Comprehensive suppression of single-molecule conductance using destructive σ-interference.

The tunnelling of electrons through molecules (and through any nanoscale insulating and dielectric material 1 ) shows exponential attenuation with increasing length 2 , a length dependence that is reflected in the ability of the electrons to carry an electrical current. It was recently demonstrated3-5 that coherent tunnelling through a molecular junction can also be suppressed by destructive quantum interference 6 , a mechanism that is not length-dependent. For the carbon-based molecules studied previously, cancelling all transmission channels would involve the suppression of contributions to the current from both the π-orbital and σ-orbital systems. Previous reports of destructive interference have demonstrated a decrease in transmission only through the π-channel. Here we report a saturated silicon-based molecule with a functionalized bicyclo[2.2.2]octasilane moiety that exhibits destructive quantum interference in its σ-system. Although molecular silicon typically forms conducting wires 7 , we use a combination of conductance measurements and ab initio calculations to show that destructive σ-interference, achieved here by locking the silicon-silicon bonds into eclipsed conformations within a bicyclic molecular framework, can yield extremely insulating molecules less than a nanometre in length. Our molecules also exhibit an unusually high thermopower (0.97 millivolts per kelvin), which is a further experimental signature of the suppression of all tunnelling paths by destructive interference: calculations indicate that the central bicyclo[2.2.2]octasilane unit is rendered less conductive than the empty space it occupies. The molecular design presented here provides a proof-of-concept for a quantum-interference-based approach to single-molecule insulators.

Understanding Current Density in Molecules Using Molecular Orbitals.

While the use of molecular orbitals (MOs) and their isosurfaces to explain physical phenomena in chemical systems is a time-honored tool, we show that the nodes are an equally important component for understanding the current density through single-molecule junctions. We investigate three different model systems consisting of an alkane, alkene, and even [n]cumulene and show that we can explain the form of the current density using the MOs of the molecule. Essentially, the MOs define the region in which current can flow and their gradients define the direction in which current flows within that region. We also show that it is possible to simplify the current density for improved understanding by either partitioning the current density into more chemically intuitive parts, such as σ- and π-systems, or by filtering out MOs with negligible contributions to the overall current density. Our work highlights that it is possible to infer a non-equilibrium property (current density) given only equilibrium properties (MOs and their gradients), and this, in turn, grants deeper insight into coherent electron transport.

Visualizing and comparing quantum interference in the π-system and σ-system of organic molecules.

Quantum interference effects in conjugated molecules have been well-explored, with benzene frequently invoked as a pedagogical example. These interference effects have been understood through a quantum interference map in which the electronic transmission is separated into interfering and non-interfering terms, with a focus on the π-orbitals for conjugated molecules. Recently, saturated molecules have also been reported to exhibit destructive quantum interference effects; however, the very different σ-orbital character in these molecules means that it is not clear how orbital contributions manifest. Herein, we demonstrate that the quantum interference effects in conjugated molecules are quite different from those observed in saturated molecules, as demonstrated by the quantum interference map. While destructive interference at the Fermi energy in the π-system of benzene arises from interference terms between paired occupied and virtual orbitals, this is not the case at the Fermi energy in saturated systems. Instead, destructive interference is evident when contributions from a larger number of non-paired orbitals cancel, leading to more subtle and varied manifestations of destructive interference in saturated systems.

Trusting our machines: validating machine learning models for single-molecule transport experiments.

In this tutorial review, we will describe crucial aspects related to the application of machine learning to help users avoid the most common pitfalls. The examples we present will be based on data from the field of molecular electronics, specifically single-molecule electron transport experiments, but the concepts and problems we explore will be sufficiently general for application in other fields with similar data. In the first part of the tutorial review, we will introduce the field of single-molecule transport, and provide an overview of the most common machine learning algorithms employed. In the second part of the tutorial review, we will show, through examples grounded in single-molecule transport, that the promises of machine learning can only be fulfilled by careful application. We will end the tutorial review with a discussion of where we, as a field, could go from here.

Quantification of the Helicality of Helical Molecular Orbitals.

