•Intramolecular circuits are constructed with charged cyclophanes•The two-channel conductance is 50-fold higher than that of a single-channel control•The finding violates the conductance superposition law in single-molecule circuits•Interchannel gating dominates the enhancement of the double-channel conductance Kirchhoff's circuit law predicts the total conductance of two parallel channels to be the sum of the individual channel conductances. In neutral single-molecule circuits, however, a theoretical upper limit of 4-fold conductance enhancement is bestowed by constructive quantum interference (CQI). Here, we report a unique strategy for constructing intramolecular circuits from charged cyclophanes, which exhibit a 50-fold conductance enhancement compared with that of a single-channel control, wherein the single-molecule conductance superposition law no longer holds. An interchannel gating effect contributes to the effective conductance of each channel, and CQI boosts the total conductance of the two-channel circuit. This breakthrough not only provides an addition to the toolbox of single-molecule-based circuits but also reveals the fundamental understanding of the interchannel communication in two-channel intramolecular circuits, opening up avenues for developing quantum circuits and devices. For neutral intramolecular circuits with two constitutionally identical branches, a maximum 4-fold increase in total conductance can be obtained according to constructive quantum interference (CQI). For charged intramolecular circuits, however, the strong electrostatic interactions entangle the quantum states of these two parallel pathways, thus introducing complicated transport behavior that warrants experimental investigation of the intramolecular circuit rules. Here, we report that a tetracationic cyclophane with parallel channels exhibits a 50-fold conductance enhancement compared with that of a single-channel control, an observation that supplements intramolecular circuit law in systems with strong Coulombic interactions. Flicker noise measurements and theoretical calculations show that strong electrostatic interactions between charged parallel channels—serving as the chemical gate to promote the effective conductance of each channel—and CQI boosts the total conductance of the two-channel circuit. The molecular design presented herein constitutes a proof-of-principle approach to charged intramolecular circuits that are desirable for quantum circuits and devices. For neutral intramolecular circuits with two constitutionally identical branches, a maximum 4-fold increase in total conductance can be obtained according to constructive quantum interference (CQI). For charged intramolecular circuits, however, the strong electrostatic interactions entangle the quantum states of these two parallel pathways, thus introducing complicated transport behavior that warrants experimental investigation of the intramolecular circuit rules. Here, we report that a tetracationic cyclophane with parallel channels exhibits a 50-fold conductance enhancement compared with that of a single-channel control, an observation that supplements intramolecular circuit law in systems with strong Coulombic interactions. Flicker noise measurements and theoretical calculations show that strong electrostatic interactions between charged parallel channels—serving as the chemical gate to promote the effective conductance of each channel—and CQI boosts the total conductance of the two-channel circuit. The molecular design presented herein constitutes a proof-of-principle approach to charged intramolecular circuits that are desirable for quantum circuits and devices. 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Venkataraman L. Hybertsen M.S. Probing the conductance superposition law in single-molecule circuits with parallel paths.Nat. Nanotechnol. 2012; 7: 663-667Crossref PubMed Scopus (266) Google Scholar conductance enhancement (γQI=2.8) in neutral two-channel molecules, analogous endeavors, involving charged two-channel molecules where pairs of channels have similar conformations, have not yet been made.20Li Z. Smeu M. Rives A. Maraval V. Chauvin R. Ratner M.A. Borguet E. Towards graphyne molecular electronics.Nat. Commun. 