Introduction

Linear carbon (Cn), an elusive sp-hybridized carbon allotrope, has attracted much interests both experimentally and among theorists for decades due to remarkable properties and significant controversy1,2,3,4,5,6. Similar to recently popular sp-hybridized cyclo[n]carbon7,8,9,10,11,12,13, linear carbon may also have two distinct structural forms, i.e., cumulene for consecutive double bonds, or polyyne for alternating triple and single bonds. Peierls transition theory predicted that for infinite linear Cn, polyyne should be more stable than cumulene, and meanwhile opening a band gap at Fermi level14,15,16.

Due to its very high reactivity, synthesis and characterization of linear carbon are exceptionally challenging. Previous works have tried different methods17,18,19,20,21, especially heavy end-capping groups22,23,24 or confined into carbon nanotube25, to synthesize carbon chains, however, atomically precise synthesis of uncapped linear carbon, and real-space characterization of its detailed structure remains very rare13,26,27. Especially, its cumulenic form, is proved to be even harder to synthesize compared to polyynic one. In solution, till now, the longest cumulene known to date is n = 10 (also with protected group at both ends)28,29,30,31.

Previous theoretical works show that in the gas phase, short linear Cn (approximately n < 52) are all cumulenic32,33,34, and Peierls transition in odd-numbered Cn will be reached at larger number of carbon atoms than that in the even-numbered Cn34. Our work on the linear C613, however, reveals that it instead already adopts a polyynic structure, a result of the NaCl surface-induced Peierls transition (Fig. 1a). This finding motivated us to investigate the influence of number of carbon atoms and odevity effect on the structures of carbon chains. Linear C5, is thus considered to be a relevant candidate. Additionally, theoretical work also indicates that for n = 5, the linear form is expected to be much more stable than the cyclic form32,35,36,37,38,39, in contrast to the case of n = 613 (where the energy difference between its linear and cyclic forms is very small).

Fig. 1: On-surface generated linear C5.
Fig. 1: On-surface generated linear C5.
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a Reaction scheme for the generation of linear C6. b Reaction scheme for the generation of linear C5. c I–c III, d I–d III AFM and Laplace-filtered AFM images of precursor, intermediate and product (linear C5). e Zoom-in AFM image of linear C5. f Calculated bond lengths (Å) of linear C5 in the gas phase and on the NaCl surface. g AFM image of linear C5 with NaCl lattice. Crossings of white lines mark Cl ion positions determined experimentally. h Side and top views of the calculated structure of linear C5 on the NaCl surface. The scale bar in (c I) applies to all experimental and Laplace-filtered AFM images except e. AFM tip offsets Δz:  +1.5 Å, −1.0 Å, −1.4 Å, −0.5 Å, −1.5 Å for c I, c II, c III, e, g. Reference set points of Δz: I = 0.5 pA, V = 0.3 V for all AFM images.

We employed the scanning tunneling microscopy (STM) tip-induced26,40,41 dehalogenation method to generate C5. We chose a fully halogenated cyclopenta-1,3-diene (perbromocyclopenta-1,3-diene, C5Br6) as the precursor, and through tip-induced entire dehalogenation and ring-opening reaction, linear C5 was generated on both 1 ML and 2 ML NaCl/Au(111) surfaces with 100 % yield (81 precursors were tested in the experiments), and no cyclic form was observed (Fig. 1b). Moreover, importantly, bond-resolved AFM images represent a nearly uniform feature resembling the cumulenic structures reported before9. This naturally indicates a cumulenic structure for linear C5, in accordance with the relaxed structure of C5 on the NaCl surface. To further explore the structures and their related electronic states of linear Cn with different number of carbon atoms, we achieved tip-induced coupling reactions of linear C5, and successfully generated various carbon chains including C9, C10, C13, C14, C15, C17, C18, C21 on the NaCl surface, together with characterization of their structures and measurement of electronic states.