The frontier molecular orbital (MO) topology of linear carbon molecules, such as polyynes, can be visually identified as helices. However, there is no clear way to quantify the helical curvature of these π-MOs, and it is thus challenging to quantify correlations between the helical curvature and molecular properties. In this paper, we develop a method that enables us to compute the helical curvature of MOs based on their nodal planes. Using this method, we define a robust way of quantifying the helical nature of MOs (helicality) by their deviation from a perfect helix. We explore several limiting cases, including polyynes, metallacumulenes, cyclic allenes, and spiroconjugated systems, where the change in helical curvature is subtle yet clearly highlighted with this method. For example, we show that strain only has a minor effect on the helicality of the frontier orbitals of cycloallenes and that the MOs of spiroconjugated systems are close to perfect helices around the spiro-carbon. Our work provides a well-defined method for assessing orbital helicality beyond visual inspection of MO isosurfaces, thus paving the way for future studies of how the helicality of π-MOs affects molecular properties.

Permethylation Introduces Destructive Quantum Interference in Saturated Silanes.

The single-molecule conductance of silanes is suppressed due to destructive quantum interference in conformations with cisoid dihedral angles along the molecular backbone. Yet, despite the structural similarity, σ-interference effects have not been observed in alkanes. Here we report that the methyl substituents used in silanes are a prerequisite for σ-interference in these systems. Through density functional theory calculations, we find that the destructive interference is not evident to the same extent in nonmethylated silanes. We find the same is true in alkanes as the transmission is significantly suppressed in permethylated cyclic and bicyclic alkanes. Using scanning tunneling microscope break-junction method we determine the single-molecule conductance of functionalized cyclohexane and bicyclo[2.2.2]octane that are found to be higher than that of equivalent permethylated silanes. Rather than the difference between carbon and silicon atoms in the molecular backbones, our calculations reveal that it is primarily the difference between hydrogen and methyl substituents that result in the different electron transport properties of nonmethylated alkanes and permethylated silanes. Chemical substituents play an important role in determining the single-molecule conductance of saturated molecules, and this must be considered when we improve and expand the chemical design of insulating organic molecules.

Close relation between quantum interference in molecular conductance and diradical existence.

An empirical observation of a relationship between a striking feature of electronic transmission through a π-system, destructive quantum interference (QI), on one hand, and the stability of diradicals on the other, leads to the proof of a general theorem that relates the two. Subject to a number of simplifying assumptions, in a π-electron system, QI occurs when electrodes are attached to those positions of an N-carbon atom N-electron closed-shell hydrocarbon where the matrix elements of the Green's function vanish. These zeros come in two types, which are called easy and hard. Suppose an N+2 atom, N+2 electron hydrocarbon is formed by substituting 2 CH2 groups at two atoms, where the electrodes were. Then, if a QI feature is associated with electrode attachment to the two atoms of the original N atom system, the resulting augmented N+2 molecule will be a diradical. If there is no QI feature, i.e., transmission of current is normal if electrodes are attached to the two atoms, the resulting hydrocarbon will not be a diradical but will have a classical closed-shell electronic structure. Moreover, where a diradical exists, the easy zero is associated with a nondisjoint diradical, and the hard zero is associated with a disjoint one. A related theorem is proven for deletion of two sites from a hydrocarbon.

Resonant Transport in Single Diketopyrrolopyrrole Junctions.

We study the single-molecule transport properties of small bandgap diketopyrrolopyrrole oligomers (DPP n, n = 1-4) with lengths varying from 1 to 5 nm. At a low bias voltage, the conductance decays exponentially as a function of length indicative of nonresonant transport. However, at a high bias voltage, we observe a remarkably high conductance close to 10-2 G0 with currents reaching over 0.1 µA across all four oligomers. These unique transport properties, together with density functional theory-based transport calculations, suggest a mechanism of resonant transport across the highly delocalized DPP backbones in the high bias regime. This study thus demonstrates the unique properties of diketopyrrolopyrrole derivatives in achieving highly efficient long-range charge transport in single-molecule devices.

Large Variations in the Single-Molecule Conductance of Cyclic and Bicyclic Silanes.

Linear silanes are efficient molecular wires due to strong σ-conjugation in the transoid conformation; however, the structure-function relationship for the conformational dependence of the single-molecule conductance of silanes remains untested. Here we report the syntheses, electrical measurements, and theoretical characterization of four series of functionalized cyclic and bicyclic silanes including a cyclotetrasilane, a cyclopentasilane, a bicyclo[2.2.1]heptasilane, and a bicyclo[2.2.2]octasilane, which are all extended by linear silicon linkers of varying length. We find an unusual variation of the single-molecule conductance among the four series at each linker length. We determine the relative conductance of the (bi)cyclic silicon structures by using the common length dependence of the four series rather than comparing the conductance at a single length. In contrast with the cyclic π-conjugated molecules, the conductance of σ-conjugated (bi)cyclic silanes is dominated by a single path through the molecule and is controlled by the dihedral angles along this path. This strong sensitivity to molecular conformation dictates the single-molecule conductance of σ-conjugated silanes and allows for systematic control of the conductance through molecular design.

