Transferrable property relationships between magnetic exchange coupling and molecular conductance

Calculated conductance through Aun–S–Bridge–S–Aun (Bridge = organic σ/π-system) constructs are compared to experimentally-determined magnetic exchange coupling parameters in a series of TpCum,MeZnSQ–Bridge–NN complexes, where TpCum,Me = hydro-tris(3-cumenyl-1-methylpyrazolyl)borate ancillary ligand, Zn = diamagnetic zinc(ii), SQ = semiquinone (S = 1/2), and NN = nitronylnitroxide radical (S = 1/2). We find that there is a nonlinear functional relationship between the biradical magnetic exchange coupling, JD→A, and the computed conductance, gmb. Although different bridge types (monomer vs. dimer) do not lie on the same JD→Avs. gmb, curve, there is a scale invariance between the monomeric and dimeric bridges which shows that the two data sets are related by a proportionate scaling of JD→A. For exchange and conductance mediated by a given bridge fragment, we find that the ratio of distance dependent decay constants for conductance (βg) and magnetic exchange coupling (βJ) does not equal unity, indicating that inherent differences in the tunneling energy gaps, Δε, and the bridge–bridge electronic coupling, HBB, are not directly transferrable properties as they relate to exchange and conductance. The results of these observations are described in valence bond terms, with resonance structure contributions to the ground state bridge wavefunction being different for SQ–Bridge–NN and Aun–S–Bridge–S–Aun systems.


Introduction
Electron transport in single-molecule devices is typically interrogated via a combination of experimental and computational probes of conductance using Metal-Bridge-Metal (M-B-M) junctions (Fig. 1A). [1][2][3][4][5][6][7][8][9][10][11][12][13][14] To account for inherent variations in molecule-electrode binding geometries, the experimental determination of conductance (g mb ) typically requires hundreds to thousands of individual conductance measurements in order to construct conductance histograms, which allow researchers to determine both conductance distributions and the most probable conductance value. 15 Since conductance calculations oen utilize a single M-B-M geometry and the molecular geometry in the actual junction is unknown, this can make direct comparisons between theory and experiment difficult to interpret. As a result, studies that correlate single-molecule conductance with physical observables such as electron transfer rate constants (k D/A ) 2,4,5,14,16 and magnetic exchange couplings (J D/A ) 1,17-20 continue to be a topic of current research. A primary impact of these efforts will be to provide key insight into orbital pathways for charge transport through molecules, which is difficult to achieve using traditional approaches. These correlations, coupled with the determination of transferable property relationships, are expected to facilitate improved molecular design concepts for molecular electronics and spintronics.
The crux of these transferable property relationships was rst described by Nitzan,21 who derived a relationship between g mb and k D/A at parity of the molecular bridge. With some approximations, Nitzan was able to show that conductance could be related to the square of the D-A electronic coupling matrix element, H D/A 2 (H D/A 2 ¼ |H DB H BA | 2 |G B (E)| 2 ), for electron transfer (eqn (1)-(4)). 21 g mb z 8e 2 here, the H ij are pairwise electronic coupling matrix elements that connect D, B, and A, the G i are broadening functions that represent the coupling between the molecule and electrodes, D3 is the tunneling energy gap, G B is the bridge Green's function with the overbar indicating that G B may differ for electron transfer (or magnetic exchange) compared to conductance, and n is the number of bridge units. These transferrable property relationships indicate that any physical observable that is a function of H D/A 2 can be related to g mb (e.g. eqn (5)).
This leads to a corresponding relationship between these parameters and the distance decay constants (b i ) for electron transfer, conductance, and magnetic exchange as indicated in eqn (6), where nL is the distance spanned by the molecular bridge (e.g.
There is both experimental and computational support for a correlation between k D/A , g mb and J D/A . 14,17,[22][23][24][25][26][27][28][29][30][31] Beratan and Waldeck 4,5 have built on Nitzan's work to show that the relationship between k D/A and g mb is nonlinear for alkane and peptide nucleic acid oligomer bridges, but they are related by a power law dependence. Their work supports an argument that the bridge Green's function, G B , is not the same for electron transfer and conductance. As a result, Beratan and Waldeck 4,5 were able to show that the distance decay constants for k D/A and g mb are, in general, inequivalent and a linear relationship between k D/A and g mb will only occur if the individual b i are identical.