2015; 6: 6321Crossref PubMed Scopus (118) Google Scholar The first circuit analyses of charged intramolecular circuits in the single-molecule junctions we report here have been realized using a tetracationic cyclophane, 1-DS⋅4PF6 (Figure 1C, right), in which the pyridinium units act as the positive gate that is not directly conjugated with the other tunneling channel. This cyclophane—consisting of two identical extended viologen (ExBIPY2+) units connected to common phenylene sulfide anchors at each end—can be synthesized in two steps (see Supplemental Section A for details). As a comparison, we prepared a single-channel control molecule, namely, 1-S⋅2PF6 (Figure 1C, left), which comprises a single channel consisting of an ExBIPY2+ unit, connected in an end-to-end manner by two phenylene-linked phenyl sulfide anchors. In a series of scanning tunneling microscopy break-junction (STM-BJ) experiments and density functional theory (DFT) calculations, we confirm the presence of the chemical gating and CQI effects in the constitutionally symmetrical 1-DS. The generality and feasibility of such a synergistic conductance-promoting effect has also been demonstrated by investigating a broad range of charged cyclophanes, affording us the opportunity to achieve a pronounced conductance-promoting factor, e.g., 53.7, when compared with the one-channel control, which is significantly larger than that (e.g., 4) in neutral systems. To investigate single-molecule charge transport through the charged cyclophanes, we measured (Figure 2A; see Experimental Procedures and Supplemental Section B) their conductance using the STM-BJ technique40Xu B. Tao N.J. Measurement of single-molecule resistance by repeated formation of molecular junctions.Science. 2003; 301: 1221-1223Crossref PubMed Scopus (1938) Google Scholar under ambient conditions in acetonitrile (MeCN) solutions containing 0.1 mM of a given cyclophane. In an attempt to suppress the background conductance of the solvent, we coated a thin layer of Apiezon wax onto the Au tip of the STM as described elsewhere.41Nagahara L.A. Thundat T. Lindsay S.M. Preparation and characterization of STM tips for electrochemical studies.Rev. Sci. Instrum. 1989; 60: 3128-3130Crossref Scopus (239) Google Scholar,42Yin X.D. Zang Y.P. Zhu L.L. Low J.Z. Liu Z.F. Cui J. Neaton J.B. Venkataraman L. Campos L.M. A reversible single-molecule switch based on activated antiaromaticity.Sci. Adv. 2017; 3: eaao2615Crossref PubMed Scopus (74) Google Scholar Conductance was repeatedly measured as a function of the tip-sample displacement. In Figure 2B, we compare several typical conductance-displacement traces obtained from the solvent (black) and two charged compounds, namely 1-S (gray) and 1-DS (blue). Unlike the direct tunneling traces obtained for the solvent, the conductance traces of 1-S and 1-DS decrease to molecule-specific plateaus after the rupture of the last Au-Au atomic contact at 1 G0 (where G0 is the conductance quantum, which equals 2e2/h [where e is the charge on an electron and h is Planck's constant]), suggesting the formation of molecular junctions for both of these two compounds. The measured data from more than 5,000 individual traces measured for each compound were used without data selection to construct one-dimensional (1D) conductance histograms, which represent (Figure 2C) distinct molecular conductance peaks. We found that the conductance of the one-channel control 1-S differs significantly by one order of magnitude lower compared with that of the double-channel symmetrical cyclophane 1-DS. Quantitatively, we find the most probable conductances (peaks of the Gaussian fit) to be 10−5.36±0.02 G0 (0.34 ± 0.02 nS) and 10−4.43±0.01 G0 (2.88 ± 0.07 nS) for 1-S and 1-DS, respectively. To gain a better understanding of the distribution of conductance,43Quek S.Y. Kamenetska M. Steigerwald M.L. Choi H.J. Louie S.G. Hybertsen M.S. Neaton J.B. Venkataraman L. Mechanically controlled binary conductance switching of a single-molecule junction.Nat. Nanotechnol. 