Classification of conductance traces with recurrent neural networks.

We present a new automated method for structural classification of the traces obtained in break junction experiments. Using recurrent neural networks trained on the traces of minimal cross-sectional area in molecular dynamics simulations, we successfully separate the traces into two classes: point contact or nanowire. This is done without any assumptions about the expected features of each class. The trained neural network is applied to experimental break junction conductance traces, and it separates the classes as well as the previously used experimental methods. The effect of using partial conductance traces is explored, and we show that the method performs equally well using full or partial traces (as long as the trace just prior to breaking is included). When only the initial part of the trace is included, the results are still better than random chance. Finally, we show that the neural network classification method can be used to classify experimental conductance traces without using simulated results for training, but instead training the network on a few representative experimental traces. This offers a tool to recognize some characteristic motifs of the traces, which can be hard to find by simple data selection algorithms.

The Role of Through-Space Interactions in Modulating Constructive and Destructive Interference Effects in Benzene.

Quantum interference effects, whether constructive or destructive, are key to predicting and understanding the electrical conductance of single molecules. Here, through theory and experiment, we investigate a family of benzene-like molecules that exhibit both constructive and destructive interference effects arising due to more than one contact between the molecule and each electrode. In particular, we demonstrate that the π-system of meta-coupled benzene can exhibit constructive interference and its para-coupled analog can exhibit destructive interference, and vice versa, depending on the specific through-space interactions. As a peculiarity, this allows a meta-coupled benzene molecule to exhibit higher conductance than a para-coupled benzene. Our results provide design principles for molecular electronic components with high sensitivity to through-space interactions and demonstrate that increasing the number of contacts between the molecule and electrodes can both increase and decrease the conductance.

Extreme Conductance Suppression in Molecular Siloxanes.

Single-molecule conductance studies have traditionally focused on creating highly conducting molecular wires. However, progress in nanoscale electronics demands insulators just as it needs conductors. Here we describe the single-molecule length-dependent conductance properties of the classic silicon dioxide insulator. We synthesize molecular wires consisting of Si-O repeat units and measure their conductance through the scanning tunneling microscope-based break-junction method. These molecules yield conductance lower than alkanes of the same length and the largest length-dependent conductance decay of any molecular systems measured to date. We calculate single-molecule junction transmission and the complex band structure of the infinite 1D material for siloxane, in comparison with silane and alkane, and show that the large conductance decay is intrinsic to the nature of the Si-O bond. This work highlights the potential for siloxanes to function as molecular insulators in electronics.

Complex band structure and electronic transmission eigenchannels.

It is natural to characterize materials in transport junctions by their conductance length dependence, ß. Theoretical estimations of ß are made employing two primary theories: complex band structure and density functional theory (DFT) Landauer transport. It has previously been shown that the ß value derived from total Landauer transmission can be related to the ß value from the smallest |ki| complex band; however, it is an open question whether there is a deeper relationship between the two. Here we probe the details of the relationship between transmission and complex band structure, in this case individual eigenchannel transmissions and different complex bands. We present calculations of decay constants for the two most conductive states as determined by complex band structure and standard DFT Landauer transport calculations for one semi-conductor and two molecular junctions. The molecular junctions show that both the length dependence of the total transmission and the individual transmission eigenvalues can be, almost always, found through the complex band structure. The complex band structure of the semi-conducting material, however, does not predict the length dependence of the total transmission but only of the individual channels, at some k-points, due to multiple channels contributing to transmission. We also observe instances of vertical bands, some of which are the smallest |ki| complex bands, that do not contribute to transport. By understanding the deeper relationship between complex bands and individual transmission eigenchannels, we can make a general statement about when the previously accepted wisdom linking transmission and complex band structure will fail, namely, when multiple channels contribute significantly to the transmission.

Single-molecule electronics: Cooling individual vibrational modes by the tunneling current.

