Promotion and suppression of single-molecule conductance by quantum interference in macrocyclic circuits

Single-molecule electronics is a sub-field of nanoelectronics, in which the individual devices are formed from single molecules placed between source and drain electrodes. During the past few years, both theory and experiment have demonstrated that that the flow of electricity through such devices is controlled by quantum interference (QI) between electrons passing from the source to the drain, but their future development is currently hampered by the difficulties in controlling such interference effects. Herein, we demonstrate a modular design of single-molecule circuits, which enable the construction of basic electronic components — namely, conductors or insulators — based on one tetracationic cyclophane platform. We demonstrate that the electron transport in cyclophane circuits is mediated by QI between channels formed from two lowest unoccupied molecular orbitals (LUMOs), while their highest occupied molecular orbitals (HOMOs) play no significant role. We further reveal that energy differences between these two LUMO channels induce constructive interference, leading to high conductance. By contrast, the phase differences between these LUMO channels result in destructive interference and a suppression in the overall conductance.


INTRODUCTION
A cornerstone of the molecular electronics 1-3 is the use of one single-molecule platform to construct 4-8 different electronic components. A common strategy is to manipulate the quantum interference 9-11 (QI) which takes place between molecular orbitals whose energies are close to the electrode Fermi energy, EF. It is, however, challenging to align [12][13][14][15][16] the energies of these frontier orbitals relative to the EF. The conductance of a ring-shaped mesoscopic structure can be manipulated 17,18 through QI between the de Broglie waves of electrons traversing the two branches of the loop structure -i.e., conductance is enhanced by constructive quantum interference (CQI) and suppressed when destructive quantum interference (DQI) occurs. The concept of using CQI and DQI to control the flow of electricity through single molecules was proposed theoretically [19][20][21][22][23] since 1988 and demonstrated experimentally 14,24,25 in 2011. The QI control strategy also applies [26][27][28] to large macrocyclic junctions, where the parallel transport paths have lengths much greater than the de Broglie wavelength of the tunneling electrons. In 2012, experimental evidence 15 was presented for a proposed superposition law 29 for these macrocyclic junctions, which predicts (equation 1) CQI for a cyclophane with two parallel electron transport channels, compared with its single-channel counterpart, i.e., one half of the cyclophane. However, as demonstrated below, DQI between two channels 30,31 , may result in significant modifications to this superposition law.
Herein, we describe the synthesis of a series of very weakly coupled two-channel cyclophanes to overcome this barrier. We demonstrate that both CQI and DQI can be achieved by manipulating the interplay between these two channels. In order to facilitate this tuning, electron withdrawing units have been included in the design of our molecules, leading to LUMO-dominated transport and the switching between CQI and DQI by simple manipulation (Figure 1A) of the LUMO on one of the two conducting channels. From a fundamental point of view, this investigation will also reveal that conductance ratios can be far higher or far lower than the value of 4 predicted by the single-molecule superposition law. 29 (C) Transmission spectra for two-and single-channel molecules with two identical conducting channels.
(D) Conductance ratio (ρ) of the total conductance of cyclophane circuits (GII) over the conductance of Channel 1 (GI).
(E) Schematic illustration showing the coherent tunneling process across an asymmetric twochannel circuit with energy differences between its two channels. The blue and red colours indicate the phases of the frontier molecular orbitals. Here the % is shifted downwards by 0.3 eV compared with & .
(F) Transmission spectra of the two-channel molecule (black) in (E) and its single-channel control molecules, namely Channel 1 (blue) and Channel 2 (red).
