Probing the Conductance of the σ-System of Bipyridine Using Destructive Interference

Methods for the analysis, interpretation, and prediction of single-molecule junction conductance behaviour

This article offers a broad overview of measurement methods in the field of molecular electronics, with a particular focus on the most common single-molecule junction fabrication techniques, the challenges in data analysis and interpretation of single-molecule junction current-distance traces, and a summary of simulations and predictive models aimed at establishing robust structure-property relationships of use in the further development of molecular electronics.

Enhancing the thermopower of single-molecule junctions by edge substitution effects

Heteroatom substitution and anchoring groups have an important impact on the thermoelectric properties of single-molecule junctions. Herein, thermoelectric properties of several anthracene derivative based single-molecule junctions are studied by means of first-principles calculations. In particular, we pay great attention to the edge substitution effects and find that edge substitution with nitrogen can induce a transmission peak near the Fermi energy, leading to large transmission coefficients and electrical conductance at the Fermi energy. Additionally, the steep shape of the transmission function gives rise to a high Seebeck coefficient. Therefore, an enhanced power factor can be expected. The robustness of this edge substitution effect has been examined by altering the electrode distance and introducing heteroatoms at different positions. The enhancement of the power factor due to edge substitution makes the studied single-molecule junction a promising candidate for efficient thermoelectric devices.

A chiral metal cluster triggers enantiospecific electronic transport

Chirality is a geometric property of matter that can be present at different scales, especially at the nanoscale. Here, we investigate the manifestation of chirality in electronic transport through a molecular junction. Spinless electronic transport through a chiral molecular junction is not enantiospecific. However, when a chiral metal cluster, C3-Au34, is attached to the source electrode, a different response is obtained in spinless electronic transport between R and L systems: this indicates the crucial role of chiral clusters in triggering enantiospecific spinless electronic transport. In contrast, when an achiral metal cluster, C3v-Au34, is attached, no change in conductance occurs between enantiomeric systems. Using the non-equilibrium green's function method, we characterized this phenomenon by calculating the transmission and conductance of spin-unpolarized electrons. Our theoretical results highlight the importance of metal clusters with specific sizes and chiral structures in electronic transport and support previously published experimental results that exhibited enantiospecific scanning tunneling measurements with intrinsically chiral tips.

Manipulating Quantum Interference between σ and π Orbitals in Single-Molecule Junctions via Chemical Substitution and Environmental Control

Understanding and manipulating quantum interference (QI) effects in single molecule junction conductance can enable the design of molecular-scale devices. Here we demonstrate QI between σ and π molecular orbitals in an ∼4 Å molecule, pyrazine, bridging source and drain electrodes. Using single molecule conductance measurements, first-principles analysis, and electronic transport calculations, we show that this phenomenon leads to distinct patterns of electron transport in nanoscale junctions, such as destructive interference through the para position of a six-membered ring. These QI effects can be tuned to allow conductance switching using environmental pH control. Our work lays out a conceptual framework for engineering QI features in short molecular systems through synthetic and external manipulation that tunes the energies and symmetries of the σ and π channels.

Exploring relationships between chemical structure and molecular conductance: from α,ω-functionalised oligoynes to molecular circuits

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-{(CC)_N}-X, N = 1, 2, 3, 4), functionalised by terminal groups, X (4-thioanisole (C₆H₄SMe), 5-(3,3-dimethyl-2,3-dihydrobenzo[b]thiophene) (DMBT), 4-aniline (C₆H₄NH₂), 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.