Since the magnetic exchange interaction (J D/A ) is proportional to H D/A 2 via eqn (5), [32][33][34][35][36] we have initiated experiments designed to explore the correlation of J D/A between donoracceptor biradical centers that are spanned by molecular bridge units (D-B-A biradicals ¼ SQ-Bridge-NN; SQ ¼ S ¼ 1/2 semiquinone, and NN ¼ S ¼ 1/2 nitronylnitroxide radical, Fig. 1B and C) 1,[17][18][19][20]26,[35][36][37][38][39][40] with computed molecular conductance values, g mb . 1 An advantage to understanding the magnitude of g mb by correlating with experimental J D/A parameters is highlighted by the fact that the variable-temperature magnetic susceptibility measurements used to determine J D/A are performed on solid-state samples with known geometries that have been determined by X-ray crystallography. Thus, there is a single conformation present that contributes to J D/A . Unlike experimental conductance measurements in a contact geometry and solution electron transfer rate measurements, the magnitude of J D/A determined by solid state magnetic susceptibility measurements is not affected by structural and solvent bath induced inhomogeneities or by decoherence effects. Relating molecular orbital pathways for J D/A to orbital transport channels for g mb has its own set of challenges, and these include (1) differences in the molecular fragments covalently attached to the bridge unit, (2) the molecular identity of surfactant groups, (3) variations in surface contacts, (4) the choice of electrode material and surface morphology, and (5) inhomogeneities in molecular structure (e.g., conformation) and in contact geometries. As alluded to above, an important related question was recently posited by Herrmann, 14 which concerns the transferability of geometric and electronic structure contributions of the bridge moiety to k D/A , g mb , and J D/A (Fig. 2). Herein, we address these difficulties and the concept of bridge electronic structure transferability between conductance and exchange. We then use our results to explicitly determine distance decay constants (b g ) for g mb from prior studies that have determined the distance dependence of J D/A . Our results are described in valence bond terms, with resonance structure contributions to the ground state bridge wavefunction being different for SQ-Bridge-NN and Au n -S-Bridge-S-Au n systems. This provides a path forward for understanding the power law relationship between g mb and J D/A in the absence of structural inhomogeneities and decoherence effects.

Resonance Raman spectroscopy
Solution (methylene chloride) resonance Raman spectra were collected in either a 180 backscattering (780 nm) or 90 scattering geometry using 407 nm excitation from a Coherent Innova 70 Kr + (1 W) ion laser. The scattered radiation was passed through a longpass lter (Semrock RazorEdge) to remove Rayleigh scattered laser light and then dispersed onto a liquid nitrogen-cooled Infrared Associates CCD detector using a Princeton Acton spectrograph. The laser power at the sample was typically kept between 40 and 100 mW in order to prevent possible photo-and thermal degradation of the sample. The sample was sealed in a glass capillary tube and spun with a custom-made sample holder. All data were scan-averaged, and any individual data set with vibrational bands compromised by cosmic events were discarded.

Molecular electronic structure calculations
Thiophene and benzene calculations were performed at the density functional level of theory using the Gaussian 09W soware package. 43 Input les were prepared using the molecular builder function in GaussView. Calculations employed the B3LYP hybrid exchange-correlation functional and a 6-31g(d 0 ,p 0 ) split valence basis set with polarizability functions was used for all atoms. Frontier molecular orbitals (MOs) were generated from fully optimized ground states.

Transport calculations
Transport calculations were performed using ATK 2016.0 v16.0, [44][45][46] as detailed in our earlier work. 1 The device conguration consists of the le Au electrode, the molecular bridge (scattering region), and the right Au electrode. Both the le and right gold electrodes consist of nine layers with each layer comprised of a 3 Â 3 array of Au(111) atoms, for a total of 81 gold atoms per electrode. For the electrodes, the C or z direction is periodic in the system. This is also the direction of electron transport. Initial geometry optimizations of the bridge molecules BCO, Py, Ph, Th, Ph 2 , Py-Th, Th 2 were performed using Gaussian 09 (ref. 43) with a 6-31g(d 0 ,p 0 ) basis set and the B3LYP functional. Electrode surfaces were constructed by cleaving the bulk crystal and using a copy of this to form the second electrode. The molecule was then placed on the surface of the le electrode and subsequently connected to the right electrode through terminal sulfur atoms to create the nal device geometry. Prior to creating the nal device geometry, the bulk conguration was optimized using a single-zeta basis set for the gold atoms (to save computational time) and a double zeta basis set for all other atoms. The optimization was performed using ATK-DFT with a Perdew-Zunger local density approximation (LDA-PZ) exchange-correlation. Aer this bulk optimization, the conguration was converted into a nal device geometry for all subsequent calculations. A 5 Â 5 Â 51 K-point sampling has been used in x, y, z-directions, respectively. The boundary conditions were Dirichlet (xed boundary condition) in the z direction, which is the direction of transport. The boundary conditions in the x and y directions were disabled so they could not be changed but the default parameterization is periodic for the x and y directions. The NEGF formalism was used to calculate the non-equilibrium electron density of the central region of the device.