Results and discussion

To generate linear C5, C5Br6 molecules were introduced on the cold NaCl/Au(111) held at ~6 K. All experiments were conducted at 4.7 K. The AFM and Laplace-filtered AFM images in Fig. 1c I, d I show C5Br6 molecule adopts a non-planer geometry, with only the topmost Br atom visible as a round protrusion. To trigger dehalogenation reactions, the tip was initially positioned on a single C5Br6 molecule, and retracted by ~6–8 Å from a setpoint (typically I  =  0.5 pA, V  =  0.3 V), after that, ~4 V pulses were applied on the molecule with currents on the order of hundreds of fA. This procedure typically resulted in the removal of one bromine atom, forming a C5Br5 intermediate (Fig. 1c II, d II, with one bromine atom aside). Subsequent voltage pulses applied to the C5Br5 intermediates can induce further dehalogenations and accompanied ring-opening reaction, resulting in the final product of linear C5 (Fig. 1c III, d III, with six bromine atoms aside). Note that cyclic C5 was not generated on either 1 ML or 2 ML NaCl surface, different from the case of C613.

AFM images of linear C5 (Fig. 1c III, d III, e and Supplementary Fig. 1) clearly reveal a uniform contrast, indicating linear C5 has a cumulenic structure, different from the polyynic linear C6 on the NaCl surface. Previous theoretical studies predicted that linear C5 adopts a cumulenic structure as the lowest energy geometry in the gas phase32,33,34 (see also the bond length calculations in Fig. 1f at the ωB97XD/def2-TZVP level). When relaxing the cumulenic linear C5 on the NaCl surface with the experimentally determined registry (Fig. 1g), it was found that linear C5 still maintains the cumulenic structure (Fig. 1f, h), consistent with the experimental results.

Interestingly, when applying voltage pulses ( ~ 4 V) between two isolated linear C5, we observed that they could couple together and lead to the formation of a linear C10 (Fig. 2a, b I, b II). Moreover, it is also feasible to couple a linear C10 and a linear C5 to generate a linear C15 (Fig. 2a, c I, c II).

Fig. 2: Tip-induced coupling reaction of linear C5.
Fig. 2: Tip-induced coupling reaction of linear C5.
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a Reaction scheme for the formations of linear C10 and C15 via tip-induced coupling reaction of linear C5. b I AFM image of two isolated linear C5. b II After applying voltage pulses, a linear C10 was generated. c I AFM image of isolated linear C10 and C5. c II After applying voltage pulses, a linear C15 was generated. The scale bar in (b I) applies to all AFM images. AFM tip offsets Δz:  −1.5 Å, −1.3 Å, −1.4 Å, −0.7 Å for b I, b II, c I, c II. Reference set points of Δz: I = 0.5 pA, V = 0.3 V for all AFM images.

We found that the efficiency of the tip-induced coupling reaction can be significantly improved by applying voltage pulses up to 4.5 V and reducing the tip height with currents up to about 10–50 pA. In addition, an appropriate molecular coverage (e.g., 0.3 ML) also helps to increase the chances of molecules encountering each other, thereby facilitating the formation of various carbon chains (Fig. 3a). Note that in these processes carbon-carbon bonds may also be broken. By optimizing the parameters, additional coupling-reaction products, including linear C9, C13, C14, C17, C18, C21 can also be generated (Fig. 3b–i). The assignments of these carbon chains are detailed in Supplementary Figs. 2 to 4.

Fig. 3: Tip-induced coupling-reaction products of linear C5.
Fig. 3: Tip-induced coupling-reaction products of linear C5.
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a I, a II STM images before (a I) and after (a II) voltage pulses. (a III) Statistical analysis. (b I to b V, c I to c V, d I to d V, e I to e V, f I to f V, g I to g V, h I to h V, i I to i V) AFM images, Laplace-filtered AFM images at far and close tip height together with superimposed model of linear C9, C10, C13, C14, C15, C17, C18, C21. The arrows in c IV, e IV, h IV indicate the carbon-carbon triple bonds of linear C10, C14, C18, respectively, and the blue arrows indicate the invisible triple bonds at the ends. The scale bar in (b I) applies to all experimental and Laplace-filtered AFM images. AFM tip offsets Δz:  +0.7 Å, +0.5 Å, −1.5 Å, −1.7 Å, +0.5 Å, +0.3 Å, −1.0 Å, −1.2 Å, −0.7 Å, −1.2 Å, +0.7 Å, +0.6 Å, +0.8 Å, +0.6 Å, +0.7 Å, +0.4 Å for b I, b III, c I, c III, d I, d III, e I, e III, f I, f III, g I, g III, h I, h III, i I and i III. Reference set points of Δz: I = 5 pA, V = 0.3 V for e I and e III, I = 0.5 pA, V = 0.3 V for all AFM images except e I and e III.