Substitution pattern controlled charge transport in BN-embedded aromatics-based single molecule junctions

The understanding of charge transport at a single molecule level is a prerequisite for the fabrication of molecular devices. Here, the relationship between molecular conductance, substitution pattern and stimuli response in BN-embedded aromatics was systematically investigated using the break junction technique. It was found that the para-phenylthioether-anchored BN molecule (p-BN-p) shows the highest conductance of 10^-4.86G₀, and the meta-phenylthioether-anchored BN molecule (m-BN-m) exhibits the lowest conductance which is lower than the instrument detection limit (<10^-6.0G₀). The m-BN-p and p-BN-m molecules, with both para- and meta-substituted anchor groups on two termini, show moderate conductances of 10^-5.50G₀ and 10^-5.45G₀, respectively. The conductance difference is interpreted as a distinct quantum interference effect caused by the substitution pattern of the anchoring groups. Notably, their conductance changes slightly upon coordination with a fluoride ion, in spite of the distinct change of their frontier orbital energy levels. These results demonstrate that, in addition to the frontier orbital energy levels, the anchors play an important role in the design of stimuli-responsive molecular electronic devices with a high on/off current ratio.

Heteroatom Effects on Quantum Interference in Molecular Junctions: Modulating Antiresonances by Molecular Design

Controlling charge transport through molecular wires by utilizing quantum interference (QI) is a growing topic in single-molecular electronics. In this article, scanning tunneling microscopy-break junction techniques and density functional theory calculations are employed to investigate the single-molecule conductance properties of four molecules that have been specifically designed to test extended curly arrow rules (ECARs) for predicting QI in molecular junctions. Specifically, for two new isomeric 1-phenylpyrrole derivatives, the conductance pathway between the gold electrodes must pass through a nitrogen atom: this novel feature is designed to maximize the influence of the heteroatom on conductance properties and has not been the subject of prior investigations of QI. It is shown, experimentally and computationally, that the presence of a nitrogen atom in the conductance pathway increases the effect of changing the position of the anchoring group on the phenyl ring from para to meta, in comparison with biphenyl analogues. This effect is explained in terms of destructive QI (DQI) for the meta-connected pyrrole and shifted DQI for the para-connected isomer. These results demonstrate modulation of antiresonances by molecular design and verify the validity of ECARs as a simple "pen-and-paper" method for predicting QI behavior. The principles offer new fundamental insights into structure-property relationships in molecular junctions and can now be exploited in a range of different heterocycles for molecular electronic applications, such as switches based on external gating, or in thermoelectric devices.

Destructive quantum interference in heterocyclic alkanes: the search for ultra-short molecular insulators

Designing highly insulating sub-nanometer molecules is difficult because tunneling conductance increases exponentially with decreasing molecular length. This challenge is further enhanced by the fact that most molecules cannot achieve full conductance suppression with destructive quantum interference. Here, we present results for a series of small saturated heterocyclic alkanes where we show that conductance is suppressed due to destructive interference. Using the STM-BJ technique and density functional theory calculations, we confirm that their single-molecule junction conductance is lower than analogous alkanes of similar length. We rationalize the suppression of conductance in the junctions through analysis of the computed ballistic current density. We find there are highly symmetric ring currents, which reverse direction at the antiresonance in the Landauer transmission near the Fermi energy. This pattern has not been seen in earlier studies of larger bicyclic systems exhibiting interference effects and constitutes clear-cut evidence of destructive σ-interference. The finding of heterocyclic alkanes with destructive quantum interference charts a pathway for chemical design of short molecular insulators using organic molecules.

Structural Memory Effects in Gold-4,4'-Bipyridine-Gold Single-Molecule Nanowires

We study the vulnerability of single-molecule nanowires against a temporary disconnection of the junction. To this end, we compare the room and low-temperature junction formation trajectories along the opening and closing of gold-4,4'-bipyridine-gold single-molecule nanowires. In the low-temperature measurements, the cross-correlations between the opening and subsequent closing conductance traces demonstrate a strong structural memory effect: around half of the molecular opening traces exhibit similar, statistically dependent molecular features as the junction is closed again. This means that the junction stays rigid and the molecule remains protruding from one electrode even after the rupture of the junction, and therefore, the same single-molecule junction can be reestablished if the electrodes are closed again. In the room-temperature measurements, however, weak opening-closing correlations are found, indicating a significant rearrangement of the junction after the rupture and the related loss of structural memory effects.

