely, the inter-unit torsion angles (C11-C12-C12*-C11*) were 180°a nd 152.8°for 3b and 4b, respectively, reflecting conformational flexibility around the freely rotatable C-C bonds (Fig. 3c, d). Consequently, the π-conjugated chains of 3b and 4b exhibited substantially different S-shaped conformations with a C i symmetry center and an arch-like shape with a C 2 symmetry axis, respectively. Accordingly, 3b and 4b adopted different packing motifs of the offset π-stacked arrays ( Fig. 3c) and one-dimensional π-stacked columns ( Fig. 3d), respectively. Reflecting the difference in packing motifs, the shortest interatomic C···C distance between stacked molecules in 3b of 3.372 Å was significantly smaller than that in arched-shape 4b (3.654 Å), indicative of more effective intermolecular interaction of π-orbitals.
Despite the marked difference in the conformation and the packing motifs, the torsional angles in 3b and 4b were sufficiently small for extending π-conjugation over the main chains. Despite these conformational differences, all carbon atoms in the biindenylidene skeletons of 3b and 4b maintained a planar geometry without pyramidalization. More specifically, the π-orbital axis vector (POAV) analysis 41 for the crystal structures of 3b and 4b revealed that the averaged values of the σ-π interorbital angle (θ σπ ) for the carbon atoms that consist of five-membered rings were 90.7(6)°and 91.0(5)°, respectively (Supplementary Tables 4 and 6). These values are markedly smaller than those of C 60 (101.6°) and corannulene (98.2°), and comparable to that of the ideal sp 2 carbon atom like in graphite (90.0°) 42 . These results demonstrate that oligo(biindenylidene)s are suitable for studying the effect of five-membered rings on the electron affinity of π-conjugated hydrocarbons without the influence of the pyramidalization of carbon atoms.

Electrochemical properties
To corroborate the dependence of the redox properties on the number of five-membered rings, the electrochemical properties of oligo(biindenylidene)s 3a-c and 4a-c were examined using cyclic voltammetry (Fig. 4a, Supplementary Figs. 5 and 6, and Supplementary Table 7). The cyclic voltammograms of trialkylsilylphenyl-capped 4a, 4b, and 4c in tetrahydrofuran (THF) showed two-, four-, and five-step reversible redox processes in the reductive region, respectively ( Fig. 4a), and irreversible redox processes in the oxidative region ( Supplementary Fig. 6). Considering that the first redox wave of 4c was characterized by two-electron redox processes based on peak current analyses (Supplementary Discussion 3), 4a, 4b, and 4c underwent two-, four-, and six-electron reductions, respectively, within the electrochemical window of THF. The phenyl-capped oligomers 3a-c also showed cyclic voltammograms essentially similar to those of 4a-c, except that 3c showed only four-step redox processes in the reductive region within the electrochemical window of THF ( Supplementary  Fig. 5). The absence of the fifth redox wave might be attributable to the low solubility of 3c in THF (0.23 g L -1 ), resulting in the fifth redox wave masked by the increase in baseline current due to the reduction of THF. Overall, these results demonstrate that oligo(biindenylidene)s can accept electrons up to equal to the number of five-membered rings in their main chains. Accordingly, the five-membered ring substructure ensures the prominent stability of the π-conjugated hydrocarbons toward multi-electron reduction, even without pyramidalized carbon atoms or electron-withdrawing substituents.
The number of five-membered rings also gave the significant impact on the electron affinity of oligo(biindenylidene)s. Similar to those of various π-conjugated oligomers, the half-wave potentials of the first redox processes in the reductive region (E 1/2,red1 ) of 4a-c shifted in the positive direction as the chain length increased (4a: -1.48 V, 4b: -1.19 V, and 4c: -1.09 V versus ferrocene/ferrocenium (Fc/ Fc + )), reflecting the decrease in the LUMO energy levels via the effective interaction between the π* orbitals of the biindenylidene moiety. Accordingly, the E 1/2,red1 value of 4c was close to that of C 60 (-0.89 V versus Fc/Fc + ), albeit slightly more negative. This result suggests that the oligo(biindenylidene) substructure of C 60 also plays a crucial role in its high electron affinity.
Oligo(biindenylidenes)s exhibit high electron affinity and stability toward multi-electron reduction close to fullerenes. However, electrochemical studies have also highlighted a feature of oligo(biindenylidene)s based on one-dimensional π-conjugated chains. Unlike C 60 that undergoes multi-electron reduction in a stepwise manner with almost constant peak separations, oligo(biindenylidene)s 4 showed distinct behavior depending on the chain length. In particular, the separation of the first and second reductive waves decreased from 0.31 V (4a) to 0.15 V (4b) as the chain length increased, and these two waves merged into a single two-electron peak at 4c. This peak separation decrease was in contrast with those of the subsequent reductive waves in 4b and 4c. The quantum chemical calculations of 4b′, a model compound of 4b wherein t-BuMe 2 Si groups were simplified to Me 3 Si groups to reduce the computational costs, demonstrated the localization of charge densities in the dianionic dimer ([4b′] 2-) on the indenylidene skeletons at both terminals (Fig. 4c). Moreover, the bond-length equalization as shown in Fig. 4b and Supplementary Fig. 11b as well as the negative values of the nuclearindependent chemical shifts (NICS, Supplementary Fig. 13) for the terminal indenylidene moieties in [4b′] 2strongly indicate the 10π Hückel aromaticity of the two indenyl anion moieties (Fig. 4d). Given these computational results, the localization of electron densities at both termini should be ascribed to the minimization of the electronic repulsion and the stabilization caused by the aromaticity of the two indenyl anion moieties. This charge separation in the dianion may be responsible for decreasing the peak separation of the first and second reduction waves as the chain length increases and reflects the structural feature of one-dimensional π-conjugated chains (see also Supplementary Discussion 5 for more detailed discussions including the results of radical anions [4b′] 2-).