(G) Conductance ratio of the two-channel system over Channel 1 (blue), Channel 2 (red), and the average (black) of Channel 1 and 2, respectively.
(H) Schematic illustration showing a coherent tunneling process across an asymmetric two-channel circuit with phase differences between its two channels. The sign of − % is set opposite to that of − & , resulting in a phase exchange in HOMO-1 and LUMO orbitals. In this case, the new LUMO and LUMO+1 interfere constructively, while the HOMO and LUMO interfere destructively.
(I) Transmission spectra of the two-channel molecule (black) in (H) and its single-channel control molecules, namely Channel 1 (blue) and Channel 2 (red).
(J) Conductance ratio of the two-channel system over Channel 1 (blue), Channel 2 (red), and the average (black) of Channel 1 and 2, respectively. All the conductance is evaluated via = $ ( ( ).
When an electron tunnels ( Figure 1B) through a non-interacting two-channel cyclophane circuit present in the same molecule represented by Channel 1 shown in blue and Channel 2 shown in red in Figures 1A and 2A, QI takes place between the two channels. In order to appreciate the mechanism, a two-orbital Hückel tight-binding model can be utilized to describe each channel.
Starting with two identical channels, CQI is observed 15,30 ( Figure 1C) over the whole energy range in the HOMO-LUMO gap, as demonstrated by the higher transmission functions for twochannel systems, and specifically when a conductance ratio ρ = GII / GI = 4 is obtained ( Figure   1D), revealing that the total conductance obeys the superposition law 29 where GII and GI is the conductance of the two-channel target and single-channel control molecules, respectively. G1 and G2 is the effective conductance of each channel and GI = G1 = G2 where these two channels are identical.
As reported previously 13,[31][32][33][34][35] if the coupling between the molecule and electrode is weak, the effect of QI on charge transport can be predicted by examining Green's function G(E) of the isolated molecule. The transmission amplitude of an electron with energy E from site i to j is proportional to #,) ( ), which can be expressed as where ! and !3% are the LUMO and LUMO+1 MO energies, ∆= − ! and = . When electrons of energy less than ! propagate through two-channel cyclophanes, α > 1. Therefore, for such sub-LUMO energies when ! and !3% have the same sign, the term ; 5 + is non-zero and CQI occurs. In contrast, when 5 and 53% have opposite signs, 6 < vanishes at a specific energy if | 53% | > | ! | and DQI will occur. In contrast, when E lies between the LUMO and LUMO+1, α < 0. Therefore, for such supra-LUMO energies, equation (3) predicts that CQI occurs when ! and !3% have opposite signs, while DQI occurs when 5 and 53% have the same sign. This means that sub-LUMO CQI is accompanied by supra-LUMO DQI and vice versa.
In order to illustrate these QI features, an energy difference of two conducting channels is introduced by decreasing the on-site energy & of Channel 2 to -0.3, while maintaining % = 0 for Channel 1. A graphical representation of the resulting frontier MOs is shown in Figure 1E with blue and red colours depicting different phases of the bonding and anti-bonding orbitals for the two weakly-coupled channels. According to equation (3), sub-LUMO CQI is realized ( Figure 1F, blue shaded region below and close to LUMO level) and a conductance ratio ρ of ~4 is obtained (Figure   1g, blue shaded region) and as expected, this is accompanied by supra-LUMO DQI (Figures 1F   and 1G, pink shaded region) between the LUMO and LUMO+1. In order to illustrate the opposite case, a phase difference between the two channels is introduced by setting − % = −1.5 and − & = +1.5, leading to an exchange of the sub-LUMO QI features between LUMO and LUMO+1 ( Figure 1H). In this case, sub-LUMO DQI is present (Figures 1I and 1J, pink shaded region) in the two-channel cyclophanes, accompanied by supra-LUMO CQI, and therefore the conductances of the single-channel molecules are higher than those of the two-channel cyclophanes, resulting in a conductance ratio ρ ≪ 1. These results demonstrate that the two-channel cyclophane circuits have the potential to provide a versatile platform for tuning room-temperature QI-mediated electron transport features.