Electronic devices composed of single molecules constitute the ultimate limit in the continued downscaling of electronic components. A key challenge for single-molecule electronics is to control the temperature of these junctions. Controlling heating and cooling effects in individual vibrational modes can, in principle, be utilized to increase stability of single-molecule junctions under bias, to pump energy into particular vibrational modes to perform current-induced reactions, or to increase the resolution in inelastic electron tunneling spectroscopy by controlling the life-times of phonons in a molecule by suppressing absorption and external dissipation processes. Under bias the current and the molecule exchange energy, which typically results in heating of the molecule. However, the opposite process is also possible, where energy is extracted from the molecule by the tunneling current. Designing a molecular "heat sink" where a particular vibrational mode funnels heat out of the molecule and into the leads would be very desirable. It is even possible to imagine how the vibrational energy of the other vibrational modes could be funneled into the "cooling mode," given the right molecular design. Previous efforts to understand heating and cooling mechanisms in single molecule junctions have primarily been concerned with small models, where it is unclear which molecular systems they correspond to. In this paper, our focus is on suppressing heating and obtaining current-induced cooling in certain vibrational modes. Strategies for cooling vibrational modes in single-molecule junctions are presented, together with atomistic calculations based on those strategies. Cooling and reduced heating are observed for two different cooling schemes in calculations of atomistic single-molecule junctions.

Electron transport in molecular junctions with graphene as protecting layer.

We present ab initio transport calculations for molecular junctions that include graphene as a protecting layer between a single molecule and gold electrodes. This vertical setup has recently gained significant interest in experiment for the design of particularly stable and reproducible devices. We observe that the signals from the molecule in the electronic transmission are overlayed by the signatures of the graphene sheet, thus raising the need for a reinterpretation of the transmission. On the other hand, we see that our results are stable with respect to various defects in the graphene. For weakly physiosorbed molecules, no signs of interaction with the graphene are evident, so the transport properties are determined by offresonant tunnelling between the gold leads across an extended structure that includes the molecule itself and the additional graphene layer. Compared with pure gold electrodes, calculated conductances are about one order of magnitude lower due to the increased tunnelling distance. Relative differences upon changing the end group and the length of the molecule on the other hand, are similar.

Breakdown of interference rules in azulene, a nonalternant hydrocarbon.

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.

Triazatriangulene as binding group for molecular electronics.

The triazatriangulene (TATA) ring system was investigated as a binding group for tunnel junctions of molecular wires on gold surfaces. Self-assembled monolayers (SAMs) of TATA platforms with three different lengths of phenylene wires were fabricated, and their electrical conductance was recorded by both conducting probe-atomic force microscopy (CP-AFM) and scanning tunneling microscopy (STM). Similar measurements were performed for phenylene SAMs with thiol anchoring groups as references. It was found that, despite the presence of a sp(3) hybridized carbon atom in the conduction path, the TATA platform displays a contact resistance only slightly larger than the thiols. This surprising finding has not been reported before and was analyzed by theoretical computations of the transmission functions of the TATA anchored molecular wires. The relatively low contact resistance of the TATA platform along with its high stability and directionality make this binding group very attractive for molecular electronic measurements and devices.

Understanding the length dependence of molecular junction thermopower.

Thermopower of molecular junctions is sensitive to details in the junction and may increase, decrease, or saturate with increasing chain length, depending on the system. Using McConnell's theory for exponentially suppressed transport together with a simple and easily interpretable tight binding model, we show how these different behaviors depend on the molecular backbone and its binding to the contacts. We distinguish between resonances from binding groups or undercoordinated electrode atoms, and those from the periodic backbone. It is demonstrated that while the former gives a length-independent contribution to the thermopower, possibly changing its sign, the latter determines its length dependence. This means that the question of which orbitals from the periodic chain that dominate the transport should not be inferred from the sign of the thermopower but from its length dependence. We find that the same molecular backbone can, in principle, show four qualitatively different thermopower trends depending on the binding group: It can be positive or negative for short chains, and it can either increase or decrease with length.

IETS and quantum interference: propensity rules in the presence of an interference feature.

Destructive quantum interference in single molecule electronics is an intriguing phenomenon; however, distinguishing quantum interference effects from generically low transmission is not trivial. In this paper, we discuss how quantum interference effects in the transmission lead to either low current or a particular line shape in current-voltage curves, depending on the position of the interference feature. Second, we consider how inelastic electron tunneling spectroscopy can be used to probe the presence of an interference feature by identifying vibrational modes that are selectively suppressed when quantum interference effects dominate. That is, we expand the understanding of propensity rules in inelastic electron tunneling spectroscopy to molecules with destructive quantum interference.