Electronic absorption
The ultraviolet/visible/near-infrared absorption spectra of 3 and 4 in CH 2 Cl 2 were compared with that of C 60 , highlighting the characteristics of oligo(biindenylidene)s ( Fig. 5a and Supplementary Fig. 7). Similar to conventional π-conjugated oligomers, the increase in chain lengths of oligo(biindenylidene)s from 3a to 3c and from 4a to 4c resulted in a substantial redshift and an increase in the molar absorption coefficients (ε) of the longest-wavelength absorption bands. In particular, the longest-wavelength absorption band of phenyl-capped 3c with an absorption maximum wavelength (λ max ) of 653 nm was substantially red-shifted by 171 nm (5400 cm -1 ) compared to that of the corresponding 3a (λ max = 482 nm), and its ε value of 5.34 × 10 4 M -1 cm -1 also increased (3a: 1.32 × 10 4 M -1 cm -1 ). Notably, all oligo(biindenylidene)s showed intense absorption bands with ε values larger than 10 4 M -1 cm -1 in the visible region, which was in contrast to the weak absorption of C 60 (ε < 10 3 M -1 cm -1 ) because of symmetryforbidden transitions. In particular, the absorption spectra of 3c and 4c cover the entire visible region and reach the NIR region. This pronounced light absorption of oligo(biindenylidene)s might represent a characteristic property owing to their topological difference from C 60 . Conversely, 3a-c and 4a-c were virtually non-luminescent in a degassed 2-methyltetrahydrofuran solution even at 77 K despite the allowed nature of the S 0 → S 1 transitions. Although the reason for this remains unclear, nonradiative decay processes via intersystem crossing or conical intersection may be responsible for the lack of fluorescence.
Time-dependent density functional theory (TD-DFT) calculations at the PBE0/6-31+G(d) level indicated that the highest-occupied molecular orbitals (HOMOs) and LUMOs of 3a-c were characterized as delocalized π and π* orbitals over the main chains with a negligible contribution from fused and terminal benzene rings, supporting the effective orbital interactions between the biindenylidene units ( Fig. 5b and Supplementary Fig. 9). In contrast to the low-lying LUMO levels of 3a-c close to C 60 , the HOMO levels of 3a, 3b, and 3c (-5.76, -5.53, and -5.45 eV, respectively) were substantially higher than that of C 60 (-6.63 eV). These high-lying HOMO levels of 3c are possibly responsible for the significantly narrower HOMO-LUMO gap than that of C 60 , resulting a smaller S 0 → S 1 vertical excitation energy (3c: 1.72 eV, C 60 : 2.16 eV). Furthermore, the oscillator strength f of the S 0 → S 1 transition in 3c (f = 1.767) was larger than that of C 60 (f = 0.000) because of its lower symmetry ( Fig. 5b and Supplementary Table 12). These relatively high-lying HOMO and the symmetry-allowed characteristic of the S 0 → S 1 transition in the oligo(biindenylidene)s can be attributed to polyene-like one-dimensional π-conjugation.