Our calculations and literature32,33,34 show that in the gas phase, these carbon chains illustrated in Fig. 3 are all cumulenic (Supplementary Fig. 5). While, on the NaCl surface, for even-numbered linear C10, AFM images at far and close tip heights reveal three and five distinct characteristic bright features, which can be assigned to the five triple bonds12,26, indicating that linear C10 adopts a polyynic structure. At a larger tip height (e.g., Fig. 3c I and c II), two triple bonds at both ends are less distinct, likely due to the non-planer adsorption configuration of linear C10 on the NaCl surface (see the relaxed structure in Supplementary Fig. 2b I to b III). For the longer linear C14 and C18, AFM images at both far and close tip heights can only reveal five and seven distinct characteristic bright features for triple bonds, and another two triple bonds at both ends for C14 and C18 are invisible (indicated by blue arrows in Fig. 3e IV and h IV). These experimental results and calculations (see Supplementary Fig. 2b I to b III, d I to d III, g I to g III) show that linear C10, C14 and C18 undergo surface-induced Peierls transitions (i.e., cumulenic one in the gas phase and polyynic one on the surface), similar to the case of linear C613.

For the odd-numbered linear C9, a nearly uniform contrast is observed (Fig. 3b), similar to C5, and our calculations show that C9 has rather small bond length alternations (Supplementary Fig. 2a I to a III), we thus assign it a cumulene-like structure9 (see the model in Fig. 3b V). Note that the observed apparent length of C9 is shorter than the model because of the two invisible bonds at both ends. While, for other longer ones, i.e., C13, C15, C17, and C21, AFM images at larger tip height normally show fainted dots (but different from the characteristic features of triple bonds), and at closer tip height, nearly uniform contrasts are observed together with two less distinct dots at both ends (similar to the even-numbered chains). In accordance with our calculations (Supplementary Fig. 2c I to c III, e I to e III, f I to f III, h I to h III), for example, the relaxed structure of linear C15 on the NaCl surface reveals that the BLAs are significantly larger at the two ends compared to the middle, but overall, smaller than the even-numbered ones. We tentatively assign hybrid structures for the odd-numbered linear C13, C15, C17, and C21, in which the both ends exhibit triple bond characteristics and the remaining moieties are still cumulene-like ones (see the models in Fig. 3d V, f V, g V, i V).

These results suggest that on the NaCl surface Peierls transition completely occurs for the even-numbered linear C10, C14, C18, while, only partly occurs for the odd-numbered linear C13, C15, C17, C21. Cumulene-like linear C9 may exhibit a Peierls-transition intermediate between cumulenic linear C5 and partly polyynic linear C13.

To further investigate the relationship between the structures and related electronic properties of the carbon chains above, we performed scanning tunneling spectroscopy (STS) measurements. The dI/dV spectra, represented by the blue and red lines, were acquired over the triple and single bonds of linear C10, C14 and C18, respectively. For the odd-numbered ones, the blue and red lines are acquired at the dot and between the dots, respectively.

STS measurements reveal that the transport gaps of the odd-numbered chains are dramatically smaller than that of the adjacent even-numbered chains, e.g., C9 vs C10, C13 vs C14, C17 vs C18 (Supplementary Fig. 6). As shown in Fig. 4, for linear C9, the dI/dV spectra show two prominent peaks at approximately V = −1.75 V and 1.46 V, yielding a transport gap of about 3.21 eV. STM images obtained at these bias voltages correspond to the positive ion resonance (PIR) and negative ion resonance (NIR) states. For both PIR and NIR, the STM images show five distinct lobes. For linear C10, the spectra show two prominent peaks at approximately V = −2.0 V and 3.3 V, yielding a transport gap of about 5.3 eV. For PIR, the STM image shows five lobes, while, for NIR, the lobes numbered 2, 3, 4 cannot be separately resolved.