2009; 4: 230-234Crossref PubMed Scopus (518) Google Scholar we created two-dimensional (2D) conductance-displacement histograms (Figures 2D and 2E) for compounds 1-S and 1-DS, respectively. Upon elongation of the junction, conductance decreases for both of these compounds until a fully extended junction is formed.44Liu J. Zhao X. Zheng J. Huang X. Tang Y. Wang F. Li R. Pi J. Huang C. Wang L. et al.Transition from tunneling leakage current to molecular tunneling in single-molecule junctions.Chem. 2019; 5: 390-401Abstract Full Text Full Text PDF Scopus (48) Google Scholar Two conductance maxima occur in control molecule 1-S (Figure 2D), one between 0 and 0.5 nm in displacement and ∼10−4.0 G0 in conductance, and another between 0.5 and 1.0 nm in displacement and ∼10−5.4 G0 in conductance. We attribute (Figure S2) these two peaks to different geometries between the Au tips and the molecules, i.e., (1) the first decay belongs to the contact between thioether S and pyridinium N, and (2) the second peak belongs to the contact made from thioether S to thioether S (see Figure S2 for more information). Accounting for an Au-Au “snap-back” distance of ∼0.5 nm,45Hong W. Manrique D.Z. Moreno-García P. Gulcur M. Mishchenko A. Lambert C.J. Bryce M.R. Wandlowski T. Single molecular conductance of tolanes: experimental and theoretical study on the junction evolution dependent on the anchoring group.J. Am. Chem. Soc. 2012; 134: 2292-2304Crossref PubMed Scopus (306) Google Scholar the molecular length obtained from the relative stretched distance distribution was determined to be ∼1.8 nm, of which 1.3 nm comes (Figure 2F) from the relative displacement distribution. This distance is quite similar to the molecular length obtained (Table S1 and Figure S1) from the single-crystal X-ray structure of 1-DS, suggesting the binding of the molecular junctions to the Au electrodes from the two-terminal anchors. The conductance of the double-channel 1-DS, determined both from the 1D and 2D histograms, is much higher than that of the one-channel 1-S. Quantitatively, we obtained a conductance enhancement of G1-DS/G1-S ≈ 8.5, where the single-molecule conductance superposition law for neutral molecules no longer holds for charged cyclophanes. Strong chemical gating effects occur between the parallel tunneling channels. To verify this hypothesis, we analyzed (Figures 2D and 2E, insets) the flicker noise characteristics of these two compounds. According to previous results,10Garner M.H. Li H. Chen Y. Su T.A. Shangguan Z. Paley D.W. Liu T. Ng F. Li H. Xiao S. et al.Comprehensive suppression of single-molecule conductance using destructive σ-interference.Nature. 2018; 558: 415-419Crossref PubMed Scopus (178) Google Scholar,46Adak O. Rosenthal E. Meisner J. Andrade E.F. Pasupathy A.N. Nuckolls C. Hybertsen M.S. Venkataraman L. Flicker noise as a probe of electronic interaction at metal–single molecule interfaces.Nano Lett. 2015; 15: 4143-4149Crossref PubMed Scopus (65) Google Scholar, 47Tang C. Chen L. Zhang L. Chen Z. Li G. Yan Z. Lin L. Liu J. Huang L. Ye Y. et al.Multicenter-bond-based quantum interference in charge transport through single-molecule carborane junctions.Angew. Chem. Int. 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We have found that these noise distributions of 1-S measurements are significantly lower than that of 1-DS. Quantitatively, the noise power scales as G1.4 for 1-S (Figure 2D, inset) and as G2.0 for 1-DS (Figure 2E, inset), indicating that the charge transport through 1-S is through-bond dominated, whereas it is through-space dominated in the case of 1-DS. These noise analyses reveal the strong interchannel interaction between the parallel tunneling channels in 1-DS, which originate from the chemical gating effect characteristic of the dicationic backbones. The analyses conducted thus far suggest that the conductance-promoting factor may be sensitive to the interplay between the placement of the Fermi energy of Au and the location of the backbone resonances. To probe this feature, we further synthesized three additional charged derivatives (Figure 3A) of both 1-S and 1-DS with various different backbones, that is, (1) 2-S and 2-DS with bipyridinium (BIPY2+) units, (2) 3-S and 3-DS with dipyridylethane (EaBIPY2+) units, and (3) 4-S and 4-DS with dipyridylethene (EeBIPY2+) units. Both 1D and 2D conductance histograms for single-channel (2-S, 3-S, and 4-S) and double-channel (2-DS, 3-DS, and 4-DS) compounds are qualitatively similar (Figures 3B–3F and S4) to the histograms for 1-S and 1-DS. We observed (Figures 3B–3D) low-conductance features