Elena
Gorenskaia‡
^{a},
Jarred
Potter‡
^{a},
Marcus
Korb
^{a},
Colin
Lambert
*^{b} and
Paul J.
Low
*^{a}
^{a}School of Molecular Sciences, University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6026, Australia. E-mail: paul.low@uwa.edu.au
^{b}Department of Physics, University of Lancaster, Lancaster LA1 4YB, England, UK. E-mail: c.lambert@lancaster.ac.uk
First published on 6th April 2023
The quantum circuit rule (QCR) allows estimation of the conductance of molecular junctions, electrode|X-bridge-Y|electrode, by considering the molecule as a series of independent scattering regions associated with the anchor groups (X, Y) and bridge, provided the numerical parameters that characterise the anchor groups (a_{X}, a_{Y}) and molecular backbones (b_{B}) are known. Single-molecule conductance measurements made with a series of α,ω-substituted oligoynes (X-{(CC)_{N}}-X, N = 1, 2, 3, 4), functionalised by terminal groups, X (4-thioanisole (C_{6}H_{4}SMe), 5-(3,3-dimethyl-2,3-dihydrobenzo[b]thiophene) (DMBT), 4-aniline (C_{6}H_{4}NH_{2}), 4-pyridine (Py), capable of serving as ‘anchor groups’ to contact the oligoyne fragment within a molecular junction, have shown the expected exponential dependence of molecular conductance, G, with the number of alkyne repeating units. In turn, this allows estimation of the anchor (a_{i}) and backbone (b_{i}) parameters. Using these values, together with previously determined parameters for other molecular fragments, the QCR is found to accurately estimate the junction conductance of more complex molecular circuits formed from smaller components assembled in series.
The conceptual construction of oligoynes X-{(CC)_{N}}-Y from a backbone composed of any number of alkyne moieties (N), capped by terminal groups capable of anchoring the molecule to electrode surfaces (X, Y) allows molecular circuits to be fashioned in a manner that highlights simple chemical structure–electrical property relationships. As such, the simplicity of the chemical structures of oligoynes make them ideal objects through which to explore emerging concepts of molecular quantum circuit rules (QCRs),^{11–13} that describe the molecular junction as a series of weakly coupled scattering regions, and apply to non-resonant tunnel junctions (i.e. those in which the Fermi energy of the electrodes falls near the middle of the transport resonances in the transmission function arising from the HOMO and LUMO). For a molecule of general form X–B–Y (where X and Y are the anchor groups that bind the molecule to the left and right electrodes, and B is the molecular backbone Fig. 1), the QCR writes the conductance of the junction, G_{XBY}, in the form
(1) |
Fig. 1 A cartoon of a molecular X–B–Y junction with conceptual partitioning into anchor groups (X and Y) and the molecular backbone (B). |
We report here a systematic study of a series of oligoyne-based molecular wires, X-(CC)_{N}-X, featuring a range of anchor groups (X = 4-thioanisole (C_{6}H_{4}SMe, 1), 5-(3,3-dimethyl-2,3-dihydrobenzo[b]thiophene) (DMBT, 2), 4-aniline (C_{6}H_{4}NH_{2}, 3), 4-pyridine (Py, 4)) and composed of different numbers of alkyne moieties in the backbone (N = 1 (a), 2 (b), 3 (c), 4 (d)) (Chart 1). The single-molecule conductance of each of these compounds, G, has been determined using the scanning tunnelling microscope based-break junction (STM-BJ) technique.^{16} The trends in molecular conductance across the series have been analysed in relation to the number of alkyne repeat units (N) in the backbone and the chemical nature of the anchor group, revealing the expected exponential decay of G with N. Extrapolation of the ln(G) vs. N plots to N = 0 allows estimates of the conductance of the various anchor groups from experimental data, which in turn can be used to determine the a_{i} parameters for the anchor groups used in this study. In addition, the experimental data and the algebraic relationships of eqn (1) support further partitioning of the anchor and bridge into a series of smaller scattering regions. Therefore, from the QCR parameters of smaller ‘components’, estimates of conductance of quite complex molecular ‘circuits’ can be made (e.g.5–8, Chart 1). Despite the simplicity of the QCR, these estimates are found to be surprisingly accurate when tested against experimental data.