Fig. 4: Electronic characterization of linear C9, C10, C13, C14, C15, C17, C18, C21.
Fig. 4: Electronic characterization of linear C9, C10, C13, C14, C15, C17, C18, C21.
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a Scanning tunneling spectroscopy (STS) of linear C9, C10, C13, C14, C15, C17, C18, C21 conducted on the NaCl surface, in which linear C10 and C14 were done on the 1 ML NaCl surface, and the others were done on the 2 ML NaCl surface. The differential conductance (dI/dV) signals show two peaks that can be attributed to the positive ion resonance (PIR) and negative ion resonance (NIR) states. b AFM images, in-gap STM images (0.3 V), STM images (PIR), and STM images (NIR) of linear C9, C10, C13, C14, C15, C17, C18, C21. The blue and red lines in a are conducted at the positions on the blue and red crosses on AFM images in b. The numbers on STM images (PIR and NIR) indicate the number of lobes. The STS spectra and STM images are all acquired with CO-terminated tip. The scale bar in (b) applies to all STM and AFM images.

For linear C13, the dI/dV spectra show two prominent peaks at approximately V = −1.65 V and 1.3 V, yielding a transport gap of about 2.95 eV. STM images obtained at PIR and NIR show seven distinct lobes. For linear C14, the dI/dV spectra show two prominent peaks at approximately V = −2.8 V and 2.5 V, yielding a transport gap of about 5.3 eV. For PIR, the STM image shows seven lobes, while, for NIR, the lobes numbered from 2 to 6 cannot be separately resolved.

For linear C17, the dI/dV spectra show two prominent peaks at approximately V = −1.63 V and 1.16 V, yielding a transport gap of about 2.79 eV. STM images obtained at PIR and NIR show nine distinct lobes. For linear C18, the dI/dV spectra show two prominent peaks at approximately V = −2.75 V and 2.0 V, yielding a transport gap of about 4.75 eV. STM images obtained at PIR and NIR show nine and ten distinct lobes, respectively. For the other two even-numbered linear C10 and C14, it is rather challenging to measure the entire dI/dV spectra on a 2 ML NaCl surface due to quite large transport gaps, i.e., at larger bias voltages, the molecular carbons normally diffuse around on the surface.

From the comparison above, it is shown that the transport gaps for the even-numbered carbon chains (with polyynic structures) are dramatically larger than the odd-numbered ones (with partly cumulenic structures), which is in a good agreement with Peierls transition theory14,15,16.

Additionally, for the linear C15, the dI/dV spectra show two prominent peaks at approximately V = −1.6 V and 1.2 V, yielding a transport gap of about 2.8 eV. STM images obtained at PIR and NIR show eight distinct lobes. For linear C21, the dI/dV spectra show two prominent peaks at approximately V = −1.6 V and 1.15 V, yielding a transport gap of about 2.75 eV. STM images obtained at PIR and NIR show eleven distinct lobes. We have also calculated the frontier orbitals of the carbon chains that reasonably matched well with the experimental results (cf. Supplementary Fig. 7 to S10). In above, the transport gaps for both odd-and even-numbered carbon chains gradually decrease with increasing number of carbon atoms.

To demonstrate the generality, linear C6 was considered as the initial point for further coupling reactions. To do so, C6Br6 precursors were introduced on the cold NaCl/Au(111) held at ~6 K (Fig. 5a). To induce the coupling reactions, similarly, voltage pulses up to 4.5 V were applied with currents up to about 10–50 pA. As expected, we find that the linear C6 can also fuse together and form longer carbon chains (Fig. 5b). The upper one in Fig. 5b was further characterized and assigned to a linear C23. The AFM image (Fig. 5d) shows similar characteristics to those odd-numbered ones, like linear C13, C15, C17, C21. The dI/dV spectra show two prominent peaks at approximately V = −1.1 V and 0.9 V, yielding a transport gap of about 2.0 eV (Fig. 5c). For both PIR and NIR, the STM images show twelve distinct lobes (Fig. 5d), confirming the assignment of the linear C23.