Preparation of Target and Control Compounds
In the case of the tetracationic cyclophanes 36 (Figure 2A The structural formulae of the two-channel tetracationic cyclophanes (n-D•4PF6, n = 1−6) and the single-channel control compounds (n-S•2PF6, n = 1−6) are shown in Figure 2A and Scheme S1. These cyclophanes -with one channel, an extended viologen unit 37 and the other channel, an identical or modified extended viologen unit, connected to common phenylene sulphide anchors at each end -can be synthesized in a straightforward two-step SN2 reaction. In this way, the cyclophane circuits can be constructed easily by changing the extended viologen building blocks, thereby providing a versatile means of building a variety of cyclophane circuits. We   (Figures S40-S42). Figure 2C shows typical singlemolecule breaking traces for the six cyclophane junctions -namely n-D 4+ (n = 1−6). Clear conductance plateaus, which are located ranging from 10 -3.8 to 10 -5.6 G0, can be attributed to the conductance signature of each molecule. We compiled ~5,000 traces into logarithmically binned one-dimensional (1D) and two-dimensional (2D) conductance histograms without data selection. Quantitatively, we obtain ( Figure 2F and Table S2) the most probable conductance values by fitting a Gaussian function. In good agreement with the theoretical predications (Figure 1 histograms across the series of the two-channel cyclophanes, we note that 3-D 4+ exhibits ( Figure   2G) a rather high and flat 2D conductance histogram, while there is a pronounced slope in the case of 4-D 4+ (Figure 2H) and 5-D 4+ (Figure 2I). The observed junction elongation -obtained by the stretching distance adding (Figures 2G-2I, insets) to ~0.6 nm Au snapping back distance 47corresponds well with the molecular length, i.e., ~2.0 nm as summarized in Figure S36.   The second way to obtain transmission curves is based on the synthetically realisable single-channel control molecules -namely, n-S 2+ (n = 1-6) ( Figure 4E). On comparing ( Figure   4F) the transmission curves of 3-D 4+ (Figure 4F, black curve) and 3-S 2+ (Figure 4F, red curve)

DFT-Based Theoretical Analysis
in the sub-LUMO region, we observed similar decreasing trends in the transmission coefficients for single-channel control molecules. The LUMO transmission resonances of 3-S 2+ were shifted upwards in energy for the simple reason that the electrostatic environment has been changed by removing one of the dicationic channels. The strong electrostatic interactions between charged parallel channels, however, serve as a chemical gate to promote 30 the effective conductance of each channel. In the case of 3-D 4+ (Figure 4F), the energy level shift of LUMOs increases the conductance of the two-channel cyclophane near the Au Fermi energy, leading to a total conductance promotion of ~60 (Figure 4G), a value much higher than ~4 caused by CQI ( Figure   4B). Such a promotion in total conductance, which originates from a combination of CQI and interchannel gating is also obtained ( Figure S51

Conclusion
We have demonstrated the ability to control the flow of electricity through two-channel

Lead Contact
Further information and requests for resources and reagents should be directed to and will be honored by the Lead Contact, Professor J. Fraser Stoddart (stoddart@northwestern.edu).

Materials Availability
This study did not generate new unique reagents.

Data and Code Availability
The data that support the findings of this investigation are available from the corresponding authors

Materials
The tetracationic cyclophanes were prepared -with 1,1′-thiobis [4-(bromomethyl)benzene] and extend bipyridine as the starting materials -by a sequence of two-step SN2 reactions in MeCN at 80 °C. Details of the synthesis and characterization can be found in the Supplemental Sections A-D, Schemes S1-S17 and Figures S1-S36.

STM-BJ Measurements
The single-molecule conductance measurements were performed using the STM-BJ technique with a home-built setup housed in a plastic glovebox filled with N2 at 298 K as described in a previous E is the conductance quantum, h is the Planck's constant, e is the charge on a proton and C is the Fermi energy.

SUPPLEMENTAL INFORMATION
Supplemental Information can be found online at https://doi.org/10.1016/j.matt.xxxx.