Mobility of electrons
To gain insights into the electron mobility of oligo(biindenylidene)s, the electronic photoconduction in a microcrystalline state was examined using flash-photolysis time-resolved microwave conductivity (FP-TRMC) 43, 44 . Photoconductivity transients were observed for 3a-c upon electrodeless photocarrier injection by the excitation at 355 nm ( Fig. 6a and Supplementary Fig. 15). For 3a and 3b, almost no transient conductivity is observed whenever the excitation intensity is increased, or the crystal orientation is optimized. In stark contrast, 3c exhibited fast decay with the transient conductivity ϕΣμ (ϕ: photogeneration efficiency of the charge carriers, Σμ: sum of the isotropic electron and hole mobility) more than one order of magnitude larger than those of 3a and 3b (Fig. 6a), indicating that trimer 3c exhibits superior charge carrier conductivity compared to the shorter-chain oligomers. The major contribution to the photoconductivity was determined to be electrons, given that the transient absorption spectrum of 3c is in good agreement with the absorption band of radical anion 3c •generated by electrochemical reduction (Fig. 6b and Supplementary Fig. 16). The photoinjected charge carrier density of 3c was estimated by monitoring the transient absorption at 800 nm with absorption coefficients ε of 7 × 10 4 M -1 cm -1 charge -1 upon excitation at 355 nm, where photocarrier efficiency ϕ of 2 × 10 -3 and intrinsic intramolecular electron mobility μ e of 0.06 cm 2 V -1 s -1 were obtained (Fig. 6c). Notably, the transient conductivities of 3c and 4c are comparable to each other despite the distinct crystal-packing structures and π-π stacking distances (Figs. 6d, 3c, and 3d), indicative of the predominant contribution of intramolecular electron transport for their electronic photoconduction. These results demonstrated a promising utility of long-chain oligo(biindenylidene)s as electron-transporting molecular wires, although inter-chain electron transport is negligible in the present system.

Discussion
To elucidate the origin of the high electron affinity and stability toward the multi-electron reduction of fullerenes with only a carbon skeleton, we designed and synthesized end-capped 3 and 4, which are π-conjugated hydrocarbons composed of a one-dimensional fragment of buckminsterfullerene C 60 with the same connectivity between the five-membered rings. Crystallographic analysis of 3 and 4 confirmed that all sp 2 carbon atoms in their π-conjugated frameworks adopt trigonal planar geometries, unlike the pyramidalized carbon atoms in conventional fullerene fragment molecules. These oligo(biindenylidene)s have one-dimensional π-conjugated chains wherein the five-membered rings are directly connected. Electrochemical studies of oligo(biindenylidene)s 4 revealed that these oligo(biindenylidene)s can accept electrons up to equal to the number of five-membered rings in their main chains and experimentally corroborated that the five-membered ring substructures play a crucial role in attaining robustness toward multi-electron reduction. Notably, ter(biindenylidene)s, which are small-molecule π-conjugated hydrocarbons that do not have a rigid structure or curvature like fullerenes, can accept up to six electrons without noticeable decomposition.
In contrast to the similarity with fullerenes in terms of electron affinity, the one-dimensional π-conjugation in oligo(biindenylidene)s resulted in pronounced absorption covering the entire visible region, unlike the weak absorption of C 60 attributable to the highly symmetrical structure. Furthermore, FP-TRMC measurements indicated that the oligo(biindenylidene)s with longer chain lengths serve as promising electron-transporting molecular wires. The current results highlight the significance of the pentagonal substructure for attaining stability toward multi-electron reduction and provide a strategy for the molecular design of electron-accepting π-conjugated hydrocarbons even without electron-withdrawing groups.

Synthesis
Selected procedures are shown below. The characterization data are described in Supplementary Data 1 in the Supplementary Information.

