@article{17971, abstract = {We study the impact of electrode band structure on transport through single-molecule junctions by measuring the conductance of pyridine-based molecules using Ag and Au electrodes. Our experiments are carried out using the scanning tunneling microscope based break-junction technique and are supported by density functional theory based calculations. We find from both experiments and calculations that the coupling of the dominant transport orbital to the metal is stronger for Au-based junctions when compared with Ag-based junctions. We attribute this difference to relativistic effects, which result in an enhanced density of d-states at the Fermi energy for Au compared with Ag. We further show that the alignment of the conducting orbital relative to the Fermi level does not follow the work function difference between two metals and is different for conjugated and saturated systems. We thus demonstrate that the details of the molecular level alignment and electronic coupling in metal–organic interfaces do not follow simple rules but are rather the consequence of subtle local interactions.}, author = {Adak, Olgun and Korytár, Richard and Joe, Andrew Y. and Evers, Ferdinand and Venkataraman, Latha}, issn = {1530-6992}, journal = {Nano Letters}, number = {6}, pages = {3716--3722}, publisher = {American Chemical Society}, title = {{Impact of electrode density of states on transport through pyridine-linked single molecule junctions}}, doi = {10.1021/acs.nanolett.5b01195}, volume = {15}, year = {2015}, } @article{17979, abstract = {Using scanning tunneling microscope break-junction experiments and a new first-principles approach to conductance calculations, we report and explain low-bias charge transport behavior of four types of metal–porphyrin–gold molecular junctions. A nonequilibrium Green’s function approach based on self-energy corrected density functional theory and optimally tuned range-separated hybrid functionals is developed and used to understand experimental trends quantitatively. Importantly, due to the localized d states of the porphyrin molecules, hybrid functionals are essential for explaining measurements; standard semilocal functionals yield qualitatively incorrect results. Comparing directly with experiments, we show that the conductance can change by nearly a factor of 2 when different metal cations are used, counter to trends expected from gas-phase ionization energies which are relatively unchanged with the metal center. Our work explains the sensitivity of the porphyrin conductance with the metal center via a detailed and quantitative portrait of the interface electronic structure and provides a new framework for understanding transport quantitatively in complex junctions involving molecules with localized d states of relevance to light harvesting and energy conversion.}, author = {Liu, Zhen-Fei and Wei, Sujun and Yoon, Hongsik and Adak, Olgun and Ponce, Ingrid and Jiang, Yivan and Jang, Woo-Dong and Campos, Luis M. and Venkataraman, Latha and Neaton, Jeffrey B.}, issn = {1530-6992}, journal = {Nano Letters}, number = {9}, pages = {5365--5370}, publisher = {American Chemical Society}, title = {{Control of single-molecule junction conductance of porphyrins via a transition-metal center}}, doi = {10.1021/nl5025062}, volume = {14}, year = {2014}, } @article{17985, abstract = {We have designed and synthesized five azulene derivatives containing gold-binding groups at different points of connectivity within the azulene core to probe the effects of quantum interference through single-molecule conductance measurements. We compare conducting paths through the 5-membered ring, 7-membered ring, and across the long axis of azulene. We find that changing the points of connectivity in the azulene impacts the optical properties (as determined from UV–vis absorption spectra) and the conductivity. Importantly, we show here that simple models cannot be used to predict quantum interference characteristics of nonalternant hydrocarbons. As an exemplary case, we show that azulene derivatives that are predicted to exhibit destructive interference based on widely accepted atom-counting models show a significant conductance at low biases. Although simple models to predict the low-bias conductance do not hold with all azulene derivatives, we demonstrate that the measured conductance trend for all molecules studied actually agrees with predictions based on the more complete GW calculations for model systems.}, author = {Xia, Jianlong and Capozzi, Brian and Wei, Sujun and Strange, Mikkel and Batra, Arunabh and Moreno, Jose R. and Amir, Roey J. and Amir, Elizabeth and Solomon, Gemma C. and Venkataraman, Latha and Campos, Luis M.