Compound | log(G/G_{0})^{a} | σ ^{ } | log(G^{th}/G_{0})^{c} | l ^{ } ^{,} ^{ } (Å) | L ^{ } (Å) | Δz*^{g} (Å) | Δz* + z_{corr}^{h} (Å) | Tilt angle θ^{i} (°) | JFP^{j} (%) | ln(G^{N}_{2C})^{k} | β ^{N} per unit –(CC)–^{l} |
---|---|---|---|---|---|---|---|---|---|---|---|
a Experimentally determined most probable molecular conductance from STM-BJ measurements in mesitylene; the error range is based on the standard error in the Gaussian fitting of the 1D conductance histograms, reflecting uncertainty in the estimated mean. For different expressions of experimental conductivity (ln(G) and G (nS)) see ESI, Table S1†. b Standard deviation from the statistical spread of the points forming the conductance histogram peak, indicating distribution of data around the mean. c Molecular conductance calculated from eqn (1). d Crystallographically determined S⋯S or N⋯N separation. e S⋯S or N⋯N separation determined by Gaussian software. f The maximum possible length of the corresponding junction (L = l + 2d, where d is the distance between the anchor atom and the centre of the contacting gold atom of an idealised pyramidal-shaped electrode: a Au–S, d = 0.24 nm; b Au–S, d = 0.24 nm; c Au–N, d = 0.24, d Au–N, d = 0.21 nm). g Experimentally determined break-off distance. h Break-off distance allowing for snap-back of the gold electrodes (0.5 nm).^{28} i Calculated from cos^{−1}((Δz* + z_{corr})/L). j Proportion of current–distance curves containing the featured molecular plateau. k Conductance of both binding groups, ln(G^{N}_{2C}), obtained from the intercept of the ln(G) vs. N plot at N = 0. l The β^{N} values were obtained from the slope of the plot of conductance vs. number units (N = 1–4 for 1a–d, 3a–d, 4a–d, and N = 0–4 for 2, 2a–d) in the molecular backbone (Fig. 2). | |||||||||||
1a^{14} | −3.1 ± 0.1 | 0.25 | −3.13 | 13.20^{d} | 18.00 | 6.5 | 11.5 | 50.3 | 100 | 4.71 ± 0.17 | 0.55 ± 0.07 |
1b | −3.25 ± 0.01 | 0.53 | −3.35 | 15.72^{d} | 20.52 | 9.1 | 14.1 | 55.5 | 100 | ||
1c | −3.44 ± 0.01 | 0.54 | −3.57 | 18.33^{d} | 23.13 | 11.5 | 16.4 | 54.7 | 100 | ||
1d | −3.84 ± 0.01 | 0.34 | −3.92 | 20.87^{d} | 25.67 | 13.0 | 18.0 | 45.5 | 100 | ||
2a^{14} | −2.7 ± 0.1 | 0.20 | −2.73 | 13.13^{d} | 17.93 | 4.5 | 9.5 | 58.0 | 100 | 5.59 ± 0.1 | 0.70 ± 0.05 |
2b | −3.10 ± 0.01 | 0.40 | −2.95 | 15.66^{d} | 20.46 | 8.1 | 12.1 | 53.7 | 100 | ||
2c | −3.34 ± 0.01 | 0.30 | −3.17 | 18.19^{e} | 22.99 | 11.6 | 16.6 | 43.9 | 100 | ||
2d | −3.74 ± 0.01 | 0.33 | −3.52 | 20.79^{d} | 25.59 | 13.3 | 18.3 | 44.4 | 100 | ||
3a^{14} | −3.2 ± 0.1 | 0.40 | −3.19 | 12.48^{d} | 17.28 | 3.5 | 8.5 | 60.5 | 90 | 4.60 ± 0.23 | 0.56 ± 0.09 |
3b | −3.31 ± 0.01 | 0.35 | −3.41 | 14.95^{d} | 19.75 | 6.4 | 11.4 | 54.8 | 90 | ||
3c | −3.57 ± 0.01 | 0.48 | −3.63 | 17.42^{e} | 22.22 | 9.2 | 14.2 | 50.3 | 90 | ||
3d | −3.91 ± 0.01 | 0.40 | −3.98 | 20.08^{d} | 24.88 | 11.1 | 16.1 | 49.7 | 90 | ||
4a | −3.56 ± 0.01 | 0.35 | −3.47 | 9.68^{d} | 13.88 | 4.2 | 9.2 | 48.5 | 90 | 3.68 ± 0.11 | 0.53 ± 0.05 |
4b | −3.77 ± 0.01 | 0.24 | −3.69 | 12.23^{d} | 16.43 | 7.5 | 12.5 | 40.5 | 90 | ||
4c | −3.95 ± 0.01 | 0.39 | −3.91 | 14.82^{d} | 19.02 | 9.1 | 14.1 | 42.2 | 90 | ||
4d | −4.19 ± 0.01 | 0.58 | −4.26 | 17.38^{d} | 21.58 | 12.5 | 17.5 | 53.8 | 90 | ||
5 | −3.39 ± 0.01 | 0.55 | — | 12.32^{e} | 17.12 | 5.1 | 10.1 | 53.9 | 100 | — | — |
6 | −4.22 ± 0.01 | 0.35 | — | 18.91^{e} | 23.71 | 8.6 | 13.6 | 55.0 | 80 | — | — |
7 | −4.35 ± 0.01 | 0.46 | — | 21.32^{e} | 26.12 | 14.7 | 19.7 | 41.0 | 100 | — | — |
8 | −4.77 ± 0.01 | 0.78 | — | 25.44^{e} | 30.24 | 19.8 | 24.8 | 34.9 | 100 | — | — |