Synthesis of oligo(biindenylidene)s 3a-c and 6a-b by the Negishi coupling of 5 with PhZnCl
To a solution of bromobenzene (335 mg, 2.13 mmol) in anhydrous THF (10 mL) was added a solution of n-BuLi in hexane (1.6 M, 1.45 mL, 2.32 mmol) dropwise over 2 min at -78°C. After stirring for 1 h, ZnCl 2 (tmeda) (593 mg, 2.35 mmol) was added to this solution, and the resulting mixture was stirred for 15 min at the same temperature to give a solution of PhZnCl. This solution was added dropwise to a solution of 5 (1.16 g, 3.00 mmol) and Pd(PPh 3 ) 4 (104 mg, 0.090 mmol) in anhydrous THF (3 mL) at -78°C. After stirring for 21 h at 70°C, the resulting mixture was quenched by H 2 O, diluted with CH 2 Cl 2 , and separated into two layers. The aqueous layer was extracted with CH 2 Cl 2 (3 × 50 mL). The combined organic layer was washed with brine and dried over anhydrous Na 2 SO 4 . After filtration and removal of all volatiles under reduced pressure, the crude product was subjected to silica gel column chromatography (hexane to CH 2 Cl 2 , then CH 2 Cl 2 to ethyl acetate as eluent, R f = 0.78 (hexane/ CH 2 Cl 2 1/1)), and further purified by recycling preparative GPC (CHCl 3 as eluent) to afford 40 mg of 3a as red solids (0.10 mmol, 4% yield), 12 mg of 3b as black solids (0.020 mmol, 1% yield), 7.3 mg of 3c as dark green solids (8.8 μmol, 0.9% yield), 169 mg of 6a as red solids (0.44 mmol, 15% yield), and 13 mg of 6b as black solids (0.021 mmol, 1% yield).

Single-crystal X-ray diffraction
Single-crystal X-ray diffraction data were collected on a Rigaku XtaLAB AFC10 diffractometer equipped with FR-X generator, Varimax optics, and PILATUS 200 K photon counting detector with MoKα radiation (λ = 0.71073 Å) for 3a, or on synchrotron radiation (λ = 0.4125-0.4137 Å) at the BL02B1 beamline in SPring-8 (JASRI) for 3b, 4a, 4b, 6a, 7a, and 8. The structure was solved by direct methods (SHELXT 2018/2) 46 and refined by the full-matrix least-squares on F 2 (SHELXL-2018/3) 47 . All hydrogen atoms were placed using AFIX instructions, while all non-hydrogen atoms were refined anisotropically. Detailed measurement conditions and crystal data for these compounds are described in the Supplementary Methods in the Supplementary Information.

Cyclic voltammetry measurements
Cyclic voltammetry (CV) measurements were performed with an ALS/ chi-610E electrochemical analyzer (BAS). The CV cell consisted of a glassy carbon electrode, a Pt wire counter electrode, and an Ag/AgNO 3 reference electrode. The measurements were carried out under a N 2 atmosphere using a sample solution in THF (reduction) or CH 2 Cl 2 (oxidation) with a concentration of 1 mM containing 0.1 M tetrabutylammonium hexafluorophosphate as a supporting electrolyte. The redox potentials were calibrated with a ferrocene/ferrocenium ion couple (Fc/Fc + ). The results are shown in Fig. 4a, Supplementary Figs. 5 and 6, and their data are summarized in Supplementary Table 7.
Steady-state electronic absorption and photoluminescence measurements UV/Vis/NIR absorption spectra were measured with a Shimadzu UV-3600 spectrophotometer with a resolution of 0.2 nm using dilute sample solutions in spectral grade CH 2 Cl 2 in a 1 cm-square quartz cuvette. The results are summarized in Fig. 5a, Supplementary Fig. 7, and Supplementary Table 8. Photoluminescence spectra of 3a-c and 4a-c were attempted to be measured with a Hamamatsu Photonics Quantaurus-QY Plus calibrated integrating sphere system C13534-02 equipped with a high-power Xe lamp L13685-01, a near-infrared multichannel detector C13684-01, and a quartz-made Dewar vessel, using dilute sample solutions in 2-methyl tetrahydrofuran. The solvent was purified by vacuum distillation over CaH 2 , and the resulting sample solutions were degassed by purging the argon gas stream for ca. 10 min. However, 3a-c and 4a-c were virtually non-luminescent in a degassed 2-methyltetrahydrofuran solution at an ambient temperature and 77 K.

