Conductance in a bis-terpyridine based single molecular breadboard circuit

We study conductance in a molecular breadboard junction accommodating up to 61 circuits and demonstrate switching between 4 conductance states.


S.1 Synthesis of TPI and associated molecules
All purchased chemicals and solvents were used as received.

Synthesis of 2,3'-bipyridine (R1)
To a solution of pyridin-3-ylboronic acid (676 mg, 5.5 mmol), Pd2(dba)3 (46 mg, 0.05 mmol), and PCy3 (34 mg, 0.12 mmol) in dioxane (13.35 ml), was added 2-chloropyridine (568 mg, 5 mmol), K3PO4 (1.80 g, 8.5 mmol) (solution in water 6.65 ml) successively under inert atmosphere. The resulting solution was stirred at 100 o C for 20 h. This reaction was carried out in a dry two neck round bottom flask. After the reaction mixture was filtered over a pad of silica gel and washed with ethyl acetate. The filtrate was concentrated under reduced pressure and the aqueous phase was extracted with ethyl acetate three times. The combined organic layers were dried over anhydrous sodium sulphate, concentrated under reduced pressure to get the crude 3 compound. Purification by silica gel column chromatography afforded orange oil. Spectral data is in accordance with the literature report 4 .

S.2. MCBJ experiments and data analysis
Details of our MCBJ set up and data analysis procedures were introduced and discussed in our previous publications given as ref. [5][6][7] All the measurements were performed by using 0.1mM concentration of target molecule in solvent 1,3,5-trimethylbenzene(TMB) +Tetrahydrofuran (THF) (4:1 v/v ratio).

Calibration of MCBJ conductance -distance curves and Snap back distance correction (Δzcorr):
The conductance-distance curves recorded by the MCBJ set-up were calibrated with using an assumption that the tunnelling decay is identical to that in a STM-BJ setup under the same experimental conditions (in presence of only solvent 1,3,5-trimethylbenzene(TMB) 4 +Tetrahydrofuran (THF) (4:1 v/v ratio) and decay constant observed in STM-BJ setup is (log(∆G/G0)/ ∆z = 5.5-6 nm -1 ). 7 In a break junction experiment, immediately after breaking a gold-gold contact, the conductance of the junction drops to approximately 10 -3 G0. Due to the so-called "snap-back" effect the gap between the two gold electrodes increases instantaneously to a certain distance Δzcorr. The snapback distance is estimated, based on the analysis of the tunneling tail of conductance distance curves (recorded in presence solvent only), typically in the range between 10 -3 G0 and 10 -6 G0, which is estimated as Δzcorr = 0.5 ± 0.1 nm ( Supplementary Fig. S1). 5,7,8 To estimate the most probable absolute electrode separation (zi* = Δzi*+Δzcorr) we used snap back distance correction.

Conductance measurements of individual molecular units (R1 and R2):
We measured the conductance of R1 and R2 molecules under similar conditions used for TP1. R1 molecule showed two distinct conductance features (High (H) and Low (L)) in 1D and 2D conductance

S.3 Geometry optimizations and conformational sampling for TP1
As the molecule is expected to exhibit significant conformational flexibility in terms of ring rotations, we considered multiple geometries of TP1 which differ in terms of their relative orientations of the pyridine rings in our calculations. Different conformations of TP1 were manually drawn wherein each aromatic ring was allowed to adopt one of two conformations, either in plane (P) or orthogonal (O) to, relative to its neighboring rings (Fig. S4A). This procedure resulting in 24 distinct starting geometries, each of which were optimized in Gaussian 09 using DFT with a B3LYP exchange correlation functional and a 6-31G* basis set. 9 The optimization yielded 18 unique geometries. Examples of two optimized geometries starting from We assume only two electrode circuits, wherein each electrode can make contact with upto three atoms within a terpyridine arms or across the terpyridine atoms (A). Some examples of single and multi-terminal circuits for the TP1 molecular breadboard are also shown (B).
ring circuits within each terpyridine arm (I), 3-ring circuits across each terpyrdine arm (II), 3ring circuits in the TP1 core (III), 4-ring circuits spanning the core and one of the terpyridine arms (IV), and 5-ring circuits spanning both terpyridine arms of TP1 (V). Circuits II and V show the largest fluctuations in terminal N-N distances. The terminal N-N distance for circuit III does not vary at all across the 18 optimized geometries.

S.4 Enumeration of TP1 circuits
In the result section we presented an enumeration of TP1 circuits. Here we elaborate upon this enumeration in more detail. Essentially we have a total of 6 nitrogen positions, three on the left terpyridine arm (C1,C2,C3) and three on the right terpyridine  ) at which the molecule can be anchored to the electrodes. We consider only two electrode circuits wherein each electrode contacts distinct sets of atoms either within each terpyridine arm or across two terpyridine arms (Fig. S6A)). If we assume that each electrode can 9 contact between 1-5 nitrogen atoms a total of 301 circuits can be generated. These comprise Here we express contact configurations in terms of the number of contacts (M, N) made by the two (L/R) electrodes as ML-NR, (where M,N=1,2,3). However, not all these configurations can be accessed within a break-junction setup. If we apply the more conservative constraint that a single electrode cannot contact both terpyridine arms simultaenously i.e each electrode can contact upto a maximum of three nitrogen atoms which lie within a single terpyrdine arm. Based on the above assumptions each electrode can contact seven combinations of atoms belonging to These assumptions lead to the enumeration provided in the main manuscript in Table 1. Examples of these circuits are shown in Fig. S6.