Extended curly arrow rules to rationalise and predict structural effects on quantum interference in molecular junctions

The ability to easily and reliably predict quantum interference (QI) behaviour would facilitate the design of functional molecular wires with potential applications in switches, transistors and thermoelectric devices. A variety of predictive methods exist, but with the exception of computationally-expensive DFT-based charge transport simulations, these often fail to account for the experimentally observed behaviour of molecules that differ significantly in structure from alternant polycyclic aromatic hydrocarbons. By considering a range of prior studies we have developed an extension to predictive "curly arrow rules". We show that, in most cases, these extended curly arrow rules (ECARs) can rationalise the type of QI exhibited by conjugated molecular wires containing heteroatoms, cross-conjugation and/or non-alternant structures. ECARs provide a straightforward "pen-and-paper" method to predict whether a molecular wire will display constructive, destructive or "shifted destructive" QI, i.e. whether or not its transmission function would be expected to show an antiresonance, and if this antiresonance would occur close to the Fermi energy or be shifted elsewhere.

Nonadditive Transport in Multi-Channel Single-Molecule Circuits

As stated in the classic Kirchhoff's circuit laws, the total conductance of two parallel channels in an electronic circuit is the sum of the individual conductance. However, in molecular circuits, the quantum interference (QI) between the individual channels may lead to apparent invalidity of Kirchhoff's laws. Such an effect can be very significant in single-molecule circuits consisting of partially overlapped multiple transport channels. Herein, an investigation on how the molecular circuit conductance correlates to the individual channels is conducted in the presence of QI. It is found that the conductance of multi-channel circuit consisting of both constructive and destructive QI is significantly smaller than the addition of individual ones due to the interference between channels. In contrast, the circuit consisting of destructive QI channels exhibits an additive transport. These investigations provide a new cognition of transport mechanism and manipulation of transport in multi-channel molecular circuits.

Voltage-Controlled Binary Conductance Switching in Gold-4,4'-Bipyridine-Gold Single-Molecule Nanowires

We investigate gold-4,4'-bipyridine-gold single-molecule junctions with the mechanically controllable break junction technique at cryogenic temperature (T = 4.2 K). We observe bistable probabilistic conductance switching between the two molecular binding configurations, influenced both by the mechanical actuation and by the applied voltage. We demonstrate that the relative dominance of the two conductance states is tunable by the electrode displacement, whereas the voltage manipulation induces an exponential speedup of both switching times. The detailed investigation of the voltage-tunable switching rates provides an insight into the possible switching mechanisms.

Simultaneous Suppression of π- and σ-Transmission in π-Conjugated Molecules

Molecular dielectric materials require ostensibly conflicting requirements of high polarizability and low conductivity. As previous efforts toward molecular insulators focused on saturated molecules, it remains an open question whether π- and σ-transport can be simultaneously suppressed in conjugated systems. Here, we demonstrate that there are conjugated molecules where the σ-transmission is suppressed by destructive σ-interference, while the π-transmission can be suppressed by a localized disruption of conjugation. Using density functional theory, we study the Landauer transmission and ballistic current density, which allow us to determine how the transmission is affected by various structural changes in the molecule. We find that in para-linked oligophenyl rings the σ-transmission can be suppressed by changing the remaining hydrogens to methyl groups due to the inherent gauche-like structure of the carbon backbone within a benzene ring, similar to what was previously seen in saturated systems. At the same time, the methyl groups fulfill a dual purpose as they modulate the twist angle between neighboring phenyl rings. When neighboring rings are orthogonal to each other, the transmission through both π- and σ-systems is effectively suppressed. Alternatively, breaking conjugation in a single phenyl ring by saturating two carbons atoms with two methyl substituents on each carbon, results in suppressed π- and σ-transport independent of dihedral angle. These two strategies demonstrate that methyl-substituted oligophenyls are promising candidates for the development of molecular dielectric materials.

