Unusual Length Dependence of the Conductance in Cumulene Molecular Wires

Abstract Cumulenes are sometimes described as “metallic” because an infinitely long cumulene would have the band structure of a metal. Herein, we report the single‐molecule conductance of a series of cumulenes and cumulene analogues, where the number of consecutive C=C bonds in the core is n=1, 2, 3, and 5. The [n]cumulenes with n=3 and 5 have almost the same conductance, and they are both more conductive than the alkene (n=1). This is remarkable because molecular conductance normally falls exponentially with length. The conductance of the allene (n=2) is much lower, because of its twisted geometry. Computational simulations predict a similar trend to the experimental results and indicate that the low conductance of the allene is a general feature of [n]cumulenes where n is even. The lack of length dependence in the conductance of [3] and [5]cumulenes is attributed to the strong decrease in the HOMO–LUMO gap with increasing length.

Long molecules generally conduct electricity less well than short ones,a nd this can be ap roblem when designing molecular wires for mediating efficient charge transport over distances of several nanometers.W hen ah omologous series of oligomers are connected between metal electrodes, and the transport mechanism is coherent tunneling, the conductance G of each oligomer typically decreases exponentially with its molecular length L according to Equation (1), [1] G / e ÀbL ð1Þ where b is the exponential attenuation factor,w hich is normally in the range of 0.2-0.5 À1 for aconjugated organic p-system. [2] It has been predicted that molecules with low bond length alternation (BLA) will give unusual attenuation factors,s uch as b % 0( i.e., conductance independent of length) or even b < 0( i.e., conductance increasing with length). [3,4] Cumulenes are the simplest type of neutral psystem not to exhibit substantial BLA. [5][6][7] Herein, we report an experimental and computational investigation of the length dependence of charge transport through these linear carbon chains.Recently,near length-independent conductances were reported for as et of cyanine dyes,w hich constitute aclass of cationic p-systems with BLA % 0. [8] Cumulenes and polyynes are the two types of linear chains of sp-hybridized carbon atoms:I nc umulenes,t he carbon atoms are linked by double bonds,whereas in polyynes,there are alternating single and triple bonds ( Figure 1). Cumulenes and polyynes have fascinated chemists for many years as models for carbyne,t he infinite 1D form of carbon. [5,6] Cumulenes are said to have a" metallic" electronic structure, [4][5][6][7][9][10][11] because an infinitely long cumulene would have ab and structure characteristic of am etal, with ap artially occupied band derived from the p and p*orbitals.Incontrast polyynes have a p-p*g ap that persists even in long chains, and an infinite polyyne is expected to be asemiconductor. [10,12] This difference in electronic structure is adirect consequence of the different BLAs.A lthough there is some BLA in cumulenes, [7] it is much more subtle than the alternation between short CCa nd long CÀCb onds in polyynes.
Here,w er eport an experimental investigation of the conductances of the family of cumulenes 1, 2, 3,and 5 shown in Figure 2. The [ 4]cumulene 4 is included in our theoretical investigation, but has not yet been tested experimentally.All of these molecules have two terminal 4-thioanisole substituents for binding to gold electrodes.S ingle-molecule conductances were measured using the scanning tunneling microscopy break junction (STM-BJ) method, using ag old tip and ag old surface, [13] as described in detail previously. [2d] Compounds 1, 2, 3,and 5 were synthesized as described in the Supporting Information. [14] Thea lkene 1 was recrystallized to give the E isomer, as confirmed by single-crystal Xray diffraction. [15] Allene 2 is racemic.Cumulenes 3 and 5 are 1:1m ixtures of the E and Z isomers (as confirmed by 1 HNMR spectroscopy);w ew ere unable to separate these stereoisomers.W eexpect them to interconvert readily under ambient conditions, [16] and to have similar conductances (see the Supporting Information, Figure S7).
Theexperimental conductance results for compounds 1-3 and 5 are summarized in Figure 3and Table 1. Forreference, we have also measured 4,4'-bis(methylthio)biphenyl, which has no double bonds between the phenyl rings (Section S3.7). The2Dhistograms (Figure 3a-d) show how the conductance (G/G 0 ,where G 0 = 2 e 2 /h)ofeach junction varies as the STM tip is retracted from the surface (increasing distance, z)f or alarge number of traces (see the Supporting Information for details on the procedure and data from multiple experimental runs). All compounds give well-defined plateaus,w hich   Compound [a] Experimental conductancepeak positions from data in Figure 3f;the run-to-run variationi npeak position is about 0.02, see Figure S19.
[b] The lengths were calibrated by adding 0.4 nm to the peak position of aGaussian fit to the total distribution of plateau lengths. [2d, 17]  become longer as the length of the molecule increases, indicating that connection occurs at the SMe groups (see Table 1f or experimental and calculated molecular lengths, L exp and L calc ,a nd Figure S9 for the plateau-length distributions). Thep ercentage of junctions giving ap lateau for each compound is given in the caption to Figure 3( and in Table S1). Them easured conductances for the alkene and allene vary slightly with distance across the plateau (z). The molecular conductances plotted in Figure 3g and listed in Table 1a re quoted from the histograms in Figure 3f,w here we have considered only points from the end of the distribution, greater than the median length determined from aG aussian fit (see the Supporting Information for details). We had previously validated this method for afamily of porphyrins. [17] This analysis procedure ensures that the conductance values can be attributed to fully stretched singlemolecule junctions.I ta lso results in good overlap between histograms (of the same compound) from periods of measurement giving different percentages of molecular junctions. We often observed an apparent increase in the molecular conductance when the percentage of molecular junctions exceeded about 40 %, which was attributed to the formation of junctions containing several wired molecules. [18] However, if we only consider the data points at longer z values,t he resulting histograms are more reproducible,i ndicating that the probability of multiple-molecule junctions diminishes as the junctions are stretched (as discussed in Sections S3.8 and S3.9). The [ 3] and [5]cumulenes have essentially the same conductance,w hich is slightly larger than that of the alkene (see Figure S19 for ac omparison of multiple experimental runs showing high reproducibility). Thea llene has ac onductance that is about 50 times smaller than those of the [3]-and [5]cumulenes,reflecting its twisted geometry.The conductances of all compounds show aw eak voltage dependence, suggesting that the Fermi level (E F )l ies far from any molecular levels,w hich is consistent with E F sitting near the center of the HOMO-LUMO gap (see Section S3.5). Junctions of [5]cumulene were stable generally to AE 1.2 V, whereas the shorter allene was stable only to AE 0.5 V. At 1.2 V, the maximum current through a [ 5]cumulene molecule approaches microamperes (see Figure S10).