The Landauer-Büttiker formula 47 relates transmission probabilities to conductance, g mb (g mb ¼ I/V). This formula is used to calculate the voltage dependent current, I(V), across a molecular junction, which is determined by integrating the transmission function, T(E,V), according to eqn (7). 47 here, the Fermi-Dirac distribution functions for the right and le electrodes are given by f( with m R and m L being the chemical potentials for the right and le electrodes, respectively, e is the charge of the electron, h is Planck's constant, eV bias is the bias window equivalent to is the transmission coefficient for the spin component, s, describing the junction at an energy E and a bias voltage V bias . All electron transport properties were computed using the ATK soware package that includes virtual nanolab associated analysis modules. The molecular projected self-consistent Hamiltonian (MPSH) technique has been used to understand the molecular orbital origin of the resonant peaks in the transmission spectra. 48,49 Results and discussion has been used in the analysis of these data, including the analysis of new magnetic susceptibility data for the pyridylbridged complex (SQ-Py-NN), which yields J D/A ¼ +72 cm À1 (see ESI †). Collectively, these SQ-Bridge-NN biradical systems possess a large range of J D/A -values, bridge-dependent electronic structures, and both sand p-coupling units. Notably, all of these molecules are ferromagnetically exchange coupled 20,35,36 with J D/A values that vary from a low of J D/A ¼ +1 cm À1 for smediated exchange in SQ-BCO-NN, to a markedly larger J D/A ¼ +220 cm À1 for p-mediated exchange in SQ-Th-NN.

Exchange coupling within the context of a valence bond conguration interaction model
Given the geometric structures of these SQ-Bridge-NN biradicals, we can conveniently divide them into two distinct bridge categories: the rst possesses single-ring molecular bridges, while the second contains two-ring molecular bridges where each bridge ring is connected to the other via a s-bond.
The electronic origins of p-mediated exchange coupling in SQ-Ph-NN and s-mediated exchange in SQ-BCO-NN have been rigorously evaluated using a combination of spectroscopy, magnetic susceptibility, and theory. 19,20,26,39,41,50 For p-mediated exchange, a valence-bond conguration interaction (VBCI) model has been used. 19,20,35,36 Within the context of more traditional orbital pathways for understanding exchange coupling, the VBCI method conveniently illustrates how specic excited state congurations admix with the ground conguration to affect the magnitude of J D   these orbitals contribute to the transferability of J D/A , k D/A , and H D/A to conductance in a biased electron transport conguration (Fig. 2).

Correlation of exchange and conductance
Electron transport calculations have been performed on M-B-M constructs (Au n -S-Bridge-S-Au n ) in order to compare the magnitude of bridge-mediated J D/A with g mb (i.e., current). In the transport computations, the bridge molecules in Fig. 1C are connected to voltage-biased Au electrodes via thiol anchoring groups. Thus, the bridges are the molecular fragments depicted in Fig. 1C with sulfur atoms attached to the bridge carbons. These calculations treat the M-B-M ensemble at the SCF level with the computational results being interpreted in terms of the Landauer-Büttiker formula, which relates transmission probabilities to conductance, g mb , according to eqn (7). 47 In Following the work of Beratan, 53 Yoshizawa and coworkers 54,55 have conveniently related the zeroth order Green's function for the bridge ðG 0 B ðE F Þ $ G B Þ to the MO coef-cients of the bridge orbitals, the Fermi energy, and the individual MO energy levels according to: here, the C rk and C * sk correspond to the MO coefficients for the sulfur atoms located on the le-and right-hand side of the bridge molecule that directly connects to the electrodes. We note that these sulfur atoms are connected to the same carbon atoms of the organic bridge as the SQ-donor and NN-acceptor moieties in our SQ-Bridge-NN biradical systems (Fig. 5B, right). The sulfur orbital contributions to the MPSH states are important in modulating the conductance, since they directly connect the electrodes to the molecule and allow for delocalization of the bridge wavefunction in the scattering region. 55 When considering only the HOMO contributions to the conductance, eqn (9) reduces to: 55 Thus, our a priori expectation is a difference in bridgemediated coupling for conductance and magnetic exchange that results from the importance of sulfur atom character in the M-B-M MPSH HOMOs and the importance of the bridge LUMO that facilitates magnetic exchange in SQ-Bridge-NN biradicals.