}, issn = {1530-6992}, journal = {Nano Letters}, number = {5}, pages = {2941--2945}, publisher = {American Chemical Society}, title = {{Breakdown of interference rules in azulene, a nonalternant hydrocarbon}}, doi = {10.1021/nl5010702}, volume = {14}, year = {2014}, } @article{17987, abstract = {We modulate the conductance of electrochemically inactive molecules in single-molecule junctions using an electrolytic gate to controllably tune the energy level alignment of the system. Molecular junctions that conduct through their highest occupied molecular orbital show a decrease in conductance when applying a positive electrochemical potential, and those that conduct though their lowest unoccupied molecular orbital show the opposite trend. We fit the experimentally measured conductance data as a function of gate voltage with a Lorentzian function and find the fitting parameters to be in quantitative agreement with self-energy corrected density functional theory calculations of transmission probability across single-molecule junctions. This work shows that electrochemical gating can directly modulate the alignment of the conducting orbital relative to the metal Fermi energy, thereby changing the junction transport properties.}, author = {Capozzi, Brian and Chen, Qishui and Darancet, Pierre and Kotiuga, Michele and Buzzeo, Marisa and Neaton, Jeffrey B. and Nuckolls, Colin and Venkataraman, Latha}, issn = {1530-6992}, journal = {Nano Letters}, number = {3}, pages = {1400--1404}, publisher = {American Chemical Society}, title = {{Tunable charge transport in single-molecule junctions via electrolytic gating}}, doi = {10.1021/nl404459q}, volume = {14}, year = {2014}, } @article{17988, abstract = {We measure conductance and thermopower of single Au–4,4′-bipyridine–Au junctions in distinct low and high conductance binding geometries accessed by modulating the electrode separation. We use these data to determine the electronic energy level alignment and coupling strength for these junctions, which are known to conduct through the lowest unoccupied molecular orbital (LUMO). Contrary to intuition, we find that, in the high-conductance junction, the LUMO resonance energy is further away from the Au Fermi energy than in the low-conductance junction. However, the LUMO of the high-conducting junction is better coupled to the electrode. These results are in good quantitative agreement with self-energy corrected zero-bias density functional theory calculations. Our calculations show further that measurements of conductance and thermopower in amine-terminated oligophenyl–Au junctions, where conduction occurs through the highest occupied molecular orbitals, cannot be used to extract electronic parameters as their transmission functions do not follow a simple Lorentzian form.}, author = {Kim, Taekyeong and Darancet, Pierre and Widawsky, Jonathan R. and Kotiuga, Michele and Quek, Su Ying and Neaton, Jeffrey B. and Venkataraman, Latha}, issn = {1530-6992}, journal = {Nano Letters}, number = {2}, pages = {794--798}, publisher = {American Chemical Society}, title = {{Determination of energy level alignment and coupling strength in 4,4′-bipyridine single-molecule junctions}}, doi = {10.1021/nl404143v}, volume = {14}, year = {2014}, } @article{17993, abstract = {We demonstrate a new method of achieving rectification in single molecule devices using the high-bias properties of gold–carbon bonds. Our design for molecular rectifiers uses a symmetric, conjugated molecular backbone with a single methylsulfide group linking one end to a gold electrode and a covalent gold–carbon bond at the other end. The gold–carbon bond results in a hybrid gold-molecule “gateway” state pinned close to the Fermi level of one electrode. Through nonequilibrium transport calculations, we show that the energy of this state shifts drastically with applied bias, resulting in rectification at surprisingly low voltages. We use this concept to design and synthesize a family of diodes and demonstrate through single-molecule current–voltage measurements that the rectification ratio can be predictably and efficiently tuned. This result constitutes the first experimental demonstration of a rationally tunable system of single-molecule rectifiers. More generally, the results demonstrate that the high-bias properties of “gateway” states can be used to provide additional functionality to molecular electronic systems.