Molecular conductance data for 1a–d–4a–d are summarised in Table 1, with plots of typical conductance (G) vs. displacement (s) traces given in Fig. S1–S5.† From these traces, 1D conductance histograms were constructed from all data (ca. 2000 traces) with bin width of Δlog(G/G_{0}) of 0.01, and normalised to the number of traces as counts/trace. The 1D histograms display prominent peaks, which are fitted to Gaussian-shaped curves in order to arrive at the most probable conductance values (Table 1). The G vs. s data were combined to give 2D conductance-relative displacement heat-maps constructed from all traces, plotted such that the zero displacement coincides with the point of cleavage of the last Au–Au contact in the metallic junction (Fig. S1–S5†).
As would be expected based on a simple tunnelling model, for each series of compounds with the same anchor group, and for data collected in the same solvent to avoid convoluting the effects of tunnel length with solvent gating phenomena,^{29} the conductance features shift to lower values as the number of CC moieties, and hence the molecular length, increases i.e. GXa > GXb > GXc > GXd (Table 1). The single molecule conductance is also found to depend on the anchor group, with the DMBT-functionalised compounds giving rise to higher conductance than the comparably structured members of the thioanisole, aniline or pyridine family (Table 1). Both features are clearly revealed by the 2D heat maps, with the high data density regions shifting to lower conductance regions with increasing relative displacement, and trending with the anchor group (i = a–d) such that G2i > 1i > 3i > 4i.
The rigid, linear structure of oligoynes and homologous chemical structure of the backbone makes compounds such as 1a–d–4a–d ideal for studies of molecular junction conductance vs. length dependence, the number of alkyne repeat units and the nature of the anchor group.^{1,8,25,30,31} From a tunnelling model, the molecular conductance (G) is expected to display an exponential decay with junction length, L, according to the relationship
G = G_{2C}e^{−βL} | (2) |
The linear fit of conductance vs. length data according to eqn (2) has often been used to explore and test coherent tunnelling transport models of molecular conductance for various combinations of anchor group and molecular backbones. However, the correlation of the experimentally determined break-off distance (after allowing for the electrode snap-back) which corresponds to the tip–substrate separation at point of cleavage of the molecular junction and the charge transport distance through the length of the molecule is convoluted by the contact angle imposed by the chemical nature of the interaction between the anchor group and the electrode surface(s) (Fig. S6† and Table 1). The transport distance L (i.e. the length of the tunnel barrier represented by the geometry of the molecular junction) is therefore often estimated as the crystallographically determined or geometry optimised distance between the anchor atoms, l. Some authors have suggested that the true junction length should also include the anchor atom – gold distance, d (i.e. L = l + 2d), where for the anchor groups used here, d = 0.24 nm (series 1, Au-SMe;^{32} series 2, Au-(S)DMBT;^{32} series 3, Au-NH_{2}^{25}) or 0.21 nm (series 4, Au-(N)Py;^{25}Table 1). Regardless of the method of estimation, the transport distance necessarily reflects the structures of both anchor groups and the bridge. Therefore, the decay parameter β reflects the specific combination of anchor group and backbone structure in the molecular series under investigation, and given this term is also solvent dependent,^{29} it has limited use as a predictive or design tool.