S.5 NEGF Transport Calculations
Within the NEGF framework, 10 the molecular junction is partitioned into three subsystems ( Fig.   1): a device region (the isolated molecule) and two structure-less electrodes. The Green's function describes the molecule and its interactions with the electrodes: H is the Hamiltonian of the isolated molecule provided by the INDO/s calculations. The selfenergies  describe the broadening and shifts in molecular energies induced by the right (R) and left (L) electrodes. The transmission coefficient sums over all pathways for charge transport at energy E from one electrode to the other: The broadening matrix:  = i [ - + ] is proportional to the imaginary part of the self-energy. We assumed that the TP1 molecule is connected to the electrodes through the nitrogen atoms of the flanking terpyridine arms (Fig. 1A). We adopt the weak coupling limit, discussed extensively in Here, i and j are atomic orbital indices and N is the nitrogen-gold coupling parameter set to 0.1 eV. We note that all nitrogen atoms are not equally accessible to electrode and assume a molecule-electrode model described in section S.7 below. We neglect the real part of the selfenergy in our calculations. In the linear response regime, the conductance is given by the Landauer expression: The Fermi functions Where is the Boltzmann constant and temperature =300 K. For tunneling charge transport, the conductance is dominated by the contribution at the Fermi energy, and we compute the tunneling conductance: The Fermi energy EF is a free parameter set to different values as described in the methods section of the main manuscript and section S.9 below. V is the applied potential bias, taken as 100 mV in the calculations here.

S.6.Decomposition of multi-terminal currents into single terminal currents
The computed conductance for the different circuit within the TP1 breadboard in Fig. 4  . We now show that the Kirchoff`s parallel circuit rule will apply in general for circuit decompositions of the type shown in Fig. S7 for the TP1 molecular breadboard. Using eqns S2 and S6, we write the near zero bias current in any general circuit within a molecular breadboard containing N atoms as: Where, we assume that the left and right electrode contact n, and m sets of distinct atoms (n+m  Here the trace is carried out in the atomic basis where the matrices of Green`s functions are not diagonal. Explicit evaluation of the trace yields. Thereby verifying Kirchoff`s rule for parallel circuits in molecular breadboards. Note that in deriving eqn. S9, we assumed conditions of a near zero bias tunneling current, where: 1) the current is dominated by the transmission at Fermi energy (eqn. S6), and 2) that the diagonal terms of the Green`s function satisfy: ( − − ∑(Γ + Γ )) −1 ≈ ( − ) −1 . Both conditions are satisfied when the tunneling barrier for tunneling is large relative to the broadening of the molecular electronic energies introduced by the electrodes. The conductance data in Fig. 4 for multi-terminal and single-terminal circuits can be thus be rationalized under these conditions wherein all multi-terminal circuits within the breadboard can be decomposed into constituent single-terminal circuits. If one constituent single terminal current is dominant (much larger than other currents), the conductance from the multi-terminal circuit will be totally determined by that single channel circuit as observed for the top two conductance bands in Fig. 4. For the specific example in Fig. S7, the current Id of the single terminal core ring circuit is the dominant current fully determining the conductance of the multi-terminal 3L-3R circuit.

S.7 Molecule-Electrode coupling model
In order to account for the different electrode accessibility of nitrogen atoms in TP1, we assumed We assumed a molecule electrode electronic coupling decays exponentially with respect to distance of each nitrogen atom. Thus, relative to the peripheral atoms, the central nitrogen atoms of each terpyridine arm should be further away from the electrode tips leading to a screening of electronic couplings between core nitrogen atoms and the electrode. We thus assumed peripheral / core = exp(*deff), where =3.0 Å -1 is the decay of the electronic coupling through vacuum. The effective screening length (deff ) was defined as the distance between the central nitrogen atom and the centre of mass of the peripheral nitrogen atoms for each terpyridine arm of TP1 (Fig.   S8). We estimated deff ~ 1.6 Å (Fig. S8), leading to an electronic coupling attenuation ratio peripheral /core = 116.  Fig. S9. We varied the ratio of peripheral to core nitrogen electrode coupling parameters Peripheral/Core to find the optimal fit to the experimental results. The data in Fig. S9 shows that the fits are sensitive to the ratio varied over two orders magnitude and the best fits were obtained for Peripheral / Core ~100. This independently corroborates the electronic coupling screening estimate extracted from the analysis of TP1 structures and the fit reported in the main manuscript is for Peripheral / Core ~116 (the value obtained from our structural analysis).

S.8 Electron vs hole dominated transport regimes for the TP1 breadboard
In the NEGF framework outlined above to compute conductance for the TP1 breadboard, the Green`s function in eqn. S1 is computed from the electronic structure of TP1 in isolation, while the effect of the electrodes is incorporated phenomenologically through the broadening function.
In this framework, the Fermi energy EF of the electrode is a variable parameter which can be set to a suitable value lying within the band gap of the organic system (   . The data in S10 show that the fits are sensitive to the ratio Peripheral / Core varied over two orders magnitude and the best fits were obtained for Peripheral / Core =100.

S.9 Experimental and Computational Tunneling decay constants for the TP1 breadboard
In this section, we estimate the tunneling decay constant () for the TP1 breadboard from theory and experimental data:  2) From the computed conductance of the dominant 2-5 ring circuits assigned to the conductance plateaus in Fig 6. In figure S11B we plot the average conductance and standard-deviation for the 2-ring, meta-3-ring, para-3-ring, 4-ring, and 5-ring circuits at the corresponding electrode separations at which they dominate. By fitting the conductance data showed in Fig. 11B, we estimated conductance decay constant as Theory = 3.8 nm -1 . Figure S12: Transmission for the five dominant circuits assigned to conductance plateaus in Fig 6. Calculations were carried out for Peripheral / Core ~116 to reflect the data in Fig 6.