}, author = {Batra, Arunabh and Darancet, Pierre and Chen, Qishui and Meisner, Jeffrey S. and Widawsky, Jonathan R. and Neaton, Jeffrey B. and Nuckolls, Colin and Venkataraman, Latha}, issn = {1530-6992}, journal = {Nano Letters}, number = {12}, pages = {6233--6237}, publisher = {American Chemical Society}, title = {{Tuning rectification in single-molecular diodes}}, doi = {10.1021/nl403698m}, volume = {13}, year = {2013}, } @article{17996, abstract = {We compare the conductance of a series of amine-terminated oligophenyl and alkane molecular junctions formed with Ag and Au electrodes using the scanning tunneling microscope based break-junction technique. For these molecules that conduct through the highest occupied molecular orbital, junctions formed with Au electrodes are more conductive than those formed with Ag electrodes, consistent with the lower work function for Ag. The measured conductance decays exponentially with molecular backbone length with a decay constant that is essentially the same for Ag and Au electrodes. However, the formation and evolution of molecular junctions upon elongation are very different for these two metals. Specifically, junctions formed with Ag electrodes sustain significantly longer elongation when compared with Au due to a difference in the initial gap opened up when the metal point-contact is broken. Using this observation and density functional theory calculations of junction structure and conductance we explain the trends observed in the single molecule junction conductance. Our work thus opens a new path to the conductance measurements of a single molecule junction in Ag electrodes.}, author = {Kim, Taekyeong and Vázquez, Héctor and Hybertsen, Mark S. and Venkataraman, Latha}, issn = {1530-6992}, journal = {Nano Letters}, number = {7}, pages = {3358--3364}, publisher = {American Chemical Society}, title = {{Conductance of molecular junctions formed with silver electrodes}}, doi = {10.1021/nl401654s}, volume = {13}, year = {2013}, } @article{17997, abstract = {We report the simultaneous measurement of conductance and thermopower of highly conducting single-molecule junctions using a scanning tunneling microscope-based break-junction setup. We start with molecular backbones (alkanes and oligophenyls) terminated with trimethyltin end groups that cleave off in situ to create junctions where terminal carbons are covalently bonded to the Au electrodes. We apply a thermal gradient across these junctions and measure their conductance and thermopower. Because of the electronic properties of the highly conducting Au–C links, the thermoelectric properties and power factor are very high. Our results show that the molecular thermopower increases nonlinearly with the molecular length while conductance decreases exponentially with increasing molecular length. Density functional theory calculations show that a gateway state representing the Au–C covalent bond plays a key role in the conductance. With this as input, we analyze a series of simplified models and show that a tight-binding model that explicitly includes the gateway states and the molecular backbone states accurately captures the experimentally measured conductance and thermopower trends.}, author = {Widawsky, J. R. and Chen, W. and Vázquez, H. and Kim, T. and Breslow, R. and Hybertsen, M. S. and Venkataraman, Latha}, issn = {1530-6992}, journal = {Nano Letters}, number = {6}, pages = {2889--2894}, publisher = {American Chemical Society}, title = {{Length-dependent thermopower of highly conducting Au–C bonded single molecule junctions}}, doi = {10.1021/nl4012276}, volume = {13}, year = {2013}, } @article{18002, abstract = {Using self-energy-corrected density functional theory (DFT) and a coherent scattering-state approach, we explain current–voltage (IV) measurements of four pyridine-Au and amine-Au linked molecular junctions with quantitative accuracy. Parameter-free many-electron self-energy corrections to DFT Kohn–Sham eigenvalues are demonstrated to lead to excellent agreement with experiments at finite bias, improving upon order-of-magnitude errors in currents obtained with standard DFT approaches. We further propose an approximate route for prediction of quantitative IV characteristics for both symmetric and asymmetric molecular junctions based on linear response theory and knowledge of the Stark shifts of junction resonance energies. Our work demonstrates that a quantitative, computationally inexpensive description of coherent transport in molecular junctions is readily achievable, enabling new understanding and control of charge transport properties of molecular-scale interfaces at large bias voltages.}, author = {Darancet, Pierre and Widawsky, Jonathan R. and Choi, Hyoung Joon and Venkataraman, Latha and Neaton, Jeffrey B.