Alternatively, structure–property relationships contained in the conductance data can be interpreted not as a function of junction length, but in terms of the number of repeat units in the molecular backbone, N. In this description, eqn (2) is re-expressed as
G = G^{N}_{2C}e^{−βNN} | (3) |
In eqn (3), the β^{N} values reflect conductance decay per repeat unit in the bridge (i.e. the number of –{CC}– moieties in the case of the oligoynes 1–4, N) whilst G^{N}_{2C} reflects the inherent conductance through both anchor groups in the junction in contact with the electrodes (as distinct from G_{2C} which describes the conductance through the two anchor atom-gold contacts). For the compounds 1a–d–4a–d, the attenuation factors β^{N} (determined from the slope of a linear fit to the ln(G) vs. N data, Fig. 2) are determined to be 0.55 per unit (series 1, C_{6}H_{4}SMe anchors), 0.70 per unit (series 2, DMBT anchors), 0.56 per unit (series 3, C_{6}H_{4}NH_{2} anchors), and 0.53 per unit (series 4, Py anchors) in mesitylene. These values are consistent with the range of previously reported decay constants of oligoynes featuring various anchor groups,^{1,8,25,29,31} and back calculation gives excellent agreement with the individually determined experimental conductance values (Table S2 and Fig. S7†).
Fig. 2 Plot of the most probable experimental conductance values ln(G) versus number of units –{CC}–, N, from STM-BJ measurements in mesitylene. |
The term associated with molecular conductance through both anchor groups (G^{N}_{2C}) can be obtained from an extrapolation of the ln(G) versus N plots to N = 0 (Fig. 2 and Table 1). In the present context, the conductance at N = 0 (i.e. G = G^{N}_{2C}) reflects the molecular conductance of the biaryl compounds 4,4′-bis(methylthiol)biphenyl (1),^{33–36} 5,5′-bis(3,3-dimethyl-2,3-dihydrobenzo[b]thiophene) (2, this work, Fig. S8 and Table S3†), 4,4′-diaminobiphenyl (3),^{36,37} and 4,4′-bipyridine (4).^{38–41} Indeed, the values of G^{N}_{2C} obtained from extrapolation are in excellent agreement with the available experimental molecular conductance data from the authentic biaryl compounds 1–4 (Table 2). The decay parameter, β^{N}, and the conductance term, G^{N}_{2C}, provide metrics that describe the properties of the bridge and the left and right anchor groups, respectively. As values for β^{N} and G^{N}_{2C} can be evaluated from the slope and intercept of a linear plot of ln(G) vs. N constructed from a small number of experimental measurements, eqn (3) allows, in principle, the molecular conductance of any member of a homologous series of wire-like molecules to be determined in a given solvent, assuming there is no change in conductance mechanism for the bridge length considered.^{42–44}
Compound | log(G/G_{0}) (solvent)^{a} | log(G^{N}_{2C}/G_{0}) | 2a_{X} |
---|---|---|---|
a Experimentally determined single molecule conductance (TCB = 1,2,4-trichlorobenzene; TMB = 1,3,5-trimethylbenzene (mesitylene)). | |||
−2.80 (TCB)^{33} | −2.84 | −2.82 | |
−2.90 (TCB)^{34} | |||
−2.89 (TCB)^{35} | |||
−2.75 (TCB)^{36} | |||
−2.56 (TMB) | −2.46 | −2.42 | |
−2.95 (TCB)^{36} | −2.89 | −2.88 | |
−2.85 (TCB)^{37} | |||
−3.30 (TCB)^{38} | −3.29 | −3.16 | |
−3.30 (unknown)^{39} | |||
−3.35 (TCB)^{40} | |||
−3.30 (TCB)^{41} |
The quantum circuit rule (eqn (1)) provides a complementary approach to rationalising structure–property relationships in oligoyne molecular wires and predicting conductance properties from independent and transferrable parameters associated with the anchor (a_{X}, a_{Y}) and bridge (b_{B}) components that, together, comprise the molecular structure (Table 3 and Fig. 3).^{12}
Fig. 3 A simple schematic of a molecular junction formed from 1d, illustrating the conceptual partitioning of the molecule into anchor groups and backbone components. |
Anchor group | ||||
---|---|---|---|---|
a _{X}^{12,14} | −1.41 | −1.21 | −1.44 | −1.58 |
Backbone | |||
---|---|---|---|
b _{B}^{15} | −1.37 | −1.03 | −0.74 |
