Synthetic Control of Quantum Interference by Regulating Charge on a Single Atom in Heteroaromatic Molecular Junctions

A key area of activity in contemporary molecular electronics is the chemical control of conductance of molecular junctions and devices. Here we study and modify a range of pyrrolodipyridines (carbazole-like) molecular wires. We are able to change the electrical conductance and quantum interference patterns by chemically regulating the bridging nitrogen atom in the tricyclic ring system. A series of eight different N-substituted pyrrolodipyridines has been synthesized and subjected to single-molecule electrical characterization using an STM break junction. Correlations of these experimental data with theoretical calculations underline the importance of the pyrrolic nitrogen in facilitating conductance across the molecular bridge and controlling quantum interference. The large chemical modulation for the meta-connected series is not apparent for the para-series, showing the competition between (i) meta-connectivity quantum interference phenomena and (ii) the ability of the pyrrolic nitrogen to facilitate conductance, that can be modulated by chemical substitution.


Details on STM-BJ Experiments
The instrument used in the experiment has been described in detail elsewhere. 8,9 In brief, we used a Keysight 5500 SPM, modified with a home-built 4-channel transimpedance amplifier based on the design proposed by Mészáros et al. 10  separation trace, and thousands of these are acquired and compiled into the conductance histograms presented in the main paper. A gaussian fit of the main peak at was used to extract the conductance value from the histogram. < 0 The same traces are aligned to the rupture of the metallic nanocontact and used to generate 2D conductance -electrode separation density plots ( Figure S1 -S8), which show the evolution of conductance as the two electrodes are pulled apart during a STM-BJ experiment.
The meta compounds 1M -5M feature sloped conductance features in the density plots ( Figures S1-S5), but the variations in conductance with the substituents on the pyrrolic N are clear. Sloped regions in the 2D density maps have been found in other quantum interference systems. 11,12 The proposed explanation was found in a stronger T(E) dependence on energy, combined with small changes in the workfunction arising from the varying electrodes shape and molecule-electrode binding mechanisms sampled in a break-junction experiment. 11 The experimental break-off distance of ~3-4 Å (end of the high-count area in the 2D density maps) is consistent with molecular length when accounting for an electrode "snap-back" of approximately 5 Å, 13 and with previous measurements performed on 3,3'-bipyridine, 14 The density plots for the para compounds 1P, 2P and 5P ( Figure S6-S8), on the other hand, showed a more plateau-like behaviour, and the bistable conductance behaviour seen with 4,4'-bipyridine 15 is retained in these planarized analogues.

Spectroscopic Data
UV-Vis data was acquired on a Perkin Elmer λ25 spectrometer, in the region 190-500 nm in dry acetonitrile (Sigma-Aldrich spectrophotometric grade), using a 1 cm quartz cell, at room temperature.

Optimised DFT Structures of Isolated Molecules
Using the density functional code SIESTA 16,17 the optimum geometries of the isolated molecules (1M -5M, 1P, 2P and 5P) were obtained by relaxing the molecules until all forces on the atoms were less than 0.05 eV / Å as shown in Figure   S17. A double-zeta plus polarization orbital basis set, norm-conserving pseudopotentials, an energy cutoff of 200 Rydbergs defined the real space grid were used and the local density approximation (LDA) was chosen to be the exchange correlation functional. We also computed results using GGA and found that the resulting transmission functions were comparable with those obtained using LDA.

Binding energy of molecules on Au
To calculate the optimum binding distance between pyridyl anchor groups and Au(111) surfaces, we used DFT and the counterpoise method, which removes basis set superposition errors (BSSE). The binding distance d is defined as the distance between the gold surface and the N terminus of the pyridyl group. Here, compound 2P is defined as entity A and the gold electrode as entity B. The ground state energy of the total system is calculated using SIESTA and is denoted . The energy of each entity is then calculated in a fixed basis, which is achieved using ghost atoms in SIESTA. E AB AB Hence, the energy of the individual 2P in the presence of the fixed basis is defined as and for the gold as . The E AB A E AB B binding energy is then calculated using the following equation: We then considered the nature of the binding depending on the gold surface structure. We calculated the binding to a Au pyramid on a (111) surface with the nitrogen atom binding at a 'top' site and then varied the binding distance d.
Figure S18 (left) shows that a value of d = 2.3 Å gives the optimum distance, at approximately 0.5 eV. As expected, the pyridyl anchor group binds favourably to under-coordinated gold atoms.

Optimised DFT Structures of Compounds in Their Junctions
Using the optimised structures and geometries for the compounds obtained as described in

Electron transfer
It is believed that the pyrrolic N atom for each compound (Figures S19-S26)   The net electron gain calculated by the three methods was plotted against conductance of 1M -5M ( Figure S27a As can be observed in Table S2 and in Figure S27, the changes in net electron gain are only minute (< 10%), but they contribute to a substantial change in the charge transport properties of the molecular junction. The overall results further stress the importance of small changes in the electronic structure of matter at the nanoscale that can be greatly amplified by quantum effects, resulting in large modulations of their physical properties.

HOMO-LUMO gaps
The calculated and optically measured HOMO-LUMO gaps are listed in Table S3. Theoretical gaps were calculated for isolated molecules and when the compounds are in the junctions, the gap between their HOMO and LUMO transmission resonances are quoted. As shown by the third and fourth columns in Table S3, isolated gaps for compounds 1M -5M, 1P, 2P and 5P are larger than the gaps between the transmission resonances. This is because the latter are shifted by the real part of the self-energy of the contact to the leads, reflecting the fact that the system is more open when contacted to electrodes. To obtain a more accurate HOMO-LUMO gap, we employed a scissor operator (discussed below).

Transport Calculations without Scissor Corrections
The transmission coefficient T(E) was calculated for compounds 1M -5M ( Figure S28) and 1P, 2P and 5P ( Figure   S29). In the absence of a scissor operator, the LUMO resonance is predicted to be pinned near the Fermi Level of the electrodes, resulting in the substituent effect on molecular conductance being washed out. As shown in Table S3 there is more than 1 eV of difference in the values of theoretical and optical bandgap, which is consistent with the fact that DFT is known to underestimate its value. 21

Transport Calculations with Scissor Corrections
As mentioned above, DFT underestimates the HOMO-LUMO gap and from Table S3 it is clear that the calculated gaps are less than the optically-measured gaps. As discussed in the main text, to overcome this deficiency a scissor correction [23][24][25] is performed, by diagonalizing the molecular sub-matrix of the full Hamiltonian, then shifting the eigenvalues below and above the Fermi energy such that the new HOMO-LUMO gap matches the experimental value of the isolated molecule. Finally, the diagonalized matrix is transformed back to the original basis to obtain the corrected full Hamiltonian.
In addition to the calculations shown in the main text for compounds 1M -5M (Figure 4a), the same transport code and scissor operator was applied to the para 2,7-diazacarbazole 1P, 2P and 5P. As can be observed in Figure S30, DFT predicts a much smaller effect on T(E) at the Fermi Level in these compounds, respective to their meta analogues, which results in the conductance being independent of the N-aryl substituent in pyrrolodipyridine.

Alternative binding geometry in compounds 5M and 5P
As discussed in the main paper, compounds 5M and 5P have a pyridyl substituent on the pyrrolic N, that can be an alternative electrode-binding site. In order to establish which possible geometry is more likely to be probed during an STM-BJ experiment, we performed DFT transport calculations. As can be observed in Figure S31, in both 5M and 5P the higher-conducting geometry is the one where the two electrodes are contacted to the two ends of the pyrrolodipyridine scaffold, and junctions assembled through the "free"  Figure S33.