Enhanced charge transport via d(δ)-p(π) conjugation in Mo2-integrated single-molecule junctions

A trans-dimolybdenum nicotinate (m-Mo2) complex and its isonicotinate isomer (p-Mo2) were synthesized and characterized crystallographically, and their single-molecule charge transport properties were investigated using the STM break junction (STM-BJ) technique. With a quadruply bonded Mo2 complex unit integrated into molecular backbones, the single-molecule conductance for complex molecules was increased by more than one order of magnitude compared with that of the organic π-conjugated analogues 1,4-bis(4-pyridyl)benzene (p-Ph) and 1,4-bis(3-pyridyl)benzene (m-Ph). More interestingly, unlike m-Ph, m-Mo2 with meta connected pyridyl anchors presents larger conductance than that of p-Mo2 with two para connected pyridyl groups. DFT-based transmission calculations revealed that the significant conductance enhancement of Mo2 molecules originates from the largely reduced HOMO-LUMO gap, and the unique d(δ)-p(π) conjugation between the Mo2 unit and the pyridine rings gives rise to a delocalized electronic structure that endows the Mo2 molecules with an unexpected high conductance.

Carbazole-Based Tetrapodal Anchor Groups for Gold Surfaces: Synthesis and Conductance Properties

As the field of molecular-scale electronics matures and the prospect of devices incorporating molecular wires becomes more feasible, it is necessary to progress from the simple anchor groups used in fundamental conductance studies to more elaborate anchors designed with device stability in mind. This study presents a series of oligo(phenylene-ethynylene) wires with one tetrapodal anchor and a phenyl or pyridyl head group. The new anchors are designed to bind strongly to gold surfaces without disrupting the conductance pathway of the wires. Conductive probe atomic force microscopy (cAFM) was used to determine the conductance of self-assembled monolayers (SAMs) of the wires in Au-SAM-Pt and Au-SAM-graphene junctions, from which the conductance per molecule was derived. For tolane-type wires, mean conductances per molecule of up to 10-4.37  G0 (Pt) and 10-3.78  G0 (graphene) were measured, despite limited electronic coupling to the Au electrode, demonstrating the potential of this approach. Computational studies of the surface binding geometry and transport properties rationalise and support the experimental results.

Revealing the electronic structure of organic emitting semiconductors at the single-molecule level

Single-molecule conductance measurements of OLED molecules show that the holes injected from metal electrode can be suppressed by adding electron-withdrawing arms, benefiting the electron–hole balance of OLED devices whose holes are excessive.

Selective formation of molecular junctions with high and low conductance states by tuning the velocity of electrode displacement

A single-molecule junction of 1,4-di(4-pyridyl)benzene (DPB) was prepared in a nano-gap between two Au electrodes using the scanning tunnelling microscopy-based break junction method (STM-BJ).

Enhanced coupling through π-stacking in imidazole-based molecular junctions

We demonstrate that imidazole based π–π stacked dimers form strong and efficient conductance pathways in single-molecule junctions using the scanning-tunneling microscope-break junction (STM-BJ) technique and density functional theory-based calculations.

We demonstrate that imidazole based π–π stacked dimers form strong and efficient conductance pathways in single-molecule junctions using the scanning-tunneling microscope-break junction (STM-BJ) technique and density functional theory-based calculations. We first characterize an imidazole-gold contact by measuring the conductance of imidazolyl-terminated alkanes (im-N-im, N = 3–6). We show that the conductance of these alkanes decays exponentially with increasing length, indicating that the mechanism for electron transport is through tunneling or super-exchange. We also reveal that π–π stacked dimers can be formed between imidazoles and have better coupling than through-bond tunneling. These experimental results are rationalized by calculations of molecular junction transmission using non-equilibrium Green's function formalism. This study verifies the capability of imidazole as a Au-binding ligand to form stable single- and π-stacked molecule junctions at room temperature.