To gain further insight into the conductance trends in the family of cumulene molecular wires,a nd how their conductances change with length, transmission spectra T(E)w ere calculated by combining the DFT package SIESTA [19] with the quantum transport code Gollum [20] (for further details,see the Supporting Information). Fort he alkene, [ 3]cumulene, and [5]cumulene,t he energetically preferred conformations have two terminal thioanisole rings that are not coplanar (see Section S2.2 for details), in agreement with crystallographic studies. [15,21] Theconformations of relaxed molecules embedded in Au-Aujunctions are shown in Figure 4a.T he frontier molecular orbitals ( Figure S3) show that the HOMO of the alkene as well as the HOMO and LUMO of [3]cumulene and [5]cumulene form extended p-conjugated transport paths through the whole molecules.I nc ontrast, the molecular orbitals of the allene and [4]cumulene are formed from p z and p x orbitals and follow chiral paths through the molecules, leading to terminal thioanisole rings that are orthogonal to each other, and the absence of an extended p-system in the HOMO and LUMO.Asshown in Figure 4b,these differences between the even-and odd-numbered cumulenes are reflected in their transmission functions.O ver ar ange of E F within the HOMO-LUMO gap,i ndicated by the shaded region in Figure 4b,t he conductances of the allene and the [4]cumulene are expected to be lower than those of the other three molecules.M ore interestingly,t he conductances of the [3]cumulene and the [5]cumulene are predicted to be about the same,d espite the substantial change in length. This prediction is consistent with previous computational studies of charge transport through cumulene molecular wires. [4,9] Thel ocal density of states (LDOS) of the alkene and allene (Figure 4c)r eveals ac lear transport path for the alkene (magenta surface), while there is no such LDOS path on the allene molecule.T he alkene is predicted to have as lightly lower conductance than both the [3]-and [5]cumulenes because of the larger angle between the two thioanisole rings  [3]cumulene, and [5]cumulene attached to two gold leads, where the gray,white, and pale-yellow balls represent carbon, hydrogen, and sulfur,respectively.The yellow balls at both ends represent gold leads. b) Transmission spectra. The shaded region indicates the range of Fermi energies within the HOMO-LUMO gap that contribute towards conduction at room temperature. c) The LDOS with magenta color in the energy window from À0.5 eV to 0eVfor the alkene and allene incorporated into two gold leads separately at the isosurface 0.00002. in the alkene,which is the result of steric interactions between the thioanisole and phenyl substituents.
Theexperimental conductances of molecules 1, 2, 3,and 5 correlate well with their HOMO-LUMO gaps,a si llustrated by the optical gaps, E g (UV), from the wavelength of the lowest-energy UV/vis absorption band, and the Kohn-Sham gaps, E g (DFT), in Table 1. [22] Thel ack of attenuation in the conductance for the series of compounds alkene, [ 3]cumulene,a nd [5]cumulene can be attributed to the decreasing HOMO-LUMO gaps,w hich compensate for the increasing length. [13,23] Thelower molecular conductance of the allene is consistent with the large HOMO-LUMO gap,which leads to ah igher barrier to electron transport. "Odd-even" conductance oscillations are anticipated from previous studies on metal atomic chains (e.g., Au,Pt, and Ir) as afunction of the number of atoms in the chain. [24] Fore xample,A ua nd Na chains,w ith single conductance channels,s how an odd-even effect that originates from quantum interference. [25,26] Oddeven oscillations have also been predicted for monoatomic carbon chains between carbon nanotubes. [27] Theo dd-even effect that we observed here is probably dominated by the fact the 4-thioanisole groups connecting the chains to the electrodes are only p-conjugated in the odd [n]cumulenes (i.e., even number of carbon atoms). Another obvious difference between our measurements and the metal atomic chains is the fact that the chain and electrode atoms differ, producing an energy offset between the molecule and the electrodes.
In conclusion, we have revealed that the conductance of aseries of cumulenes shows remarkably little dependence on the molecular length (n). This behavior is ac onsequence of the lack of strong BLA in these compounds,w hich results in asteep reduction in the HOMO-LUMO gap with increasing length. [6,7] In contrast, polyynes show strong BLA, resulting in an exponential attenuation of conductance with length (b % 0.2-0.3 À1 at low bias voltage). [28] The [ 5]cumulene exhibits ah igh conductance of log(G/G 0 ) = À3.7(AE 0.5) and shows stable junctions up to abias of 1.2 V. Thediscovery that cumulenes exhibit length-independent conductance suggests that they might be used to construct longer highly conductive molecular wires;h owever,t his would require the development of effective strategies for controlling the reactivity of long cumulenes. [7,29]