for all three single-channel compounds, 2-S, 3-S, and 4-S. These features traverse the range of 10−5.20±0.02 G0 to 10−5.55±0.02 G0, a range comparable with that of 1-S. Furthermore, double-channel junctions for 2-DS, 3-DS, and 4-DS show conductance values almost one order of magnitude higher than their single-channel counterparts, i.e., similar to the case of 1-DS. In addition, although the conductance shows (Table S2) the dependence of the conjugation pattern, it is not a pure length or torsion angle dependence (Figure S5). We have detected a conductance order of 1-DS < 2-DS < 3-DS < 4-DS for double-channel cyclophanes, while almost an opposite order (4-S < 3-S < 1-S < 2-S) is observed for the single-channel controls. An elaborate interpretation of the differences in conductance relies on the gating efficiencies, molecular lengths, torsion angles, and aromaticity, which lies outside the scope of this article. We have focused quantitatively on the promoting factor for the two-channel cyclophanes and the corresponding controls. For the BIPY2+-substituted 2-DS and 2-S, the promoting factor is 6.2, slightly larger than 4, perhaps as a consequence of the large torsional angle between the two pyridinium units (Figure S1). By contrast, in the case of 3-DS and 3-S, where smaller torsional angles and broken conjugation exists in the EaBIPY2+ backbone, the conductance enhancement is 22.4. When we consider 4-DS and 4-S with planar and highly conjugated EeBIPY2+ backbones, respectively, the two-channel conductance (Figure 3F) can be as high as 10−3.82±0.01 G0 compared with the relatively low single-channel conductance (Figure 3E) of 10−5.55±0.02 G0, leading to the largest promoting factor of all, namely, 53.7. All the promoting factors of the charged molecules are beyond the single-molecule superposition limit (Figure 3G), confirming that the charge transport mechanism through the double-channel junctions is controlled by the synergistic promoting effects of both chemical gating and CQI. To understand the origin of the conductance enhancement in the charged double-channel cyclophanes, we investigated theoretically the electronic structures of the isolated molecules and the quantum transport properties of the corresponding molecular junctions, formed by single-channel control and double-channel target molecules, connected to the Au electrodes (see Experimental Procedures and Figure S6 for details). As for the double-channel cyclophane, two LUMOs, one from each backbone, have (Figure 4A, inset) very close eigenenergies—the difference is below 10 meV—suggesting a weak chemical bonding effect between these two backbones; thus, the orbital states of each backbone can be effectively chemically gated. The first-principle calculations show (Figure 4A) the energy level shifting for the LUMO from −4.52 eV (single-channel) to −5.12 eV (double-channel). This energy shifting originates38Lo W.-Y. Bi W. Li L. Jung I.H. Yu L. Edge-on gating effect in molecular wires.Nano Lett. 2015; 15: 958-962Crossref PubMed Scopus (32) Google Scholar,39Meng L. Xin N. Hu C. Wang J. Gui B. Shi J. Wang C. Shen C. Zhang G. Guo H. et al.Side-group chemical gating via reversible optical and electric control in a single molecule transistor.Nat. Commun. 2019; 10: 1450Crossref PubMed Scopus (68) Google Scholar from the intrinsic chemical gating effect (electrostatic interactions) between two charged backbones, i.e., one backbone gates the other one and vice versa. In an attempt to investigate this gating effect further, we built (Figure 4B, inset) a model dimer system in the computer, consisting of two bipyridinium dications, separated by a distance, d. The calculation shows (Figure 4B) that the energy shifting—or the gating strength—ΔEL is approximately proportional to 1/d, an observation consistent with Coulomb's law, namely, V∝1/d, where V is the electrostatic potential. So the calculations verify the physical origin of the energy shifting. It is also observed that the gating effect in double-channel cyclophanes can shift the LUMO level—dominant conducting states—toward the Fermi level (EF) of the Au electrodes (Figure 4A), suggesting the preference of near-resonance charge transport and a lowering of the tunneling barrier, leading to a larger conductance according to the transition voltage spectroscopy model.38Lo W.