}, issn = {1530-6992}, journal = {Nano Letters}, number = {12}, pages = {6250--6254}, publisher = {American Chemical Society}, title = {{Quantitative current–voltage characteristics in molecular junctions from first principles}}, doi = {10.1021/nl3033137}, volume = {12}, year = {2012}, } @article{18010, abstract = {Electronic factors in molecules such as quantum interference and cross-conjugation can lead to dramatic modulation and suppression of conductance in single-molecule junctions. Probing such effects at the single-molecule level requires simultaneous measurements of independent junction properties, as conductance alone cannot provide conclusive evidence of junction formation for molecules with low conductivity. Here, we compare the mechanics of the conducting para-terminated 4,4′-di(methylthio)stilbene and moderately conducting 1,2-bis(4-(methylthio)phenyl)ethane to that of insulating meta-terminated 3,3′-di(methylthio)stilbene single-molecule junctions. We simultaneously measure force and conductance across single-molecule junctions and use force signatures to obtain independent evidence of junction formation and rupture in the meta-linked cross-conjugated molecule even when no clear low-bias conductance is measured. By separately quantifying conductance and mechanics, we identify the formation of atypical 3,3′-di(methylthio)stilbene molecular junctions that are mechanically stable but electronically decoupled. While theoretical studies have envisaged many plausible systems where quantum interference might be observed, our experiments provide the first direct quantitative study of the interplay between contact mechanics and the distinctively quantum mechanical nature of electronic transport in single-molecule junctions.}, author = {Aradhya, Sriharsha V. and Meisner, Jeffrey S. and Krikorian, Markrete and Ahn, Seokhoon and Parameswaran, Radha and Steigerwald, Michael L. and Nuckolls, Colin and Venkataraman, Latha}, issn = {1530-6992}, journal = {Nano Letters}, number = {3}, pages = {1643--1647}, publisher = {American Chemical Society}, title = {{Dissecting contact mechanics from quantum interference in single-molecule junctions of stilbene derivatives}}, doi = {10.1021/nl2045815}, volume = {12}, year = {2012}, } @article{18012, abstract = {We report the first concurrent determination of conductance (G) and thermopower (S) of single-molecule junctions via direct measurement of electrical and thermoelectric currents using a scanning tunneling microscope-based break-junction technique. We explore several amine-Au and pyridine-Au linked molecules that are predicted to conduct through either the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LUMO), respectively. We find that the Seebeck coefficient is negative for pyridine-Au linked LUMO-conducting junctions and positive for amine-Au linked HOMO-conducting junctions. Within the accessible temperature gradients (<30 K), we do not observe a strong dependence of the junction Seebeck coefficient on temperature. From histograms of thousands of junctions, we use the most probable Seebeck coefficient to determine a power factor, GS2, for each junction studied, and find that GS2 increases with G. Finally, we find that conductance and Seebeck coefficient values are in good quantitative agreement with our self-energy corrected density functional theory calculations.}, author = {Widawsky, Jonathan R. and Darancet, Pierre and Neaton, Jeffrey B. and Venkataraman, Latha}, issn = {1530-6992}, journal = {Nano Letters}, number = {1}, pages = {354--358}, publisher = {American Chemical Society}, title = {{Simultaneous determination of conductance and thermopower of single molecule junctions}}, doi = {10.1021/nl203634m}, volume = {12}, year = {2011}, } @article{18017, abstract = {The conductance of individual 1,4-benzenediamine (BDA)–Au molecular junctions is measured in different solvent environments using a scanning tunneling microscope based point-contact technique. Solvents are found to increase the conductance of these molecular junctions by as much as 50%. Using first principles calculations, we explain this increase by showing that a shift in the Au contact work function is induced by solvents binding to undercoordinated Au sites around the junction. Increasing the Au contact work function reduces the separation between the Au Fermi energy and the highest occupied molecular orbital of BDA in the junction, increasing the measured conductance. We demonstrate that the solvent-induced shift in conductance depends on the affinity of the solvent to Au binding sites and also on the induced dipole (relative to BDA) upon adsorption. Via this mechanism, molecular junction level alignment and transport properties can be statistically altered by solvent molecule binding to the contact surface.}, author = {Fatemi, V. and Kamenetska, M. and Neaton, J. B. and Venkataraman, Latha}, issn = {1530-6992}, journal = {Nano Letters}, number = {5}, pages = {1988--1992}, publisher = {American Chemical Society}, title = {{Environmental control of single-molecule junction transport}}, doi = {10.1021/nl200324e}, volume = {11}, year = {2011}, } @article{18018, abstract = {Controlling electron transport through a single-molecule device is key to the realization of nanoscale electronic components. A design requirement for single molecule electrical devices is that the molecule must be both structurally and electrically connected to the metallic electrodes. Typically, the mechanical and electrical contacts are achieved by the same chemical moiety. In this study, we demonstrate that the structural role may be played by one group (for example, a sulfide) while the electrical role may be played by another (a conjugated chain of C═C π-bonds). We can specify the electrical conductance through the molecule by modulating to which particular site on the oligoene chain the electrode binds. The result is a device that functions as a potentiometer at the single-molecule level.