Quantum chemical calculations
The geometry optimizations for the oligo(biindenylidene)s 3a-c and 4a′-c′, the radical anions [4a′] •and [4b′] •-, dianions [4a′] 2and [4b ′] 2-, and fullerene C 60 were carried out using the Gaussian16 Revision B.01 48 with default thresholds and algorithms. The oligo(biindenylidene)s 4a′, 4b′, and 4c′ are the model compounds of 4a, 4b, and 4c wherein t-BuMe 2 Si groups were simplified to Me 3 Si groups to reduce the computational costs. Initially, the geometry optimizations for 4a′-c′ were performed by using various types of density functionals, including B3LYP, CAM-B3LYP, PBE0, M06-2X, and ωB97XD functionals with the 6-31+G(d) basis set, and the optimized geometries and the orbital energy levels of Kohn-Sham HOMOs and LUMOs were compared (Supplementary Fig. 8 , the optimized geometries for the corresponding charge-neutral species 4a′ and 4b′ were used as initial guesses. The stationary points were optimized without any symmetry assumptions and characterized by frequency analysis at the same level of theory (the number of imaginary frequencies was 0). The cartesian coordinates for the optimized geometries are given in Supplementary Tables 13-35. The selected C-C bond lengths of the optimized geometries of chargeneutral biindenylidene monomers 3a and 4a′, dimers 3b and 4b′, and trimers 3c and 4c′ were summarized in Supplementary Tables 9-11 and Supplementary Fig. 10. Those for [4b′] •and [4b′] 2were also given in Fig. 4b and Supplementary Fig. 11. Mulliken spin densities of [4a′] •and [4b′] •were shown in Supplementary Fig. 12. The electrostatic potential map for the optimized geometry of [4b′] 2was calculated at the MP2/6-31+G(d) level of theory and the result was shown in Fig. 4c. Time-dependent (TD)-DFT vertical excitation energy calculations for the optimized geometries of 3a-c and 4a′-c′ were performed at the same level of theory. The results are summarized in Fig. 5b, Supplementary Figs. 9 and 14, and Supplementary  Table 12. The nucleus-independent chemical shift (NICS) [49][50][51] values of 4b and [4b′] 2were calculated for the centroid of each ring using the GIAO method at the PBE0/6-31 + G(d) level of theory, and the results were summarized in Supplementary Fig. 13.
Time-resolved microwave conductivity (TRMC) measurements 43,44 3a, 3b, 3c, and 4c were deposited onto quartz plates in their polycrystalline states. The polycrystalline thin films were overcoated by Cytop®, and evacuated under vacuo for 1 h at 40°C prior to TRMC measurements. The films were fixed into a N 2 -filled microwave cavity with Q of ca. 2400 at~9 GHz, and excited at 355 nm of third harmonic generation from a Spectra-Physics INDI Nd:YAG laser. Transmittance of all the films was measured with a Ophir VEGA power meter with a PE-25 head. Transient conductivity signals were evolved through a Schottky diode, amplified, and monitored by a Tektronics TDS3054 digital oscilloscope. All the measurements were carried out at an ambient temperature.

Transient absorption spectroscopy measurements
An identical polycrystalline film of 3c was used for the spectroscopy measurements. White light continuum from a 150 W Xenon lamp (Ushio) was used as an probe, and transmitted light through the film has been spectrally dispersed by a monochromater with focal plane of 300 or 150 mm (C11119-04, Hamamatsu Photonics). Dispersed spectral lines were guided into a high dynamic range streak camera (C13410-01A, Hamamatsu Photonics), amplified by an image intensifier (V12303, Hamamatsu Photonics), and detected with a digital CMOS camera (ORCA-Flash4.0). The 3rd harmonic generation at 355 nm from a nanosecond Nd:YAG laser (NT341A, EKSPLA) was used as an excitation light source. All the measurements were carried out at an ambient temperature.

Electrochemical spectroscopy measurements
Spectroelectrochemical measurements were carried out with a custom-made optically transparent thin-layer electrochemical (OTTLE) cell (light pass length = 1 mm) equipped with a platinum mesh, a platinum coil, and a silver wire as the working electrode, the counter electrode, and the pseudo-reference electrode, respectively. Spectroscopy was carried out with a JASCO V-570 spectrophotometer, and the potential was applied with an ALS/chi Electrochemical Analyzer model 612A. All the measurements were carried out at an ambient temperature.

Reporting summary
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Data availability
The crystallographic data (CIF files) for the structures reported in this Article have been deposited with the Cambridge Crystallographic Data Centre (CCDC), under deposition numbers CCDC 2184333 (3a), 2184328 (3b), 2184330 (4a), 2184329 (4b), 2184334 (6a), 2184332 (7a), and 2184331 (8). These data can be obtained free of charge from CCDC at [www.ccdc.cam.ac.uk/data_request/cif]. All experimental data within the article and its Supplementary Information are available from the corresponding authors upon request. Source data are available as a Source data file. Source data are provided with this paper.