The computed conductance as a function of the experimentally determined SQ-Bridge-NN magnetic exchange coupling constants using monomeric and dimeric bridge molecules is presented in Fig. 6. We have t these data to the power law expression: where J 0 D/A is the exchange parameter for SQ-NN with no bridge (J 0 D/A ¼ +550 cm À1 ). 19,35,36 The best t to the data shown in Fig. 6 yields a ¼ 2012 and g ¼ 0.675. One immediately notices two important aspects of this J D/A vs. g mb correlation. The rst is that although there is a functional relationship between J D/A and g mb , it is not a linear relationship (i.e., g s 1). The second observation is that the data for different bridge types (monomer vs. dimer) do not lie on the same curve. However, the ts to the data do indicate that there is a scale invariance that relates J D/A and g mb , for monomeric and dimeric bridges (c ¼ 1 and c ¼ 0.28 for monomeric and dimeric bridges, respectively), showing that This journal is © The Royal Society of Chemistry 2020 Chem. Sci., 2020, 11, 11425-11434 | 11429 the two data sets are related by a proportionate scaling of the exchange interaction, J D/A . As a result, we nd that J D/A and g mb are indeed highly correlated amongst this bridge set, but the simple proportionality relationship, is not generally valid across a series of monomeric or dimeric bridge molecules. Fig. 7 shows the computed current as a function of magnetic exchange coupling for thiophene and phenylene bridges (0-2 bridge units). Following the formalism of Beratan and Waldeck, 5 these data have been t to eqn (12), in order to understand the relative ratios of distance dependent decay constants for conductance (b g ) and magnetic exchange coupling (b J ). The best ts of eqn (12) to our g mb vs. J D/A data yield b g /b J ¼ 1.15 for the phenylene series and b g /b J ¼ 1.58 for the thiophene series (Fig. 7). Beratan and Waldeck also observed a nonlinear relationship between g mb and heterogeneous electron transfer rate constants, k ET . 4,5 However, in their study they showed that b g /b ET < 1 for a series of alkanethiol and peptide nucleic acid oligomer bridges, with electron transfer decaying more rapidly with increasing bridge distance than conductance. Here, we observe the opposite correlation, with conductance falling off more rapidly with distance than the magnetic exchange coupling (b g /b J > 1), albeit using very different molecular bridges. The relationship between g mb and J D/A for thiophenes is markedly more nonlinear than what we observe in the phenylene data. Eqn (13) describes how differences in these exponential decay constants (b i ) directly relate to inherent differences in the tunneling energy gaps, D3, the bridge-bridge electronic coupling, H BB , and L, the length of the bridge unit. 56,57 The tunneling energy gap (D3) is dened as the energy required to promote an electron from the donor (anode) to the bridge LUMO, or to promote a hole from the acceptor (cathode) to the bridge HOMO, and the distance between the donor and acceptor (or the electrodes) is given by R DA (R DA ¼ R 0 + nL). Thus, a combination of large H BB and a small D3 lead to low b-values and more shallow distance decays that promote long range magnetic superexchange coupling and conductance. Eqn (14) relates these distance decay constants to effective barrier heights, DE eff , with m e being the mass of the tunneling electron. 56,57 Beratan and Waldeck elegantly attributed their observed deviations in b g /b ET from unity to a combination of charge transfer energy barrier differences between electron transfer in D-B-A ensembles and electron transport in M-B-M congurations, bath-induced decoherences on the bridge molecule, and bridge-bridge electronic coupling (H BB ). 4,5 Their work comparing conductance values and electron transfer rate constants indicated that differences in effective barrier heights derive from differences between the electrode work function in a transport geometry and donor/acceptor redox potentials in D-B-A systems. 4,5 With respect to b i values, differences in the work function and redox potentials derive from different values for D3. In general, due to the interdependence of D3 and H BB on b i values it is difficult to separate these individual contributions to DE eff . 