}, author = {Meisner, Jeffrey S. and Kamenetska, Masha and Krikorian, Markrete and Steigerwald, Michael L. and Venkataraman, Latha and Nuckolls, Colin}, issn = {1530-6992}, journal = {Nano Letters}, number = {4}, pages = {1575--1579}, publisher = {American Chemical Society}, title = {{A single-molecule potentiometer}}, doi = {10.1021/nl104411f}, volume = {11}, year = {2011}, } @article{18019, abstract = {We simultaneously measure conductance and force across nanoscale junctions. A new, two-dimensional histogram technique is introduced to statistically extract bond rupture forces from a large data set of individual junction elongation traces. For the case of Au point contacts, we find a rupture force of 1.4 ± 0.2 nN, which is in good agreement with previous measurements. We then study systematic trends for single gold metal−molecule−metal junctions for a series of molecules terminated with amine and pyridine linkers. For all molecules studied, single molecule junctions rupture at the Au−N bond. Selective binding of the linker group allows us to correlate the N−Au bond-rupture force to the molecular backbone. We find that the rupture force ranges from 0.8 nN for 4,4′ bipyridine to 0.5 nN in 1,4 diaminobenzene. These experimental results are in excellent quantitative agreement with density functional theory based adiabatic molecular junction elongation and rupture calculations.}, author = {Frei, Michael and Aradhya, Sriharsha V. and Koentopp, Max and Hybertsen, Mark S. and Venkataraman, Latha}, issn = {1530-6992}, journal = {Nano Letters}, number = {4}, pages = {1518--1523}, publisher = {American Chemical Society}, title = {{Mechanics and chemistry: Single molecule bond rupture forces correlate with molecular backbone structure}}, doi = {10.1021/nl1042903}, volume = {11}, year = {2011}, } @article{18024, abstract = {Using photoemission spectroscopy, we determine the relationship between electronic energy level alignment at a metal−molecule interface and single-molecule junction transport data. We measure the position of the highest occupied molecular orbital (HOMO) relative to the Au metal Fermi level for three 1,4-benzenediamine derivatives on Au(111) and Au(110) with ultraviolet and resonant X-ray photoemission spectroscopy. We compare these results to scanning tunnelling microscope-based break-junction measurements of single molecule conductance and to first-principles calculations. We find that the energy difference between the HOMO and Fermi level for the three molecules adsorbed on Au(111) correlate well with changes in conductance and agree well with quasiparticle energies computed from first-principles calculations incorporating self-energy corrections. On the Au(110) that presents Au atoms with lower-coordination, critical in break-junction conductance measurements, we see that the HOMO level shifts further from the Fermi level. These results provide the first direct comparison of spectroscopic energy level alignment measurements with single molecule junction transport data.}, author = {Dell’Angela, M. and Kladnik, G. and Cossaro, A. and Verdini, A. and Kamenetska, M. and Tamblyn, I. and Quek, S. Y. and Neaton, J. B. and Cvetko, D. and Morgante, A. and Venkataraman, Latha}, issn = {1530-6992}, journal = {Nano Letters}, number = {7}, pages = {2470--2474}, publisher = {American Chemical Society}, title = {{Relating energy level alignment and amine-linked single molecule junction conductance}}, doi = {10.1021/nl100817h}, volume = {10}, year = {2010}, } @article{13416, abstract = {The reversible molecular template-directed self-assembly of gold nanoparticles (AuNPs), a process which relies solely on noncovalent bonding interactions, has been demonstrated by high-resolution transmission electron microscopy (HR-TEM). By employing a well-known host−guest binding motif, the AuNPs have been systemized into discrete dimers, trimers, and tetramers. These nanoparticulate twins, triplets, and quadruplets, which can be disassembled and reassembled either chemically or electrochemically, can be coalesced into larger, permanent polygonal structures by thermal treatment using a focused HR-TEM electron beam.