-Y. Bi W. Li L. Jung I.H. Yu L. Edge-on gating effect in molecular wires.Nano Lett. 2015; 15: 958-962Crossref PubMed Scopus (32) Google Scholar,49Araidai M. Tsukada M. Theoretical calculations of electron transport in molecular junctions: inflection behavior in Fowler-Nordheim plot and its origin.Phys. Rev. B. 2010; 81: 235114Crossref Scopus (94) Google Scholar,50Gu C. Hu C. Wei Y. Lin D. Jia C. Li M. Su D. Guan J. Xia A. Xie L. et al.Label-free dynamic detection of single-molecule nucleophilic-substitution reactions.Nano Lett. 2018; 18: 4156-4162Crossref PubMed Scopus (36) Google Scholar Using DFT within the nonequilibrium Green's function (NEGF) technique,51Brandbyge M. Mozos J.-L. Ordejón P. Taylor J. Stokbro K. Density-functional method for nonequilibrium electron transport.Phys. Rev. B. 2002; 65: 165401Crossref Scopus (4541) Google Scholar,52Fan Z.-Q. Chen K.-Q. Negative differential resistance and rectifying behaviors in phenalenyl molecular device with different contact geometries.Appl. Phys. Lett. 2010; 96: 053509Crossref Scopus (164) Google Scholar we have also calculated the quantum transport properties of the molecular junction formed by the single-channel control and double-channel cyclophanes connected to the Au electrodes (see Experimental Procedures and Figure S7 for details). In the case of the double-channel cyclophanes, the chemical gating and CQI effects are expected to promote conductance in a synergistic manner. In an attempt to investigate these two effects separately, we built and studied (Figure 4C) another control system, i.e., the double-channel-cut (4-DS-cut) with ‒CH2‒ bridges severed in one of the backbones of 4-DS. In 4-DS-cut, since the electron cannot propagate through the severed backbone, the CQI disappears. The isolated charged segments, however, still provide effective gating effects to the other transport channel. In Figure 4D, we plot the calculated transmission spectra for three compounds: (1) the single-channel 4-S (black line), (2) the double-channel-cut 4-DS-cut (red dashed line), and (3) the double-channel 4-DS (blue line). We found that the gating effect makes the perturbed LUMO (p-LUMO) peak (dominating the transport) move toward the EF and increases the zero-bias conductance from 10−4.98 G0 (single-channel) to 10−3.75 G0 (double-channel-cut), with a promoting factor γG=16.9. Conversely, by comparing the transmission spectra of 4-DS (blue line) and 4-DS-cut (red dashed line) with the same gating effect and p-LUMO shifting position, we investigated the CQI independently, and found that the conductance is increased to 10−3.20 G0 (double-channel) with a promoting factor γQI=3.55, close to the ideal value of 4. Collectively, in the charged double-channel cyclophane 4-DS, the self-gating and CQI effect can promote synergistically the conductance, namely, G2-DS/G2-S=γGγQI=60, an observation consistent with the experimental value of 53.7. The quantitative values of the energy shifting, interference term, and increased conductance are sensitive to realistic contact geometries, solution environments, and energies of the link states, among others. Nevertheless, the basic and general physical mechanism and the features can be well revealed by the theoretical model analysis performed above. In summary, we evaluated the single-molecule conductance behavior in strongly Coulomb-interacting charged cyclophane junctions by combining chemical syntheses, STM-BJ measurements, and transport calculations. A self-gating effect contributes to the effective conductance of each channel and CQI enhances the total conductance in parallel two-channel intramolecular circuits, synergistically leading to a giant conductance that is more than 50-fold that of a control molecule with a single backbone. Transport calculations also show a characteristic left shift and upshift of the primary transmission resonances for the tetracationic double-channeled cyclophanes, thus indicating that the electronic structure of the cationic tunneling backbone plays a delicate, yet important quantitative role in determining the conductance value. The molecular design presented here provides a proof-of-principle for a self-gating enhanced quantum-interference-based approach to intramolecular circuits.