In order to determine or verify the various anchor group parameters, a_{X}, it is helpful to consider the polyyne molecules 1a–d–4a–d in terms of the general structural description X-(CC)_{N}-X, where N has the usual meaning of number of CC repeat units and X represents the anchor group (X = 4-thioanisole (C_{6}H_{4}SMe, 1), 5-(3,3-dimethyl-2,3-dihydro benzo[b]thiophene) (DMBT, 2), 4-aniline (C_{6}H_{4}NH_{2}, 3), 4-pyridine (Py, 4)). In the case N = 0 described above (i.e. b_{B} = 0) the QCR (eqn (1)) predicts
(4) |
There is excellent agreement between the experimentally determined values of molecular conductance of the biaryls X–X (1–4, Table 2), the previously determined anchor parameters, a_{X} (Table 3), and the value obtained from extrapolation of the data shown in Fig. 2 (Table 2). This excellent agreement between experiment and the predictions of the QCR is no doubt due in part to the non-planar structure of biaryls, which limits conjugation between the two rings and allows approximation of the structure as two weakly coupled scattering sites.
From the QCR (eqn (1)), the a_{X} parameters (Table 3) and the experimental conductance data presented as log(G/G_{0}) (Table 1), the backbone parameters, b_{B}, for the various homologous members of the polyyne series investigated here (b_{CC}, b_{CCCC}, b_{CCCCCC} and b_{CCCCCCCC}) are readily calculated (Table 3); these values differ slightly from those derived earlier from studies of related series,^{12} but each set of parameters employed with eqn (1) give remarkably good agreement with the experimentally determined conductance values.
Since the QCR treats each region of the molecule as an independent scattering region, an alternative analysis of the data can be made by incorporating the anchor groups within the scattering region associated with the junction electrode, and considering the conductance due to the (arbitrarily partitioned) bridge portion alone (Fig. 4).
Fig. 4 Schematic illustration of incorporating the anchor groups within the electrode scattering region. |
In such a model, the Simmons-like eqn (3) for molecules in which the backbone is composed of a homologous series of N molecular repeat units (i.e. such as 1a–d–4a–d) allows an expression for conductance of the bridge, G_{B}, to be written
(5) |
(6) |
Fig. 5 Plot of the most probable experimental conductance values of backbone ln(G_{B}) versus number of units. |
The ln(G^{N}_{2B}) term obtained as the intercept at N = 0 in Fig. 5 represents the conductance through the contacts between backbone and the modified electrode through the two C_{sp}–C_{sp2} bonds (beige shaded regions of Fig. 4). From Fig. 5, the numerical value of the intercept (ln(G^{N}_{2B}) = 11.20) gives G^{N}_{2B} = 73130 nS, very close to quantum conductance (G_{0} = 73480 nS) supporting the effective partitioning description of Fig. 4.
The QCR (eqn (1)) has immense potential for use in molecular circuit design, giving a simple algebraic expression that can estimate single-molecule conductance with surprising accuracy should the unique numerical parameters be known for the particular anchor group(s) (a_{X}, a_{Y}) and bridge structure (b_{B}) in the molecule of interest. The strategies outlined above provide convenient methods to estimate these terms from a small set of experimental data. With a view to developing a bigger library of transferrable parameters associated with smaller fragments and further exploring the application and limits of the QCR, attention is now turned to oligo(phenylene) compounds, MeS-{(C_{6}H_{4})_{N}}-SMe and H_{2}N{(C_{6}H_{4})_{N}}NH_{2}, for which experimentally determined molecular conductance values are known (Table 4).^{36} From these data, treating the SMe or NH_{2} groups as the anchors and the oligo(para-phenylene) moiety as the ‘bridge’ permits an analysis of molecular conductance (as ln(G)) vs. number of phenylene rings, similar to that described in Fig. 2 to be conducted (Fig. 6). The intercept of the linear plots shown in Fig. 6 at N = 0 gives values ln(G^{N}_{2C}) corresponding to the contact conductance of the very short compounds dimethyldisulfide (MeSSMe) and hydrazine (H_{2}NNH_{2}), which would be extraordinarily challenging to measure directly and from which the anchor parameters of the individual thiomethyl (a_{SMe}) and amine (a_{NH2}) groups can be determined (eqn (4) and Table 5).