}, author = {Olson, Mark A. and Coskun, Ali and Klajn, Rafal and Fang, Lei and Dey, Sanjeev K. and Browne, Kevin P. and Grzybowski, Bartosz A. and Stoddart, J. Fraser}, issn = {1530-6992}, journal = {Nano Letters}, keywords = {Mechanical Engineering, Condensed Matter Physics, General Materials Science, General Chemistry, Bioengineering}, number = {9}, pages = {3185--3190}, publisher = {American Chemical Society}, title = {{Assembly of polygonal nanoparticle clusters directed by reversible noncovalent bonding interactions}}, doi = {10.1021/nl901385c}, volume = {9}, year = {2009}, } @article{18037, abstract = {A combination of theory and experiment is used to quantitatively understand the conductance of single-molecule benzenediamine−gold junctions. A newly developed analysis is applied to a measured junction conductance distribution, based on 59 000 individual conductance traces, which has a clear peak at 0.0064 G0 and a width of ±47%. This analysis establishes that the distribution width originates predominantly from variations in conductance across different junctions rather than variations in conductance during junction elongation. Conductance calculations based on density functional theory (DFT) for 15 distinct junction geometries show a similar spread. We show explicitly that differences in local structure have a limited influence on conductance because the amine−Au bonding motif is well-defined and flexible, explaining the narrow distributions seen in the experiments. The minimal impact of junction structure on conductance permits an unambiguous comparison of calculated and measured conductance values and a direct assessment of the widely used DFT theoretical framework. The average calculated conductance (0.046 G0) is found to be seven times larger than experiment. This discrepancy is explained quantitatively in terms of electron correlation effects to the molecular level alignments in the junction.}, author = {Quek, Su Ying and Venkataraman, Latha and Choi, Hyoung Joon and Louie, Steven G. and Hybertsen, Mark S. and Neaton, J. B.}, issn = {1530-6992}, journal = {Nano Letters}, number = {11}, pages = {3477--3482}, publisher = {American Chemical Society}, title = {{Amine−gold linked single-molecule circuits:  Experiment and theory}}, doi = {10.1021/nl072058i}, volume = {7}, year = {2007}, } @article{18040, abstract = {We measure the low bias conductance of a series of substituted benzene diamine molecules while breaking a gold point contact in a solution of the molecules. Transport through these substituted benzenes is by means of nonresonant tunneling or superexchange, with the molecular junction conductance depending on the alignment of the metal Fermi level to the closest molecular level. Electron-donating substituents, which drive the occupied molecular orbitals up, increase the junction conductance, while electron-withdrawing substituents have the opposite effect. Thus for the measured series, conductance varies inversely with the calculated ionization potential of the molecules. These results reveal that the occupied states are closest to the gold Fermi energy, indicating that the tunneling transport through these molecules is analogous to hole tunneling through an insulating film.}, author = {Venkataraman, Latha and Park, Young S. and Whalley, Adam C. and Nuckolls, Colin and Hybertsen, Mark S. and Steigerwald, Michael L.}, issn = {1530-6992}, journal = {Nano Letters}, number = {2}, pages = {502--506}, publisher = {American Chemical Society}, title = {{Electronics and dhemistry:  Varying single-molecule junction conductance using chemical substituents}}, doi = {10.1021/nl062923j}, volume = {7}, year = {2007}, } @article{18043, abstract = {We measure the conductance of amine-terminated molecules by breaking Au point contacts in a molecular solution at room temperature. We find that the variability of the observed conductance for the diamine molecule−Au junctions is much less than the variability for diisonitrile− and dithiol−Au junctions. This narrow distribution enables unambiguous conductance measurements of single molecules. For an alkane diamine series with 2−8 carbon atoms in the hydrocarbon chain, our results show a systematic trend in the conductance from which we extract a tunneling decay constant of 0.91 ± 0.03 per methylene group. We hypothesize that the diamine link binds preferentially to undercoordinated Au atoms in the junction. This is supported by density functional theory-based calculations that show the amine binding to a gold adatom with sufficient angular flexibility for easy junction formation but well-defined electronic coupling of the N lone pair to the Au. Therefore, the amine linkage leads to well-defined conductance measurements of a single molecule junction in a statistical study.}, author = {Venkataraman, Latha and Klare, Jennifer E. and Tam, Iris W. and Nuckolls, Colin and Hybertsen, Mark S. and Steigerwald, Michael L.}, issn = {1530-6992}, journal = {Nano Letters}, number = {3}, pages = {458--462}, publisher = {American Chemical Society}, title = {{Single-molecule circuits with well-defined molecular conductance}}, doi = {10.1021/nl052373+}, volume = {6}, year = {2006}, }