Fig. 5: Tip-induced coupling reactions of linear C6.
Fig. 5: Tip-induced coupling reactions of linear C6.
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STM images (0.3 V) before (a) and after (b) voltage pulses. Two carbon chains were generated after applying voltage pulses. Inset: AFM image of a C6Br6. c STS of the linear C23 (the upper one in b). d AFM image, in-gap STM image (0.3 V), STM image (PIR, −1.1 V), and STM image (NIR, 0.9 V) of the linear C23. The numbers on the STM images (PIR and NIR) indicate the number of lobes. The STS spectra and STM images are all acquired with CO-terminated tip. The scale bar in (d) applies to all STM and AFM images in (d).

Moreover, we find that some longer carbon chains have shown the flexibility with curved geometries, for example, the generated linear C30 demonstrates the possibility as the precursor to forming the corresponding cyclocarbon (Supplementary Fig. 11).

In conclusion, we have demonstrated the feasibility of generating various carbon chains via tip-induced coupling reactions of linear C5 or C6. This enables to experimentally identify that on the NaCl surface, Peierls transition completely occurs for even-numbered carbon chains, leading to the formation of polyynic structure, while, for odd-numbered ones, the both ends exhibit triple bond characteristics and the remaining moieties are still cumulene-like. Such a structural difference between odd- and even-numbered carbon chains was reflected by STS measurements that the electronic transport gaps of the odd-numbered chains are smaller than that of the adjacent even-numbered chains due to Peierls transition. This study offers an approach for atomically precise synthesis of a series of uncapped carbon chains, and may also provide a new strategy to synthesize their corresponding isomers, cyclocarbons.

Methods

Experimental details for STM and AFM measurements

STM and AFM measurements were carried out in a commercial (Createc) low-temperature system operated at 4.7 K with a base pressure better than 1 × 10−10 mbar. The single crystalline Au(111) surface was cleaned by several sputtering and annealing cycles. The NaCl films were obtained by thermally evaporating NaCl crystals onto a clean Au(111) surface at room temperature, resulting in islands of one and two monolayer (ML) thickness. The perbromocyclopenta-1,3-diene (C5Br6, purchased from Shaanxi Yikunte Pharmaceutical Technology Co., Ltd., 98 %) and hexabromobenzene (C6Br6, purchased from Adamas-beta, 98 %) molecules were separately deposited on cold NaCl/Au(111) surface by thermal sublimation from a molecular evaporator (sublimation temperature: 44˚C for C5Br6, 85 ˚C for C6Br6). CO molecules for tip modification42 were dosed onto the cold sample via a leak valve. We used qPlus sensors43 with a resonance frequency f0 = 29.49 kHz, quality factor Q ≈ 45,000 and a spring constant k ≈ 1800 N/m operating in frequency-modulation mode44. The bias voltage V was applied to the sample with respect to the tip. AFM images were acquired in constant-height mode at V = 0 V and an oscillation amplitude of A = 1 Å. The tip-height offsets Δz for constant-height AFM images are defined as the offset in tip-sample distance relative to the STM set point at the NaCl surface. The positive (negative) values of Δz correspond to the tip-sample distance increased (decreased) with respect to a STM set point. The charge-state determination of linear carbons on NaCl was shown in Supplementary Fig. 12.

Density functional theory calculations

Density functional theory (DFT) calculations were carried out in the gas phase using Gaussian 16 program package45. ωB97XD exchange-correlation functional46 in conjunction with def2-TZVP47 basis sets was used for linear carbons calculations in gas phase.

The Vienna ab initio simulation package (VASP)48,49 was used to perform the DFT calculations on NaCl surface. For describing the interaction between electrons and ions, the projector-augmented wave method50,51 was used, and the Perdew−Burke−Ernzerhof generalized gradient approximation exchange−correlation functional was employed52. Van der Waals corrections to the PBE density functional were also included using the DFT-D3 method of Grimme53. The kinetic energy cutoff was set to 400 eV. We used a 1 ML NaCl(001) slab on top of Au(111) substrate modeled by a three-layer slab, and the bottom layer of the Au(111) was fixed. The atomic structures were relaxed until the atomic forces were less than 0.03 eV/Å. Simulated STM images were obtained based on the Tersoff−Hamann method54,55.