58 Since decoherence effects are not important for the J D/A vs. g mb correlation presented here, the dominant contributors to the nonlinearity between J D/A and g mb must relate to differences in bridge-bridge electronic coupling (H BB ) and the tunneling energy The data indicate that current is not directly proportional to magnetic exchange coupling. The data are fit to separate empirical power law functions with identical exponents, with best fits shown as black lines. Computations were performed using a bias voltage of +2 V which approximates the intraligand charge transfer energy in SQ-Bridge-NN complexes. Fig. 7 Computed current (conductance) vs. exchange coupling for phenylene bridges (red circles) and for thiophene bridges (blue circles). Best fits to the Eq. in the text are shown as red and blue lines, respectively. Note that the value of the exponents, m ¼ b g /b J , lead to a greater degree of linearity for the phenylene data set (see text). The black circle is located at (0,0), since g mb / 0 as J D/A / 0. Conductance values for M-B-M systems were computed at +2 V bias using the Landauer-Büttiker formalism, which relates transmission probabilities to conductance (g mb ¼ I/V). gaps (D3). For our SQ-Bridge-NN biradical complexes, we have used the ILCT energy as an approximation to the tunneling energy gap. This ILCT transition energy increases going from SQ-Ph-NN to SQ-Ph 2 -NN and decreases when going from SQ-Th-NN to SQ-Th 2 -NN. 17 This contributes to the observed differences in b J between SQ-(Ph) n -NN and SQ-(Th) n -NN, but also contributes to the magnitude of b g /b J and differences in DE eff for magnetic exchange coupling and conductance.
Previously, we used magnetic susceptibility measurements to determine DE eff for superexchange-mediated magnetic coupling in SQ-Bridge-NN biradical systems, and this yielded DE eff ¼ 1173 cm À1 and 373 cm À1 for phenylene and thiophene bridges, respectively. 17 Given the conductance to magnetic exchange distance decay ratios (b g /b J ) for phenylenes and thiophenes determined here, we compute conductance barrier heights (DE eff ) of 1555 cm À1 and 941 cm À1 for phenylene and thiophene bridges that span electrodes in a transport geometry. This translates to a decrease in DE eff for magnetic exchange coupling of $25% (phenylenes) and $60% (thiophenes) when compared to conductance values using these same organic bridge fragments. Our b J values determined from magnetic susceptibility experiments (b J ¼ 0.39Å À1 (Ph n ); b J ¼ 0.22Å À1 (Th n )) 17 and the magnitude of b g /b J determined in this work reveal the corresponding b g values for conductance using these molecular bridges ( Table 1). The b g ¼ 0.45Å À1 value we determine for paraphenylene bridges is very close to the b g ¼ 0.42Å À1 value determined by conducting probe atomic force microscopy on oligo(para-phenylene)-monothiols suspended between metal contacts. 59 Additionally, the b g ¼ 0.35Å À1 value that we have determined for oligothiophene bridges is also in good agreement with conductance studies performed on thiophene bridges with repeat units (n) equal to 1, 2, 3 and 5 (b g ¼ 0.29Å À1 ). 60 Resonance contribution to bridge mediated conductance and exchange Since b i and DE eff are also a function of H BB , the bridge-bridge electronic coupling, differences in the nature of the frontier bridge MOs that promote both g mb and J D/A will also affect the magnitude of the distance decay constants. It is generally assumed that the bridge-bridge electronic couplings encountered in electron transfer, conductance, and magnetic exchange are equivalent, and the donor, acceptor, and electrode contacts do not affect the magnitude of H BB . However, this assumption may not be true. A convenient vehicle for understanding electronic structure contributions to b i values is the use of contributing resonance structures to highlight excited state congurations that mix with the ground state conguration within a valence bond framework. 41,[61][62][63][64] As introduced above, the resonance structures shown in Fig. 4 describe the charge and spin distributions of the ground state conguration (GC) and four excited state congurations (ECs) for the SQ-Ph 2 -NN biradical complex. Quinoidal EC1 and EC3 possess enhanced Ph-Ph p-coupling, which provides a mechanism for increasing the magnitude of H BB . Contributions of resonance structures EC1-EC4 to the ground state all lead to enhanced magnetic exchange coupling in SQ-Bridge-NN biradicals. This occurs via a combination of B-B, D-B, and B-A electronic couplings (H BB , H DB , H BA ), which are different than those provided by the coupling of these same bridge molecules with the electrodes (|G B |, G LB , G RB ). This is partly due to the fact that only high energy zwitterionic and biradical resonance structures can be drawn for the S-Ph-Ph-S electrode linkage. In contrast, these CT congurations lead to a lowenergy ILCT state at $24 000 cm À1 in SQ-Bridge-NN biradicals, which has been shown to admix with the electronic ground state by resonance Raman spectroscopy. 