Transmission mechanism and quantum interference in fused thienoacenes coupling to Au electrodes through the thiophene rings

So far, quantum interference in molecular devices where the anchors are inseparable parts of the whole molecule has been seldom discussed. In this article, we perform first-principles calculations on the electronic transmission properties of a series of Au-thienoacene-Au junctions where the molecule interacts with electrodes through the S atoms in thiophene rings in a fused-ring system. The calculated binding energy of the Au-S interaction is highly dependent on the substitution sites of the thiophene rings, which agrees with the experimental report that the Au-S interaction is too weak to form a junction for some molecules. The electronic coupling at the molecule-electrode contact is also affected by the molecular structure. To distinguish the coupling mechanism, we show the importance of investigating the electron distribution of frontier molecular orbitals in combination with the percentage of the π system in the partial density of states on the S atoms. Because of the difference in electronic coupling, comparison between molecules should be done with care. On the other hand, conductance suppression due to the destructive quantum interference originating from the molecular topology is demonstrated by comparing the properties of isomers with similar molecule-electrode coupling.

On the resilience of magic number theory for conductance ratios of aromatic molecules

If simple guidelines could be established for understanding how quantum interference (QI) can be exploited to control the flow of electricity through single molecules, then new functional molecules, which exploit room-temperature QI could be rapidly identified and subsequently screened. Recently it was demonstrated that conductance ratios of molecules with aromatic cores, with different connectivities to electrodes, can be predicted using a simple and easy-to-use "magic number theory." In contrast with counting rules and "curly-arrow" descriptions of destructive QI, magic number theory captures the many forms of constructive QI, which can occur in molecular cores. Here we address the question of how conductance ratios are affected by electron-electron interactions. We find that due to cancellations of opposing trends, when Coulomb interactions and screening due to electrodes are switched on, conductance ratios are rather resilient. Consequently, qualitative trends in conductance ratios of molecules with extended pi systems can be predicted using simple 'non-interacting' magic number tables, without the need for large-scale computations. On the other hand, for certain connectivities, deviations from non-interacting conductance ratios can be significant and therefore such connectivities are of interest for probing the interplay between Coulomb interactions, connectivity and QI in single-molecule electron transport.

The Bicyclo[2.2.2]octane Motif: A Class of Saturated Group 14 Quantum Interference Based Single-Molecule Insulators

The electronic transmission through σ-conjugated molecules can be fully suppressed by destructive quantum interference, which makes them potential candidates for single-molecule insulators. The first molecule with clear suppression of the single-molecule conductance due to σ-interference was recently found in the form of a functionalized bicyclo[2.2.2]octasilane. Here we continue the search for potential single-molecule insulators based on saturated group 14 molecules. Using a high-throughput screening approach, we assess the electron transport properties of the bicyclo[2.2.2]octane class by systematically varying the constituent atoms between carbon, silicon, and germanium, thus exploring the full chemical space of 771 different molecules. The majority of the molecules in the bicyclo[2.2.2]octane class are found to be highly insulating molecules. Though the all-silicon molecule is a clear-cut case of σ-interference, it is not unique within its class and there are many potential molecules that we predict to be more insulating. The finding of this class of quantum interference based single-molecule insulators indicates that a broad range of highly insulating saturated group 14 molecules are likely to exist.

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.

Molecular Orbital Rule for Quantum Interference in Weakly Coupled Dimers: Low-Energy Giant Conductivity Switching Induced by Orbital Level Crossing

Destructive quantum interference (QI) in molecular junctions has attracted much attention in recent years. It can tune the conductance of molecular devices dramatically, which implies numerous potential applications in thermoelectric and switching applications. There are several schemes that address and rationalize QI in single molecular devices. Dimers play a particular role in this respect because the QI signal may disappear, depending on the dislocation of monomers. We derive a simple rule that governs the occurrence of QI in weakly coupled dimer stacks of both alternant and nonalternant polyaromatic hydrocarbons (PAHs) and extends the Tada-Yoshizawa scheme. Starting from the Green's function formalism combined with the molecular orbital expansion approach, it is shown that QI-induced antiresonances and their energies can be predicted from the amplitudes of the respective monomer terminal molecular orbitals. The condition is illustrated for a toy model consisting of two hydrogen molecules and applied within density functional calculations to alternant dimers of oligo(phenylene-ethynylene) and nonalternant PAHs. Minimal dimer structure modifications that require only a few millielectronvolts and lead to an energy crossing of the essentially preserved monomer orbitals are shown to result in giant conductance switching ratios.