Fig. 6 Plot of the most probable experimental conductance values ln(G) of MeS{(C_{6}H_{4})_{N}}SMe and H_{2}N{(C_{6}H_{4})_{N}}NH_{2},^{36}versus number of para-phenylene units –C_{6}H_{4}–, N. |
To assess the bridge parameter associated with the para-phenylene moiety, a common ‘component’ of many molecular circuits, recall that the QCR begins by treating the molecular structure as a series of independent scattering regions, arbitrarily partitioned as ‘anchor’ or ‘bridge’ regions, with the overall conductance given by the sum of the unique and transferrable parameters associated with each of these regions (eqn (1)). It follows that for a more complex molecular structure that can be partitioned into a number of smaller scattering regions, eqn (1) might be usefully re-expressed as
(7) |
The oligo(para-phenylene) backbones in MeS{(C_{6}H_{4})_{N}}SMe and H_{2}N{(C_{6}H_{4})_{N}}NH_{2}, present as an ideal case of a bridge composed of a number of independent scattering regions and as such we can write for the SMe-anchored compounds series of Table 4
(8a) |
(8b) |
Average solutions for b_{C6H4} using the data in Table 4 from the SMe (eqn (8a), b_{C6H4} = −0.71) and NH_{2} series (eqn (8b), b_{C6H4} = −0.77) are comparable, leading to a proposed value of b_{C6H4} = −0.74 (Table 3). Pleasingly, the sum of a_{SMe} (−0.69) or a_{NH2} (−0.71) and b_{C6H4} (−0.74) are close to the previous estimates of the aryl anchor parameter a_{C6H4SMe} (−1.41) and a_{C6H4NH2} (−1.44). Consequently, if one considers the anchors and backbones in molecules partitioned as shown in Fig. 7 for 1a–d, by way of example, and applies eqn (7) using the parameters in Tables 3 and 5, excellent agreement with experiment is also achieved (Table S2†).
To more rigorously test the approach described by eqn (7), a series of ‘modular’ molecular circuits (5–8) have been designed, with various chemical ‘components’ assembled in series in such a way that a variety of partitioning strategies are possible and feature different anchors at each terminus (Fig. 8). For each of these partitioning conditions, the single-molecule conductance has been estimated from eqn (7) and the various a_{i} and b_{i} parameters summarised above. The accuracy of these estimates (log(G^{th}/G_{0})) can be tested against the single-molecule conductance of authentic samples measured using STM-BJ methods (Table 1 and Table S1†). As summarised in Fig. 8, the algebraic ‘circuit rule’ approach allows the estimation of conductance through these rather complex molecules with a remarkable degree of accuracy.
Fig. 8 Schematics of compounds 5–8 illustrating various partitioning strategies dividing the molecule into separate ‘components’ of the anchor groups and backbone fragments for which a_{i} and b_{B} parameters are known, assembled in series, the resulting calculated conductance values (log(G^{th}/G_{0})) from the QCR (eqn (7)) and experimentally determined values from STM-BJ measurements (log(G^{exp}/G_{0})). |
Further application of the quantum circuit rule (QCR) allows estimation of the conductance of molecular junctions by considering the molecule as a series of independent scattering regions with corresponding numerical parameters associated with the anchor groups (a_{i}) and molecular backbones (b_{i}). Results from this method of analysis have shown excellent agreement with the experimentally determined data. Also, the exponential dependence of molecular conductance with the number of repeating –(CC)– units allows experimental estimates of the anchor and backbone parameters. Furthermore, the QCR was verified for a series of ‘modular’ molecular circuits by applying a variety of partitioning strategies allowing subdivision of anchor groups and backbones on circuits into smaller components assembled in series with known numerical parameters. Estimated results for complex molecules are well-supported by experimentally determined molecular conductances. The fact that the QCR can predict molecular conductance with high accuracy allows the electrical conductance of future molecules to be predicted, ahead of their synthesis and demonstrates that the QCR is a useful design tool for molecular-based electronic devices.
Footnotes |
† Electronic supplementary information (ESI) available. CCDC 2244309–2244317. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d3nr01034a |
‡ Gorenskaia and Potter contributed equally. |
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