20,41 Specically, the effect of this enhanced electronic coupling has been observed in SQ-Bridge-NN biradical compounds by optical pumping into the excited state ILCT and observing a large resonance enhancement of the phenylene quinoidal stretching vibration, which decreases in intensity with increased SQ-Bridge and Bridge-NN bond torsions. 41 For di-bridged SQ-Ph 2 -NN, a large resonance enhancement of the 1600 cm À1 quinoidal stretch is also observed when pumping into the SQ / Ph-NN ILCT band 17 (Fig. 8). The nature of the charge transfer is indicated by the computed electron density difference map (EDDM) in Fig. 8, which shows net charge transfer from the SQ donor (red) to the Ph-NN acceptor fragment (blue). Thus, the nature of the charge transfer in di-bridged SQ-Ph 2 -NN is analogous to what has been observed previously in the mono-bridged SQ-Ph-NN biradical, 20,39 highlighting quinoidal resonance structure contributions to the ground state wavefunction.

Conclusions
This work provides a detailed account of the transferability of electronic coupling with regard to exchange coupling and conductance. We have developed an electronic structure description of the functional relationship between J D/A and g mb , which we observed to be nonlinear (b g /b J s 1). Plots of J D/ A vs. g mb for monomeric and dimeric bridges lie on different curves due to a scale invariance between these bridge types, which indicates a proportionate scaling of the exchange interaction, J D/A . Our g mb vs. J D/A data yield b g /b J ¼ 1.15 for the phenylene series and b g /b J ¼ 1.58 for the thiophene series, and these ratios accurately replicate recently reported b-values for electron transport through oligothiophene and oligophenylene bridges. 59,60 In addition, these b g /b J ratios have been used to determine conductance tunneling barrier heights for oligophenylenes (DE eff ¼ 1555 cm À1 ) and oligo-thiophenes (DE eff ¼ 941 cm À1 ) that span electrodes in a transport geometry. This translates to a decrease in effective barrier heights DE eff for magnetic exchange coupling of $25% for phenylenes and $60% for thiophenes when compared to conductance values using these same organic bridge fragments. Tunneling gaps and bridge-bridge electronic coupling, H BB , calculated from experimental data for the phenylene-and thiophene series provide a convincing explanation for the more pronounced g mb vs. J D/A nonlinearity observed in the thiophene series compared to the phenylene series. Additionally, resonance Raman spectroscopy indicates that H BB may be enhanced by quinoidal resonance structure contributions in SQ-Bridge-NN biradicals relative to M-B-M devices for conductance. Namely, contributions from ECN resonance structures (Fig. 4) are expected to be more pronounced for SQ-Th n -NN than for SQ-Ph n -NN or Au n -S-Bridge-S-Au n constructs.
Resonance enhancement of the bridge quinoidal stretching mode illustrates the key bridge distortion that is the hallmark of a large H BB , and the magnitude of this excited state distortion is proportional to the degree of SQ / B-NN charge transfer, which contributes to the magnitude of the magnetic exchange interaction in SQ-Bridge-NN biradicals. From a valence bond/ resonance perspective, contributing ECN resonance structures accurately reect both the spin-and charge distribution of lowlying SQ-Bridge-NN CT states, for which the corresponding quinoidal bridge-containing excited states in M-Bridge-M constructs lie far higher in energy. With respect to the importance of quinoidal resonance contributions, aromaticity has been shown to reduce conductance values in single molecule junctions. 65 Critically, the quinoidal resonance structure contributions in Fig. 4 result in diminished aromaticity and contribute more to exchange than to conductance, leading to g s 1 and b g /b J > 1 for these molecular bridges.

Conflicts of interest
There are no conicts to declare.