Quantum chemistry calculations for molecules coupled to reservoirs: formalism, implementation, and application to benzenedithiol

Evaluating the Ability of External Electric Fields to Accelerate Reactions in Solution

This study investigates the catalytic effects of external electric fields (EEFs) on two reactions in solution: the Menshutkin reaction and the Chapman rearrangement. Utilizing a scanning tunneling microscope-based break-junction (STM-BJ) setup and monitoring reaction rates through high-performance liquid chromatography connected to a UV detector (HPLC-UV) and ultraperformance liquid chromatography coupled with quadrupole time-of-flight mass spectrometry (UPLC-q-ToF-MS), we observed no rate enhancement for either reaction under ambient conditions. Density functional theory (DFT) calculations indicate that electric field-induced changes in reactant orientation and the minimization of activation energy are crucial factors in determining the efficacy of EEF-driven catalysis. Our findings suggest that the current experimental setups and field strengths are insufficient to catalyze these reactions, underscoring the importance of these criteria in assessing the reaction candidates.

Single-Molecule Conductance of Staffanes

We report the first conductance measurements of [n]staffane (bicyclopentane) oligomers in single-molecule junctions. Our studies reveal two quantum transport characteristics unique to staffanes that emerge from their strained bicyclic structure. First, though staffanes are composed of weakly conjugated C-C σ-bonds, staffanes carry a shallower conductance decay value (β=0.84±0.02 n-1) than alkane chain analogs (β=0.96±0.03 n-1) when measured with the scanning tunneling microscopy break junction (STM-BJ) technique. Staffanes are thus more conductive than other σ-bonded organic backbones reported in the literature on a per atom basis. Density functional theory (DFT) calculations suggest staffane backbones are more effective conduits for charge transport because their significant bicyclic ring strain destabilizes the HOMO-2 energy, aligning it more closely with the Fermi energy of gold electrodes as oligomer order increases. Second, the monostaffane is significantly lower conducting than expected. DFT calculations suggest that short monostaffanes sterically enforce insulating gauche interelectrode orientations over syn orientations; these steric effects are alleviated in longer staffanes. Moreover, we find that [2-5]staffane wires may accommodate axial mechanical strain by "rod-bending". These findings show for the first time how bicyclic ring strain can enhance charge transmission in saturated molecular wires. These studies showcase the STM-BJ technique as a valuable tool for uncovering the stereoelectronic proclivities of molecules at material interfaces.

Secondary structure determines electron transport in peptides

Proteins play a key role in biological electron transport, but the structure-function relationships governing the electronic properties of peptides are not fully understood. Despite recent progress, understanding the link between peptide conformational flexibility, hierarchical structures, and electron transport pathways has been challenging. Here, we use single-molecule experiments, molecular dynamics (MD) simulations, nonequilibrium Green's function-density functional theory (NEGF-DFT), and unsupervised machine learning to understand the role of secondary structure on electron transport in peptides. Our results reveal a two-state molecular conductance behavior for peptides across several different amino acid sequences. MD simulations and Gaussian mixture modeling are used to show that this two-state molecular conductance behavior arises due to the conformational flexibility of peptide backbones, with a high-conductance state arising due to a more defined secondary structure (beta turn or 310 helices) and a low-conductance state occurring for extended peptide structures. These results highlight the importance of helical conformations on electron transport in peptides. Conformer selection for the peptide structures is rationalized using principal component analysis of intramolecular hydrogen bonding distances along peptide backbones. Molecular conformations from MD simulations are used to model charge transport in NEGF-DFT calculations, and the results are in reasonable qualitative agreement with experiments. Projected density of states calculations and molecular orbital visualizations are further used to understand the role of amino acid side chains on transport. Overall, our results show that secondary structure plays a key role in electron transport in peptides, which provides broad avenues for understanding the electronic properties of proteins.

Electroluminescence Rectification and High Harmonic Generation in Molecular Junctions

The field of molecular electronics has emerged from efforts to understand electron propagation through single molecules and to use them in electronic circuits. Serving as a testbed for advanced theoretical methods, it reveals a significant discrepancy between the operational time scales of experiments (static to GHz frequencies) and theoretical models (femtoseconds). Utilizing a recently developed time-linear nonequilibrium Green function formalism, we model molecular junctions on experimentally accessible time scales. Our study focuses on the quantum pump effect in a benzenedithiol molecule connected to two copper electrodes and coupled with cavity photons. By calculating both electric and photonic current responses to an ac bias voltage, we observe pronounced electroluminescence and high harmonic generation in this setup. The mechanism of the latter effect is more analogous to that from solids than from isolated molecules, with even harmonics being suppressed or enhanced depending on the symmetry of the driving field.

Conductance and assembly of quasi-1D coordination chain molecular junctions with triazole derivatives

Incorporating transition metal atoms into metal-molecule-metal junctions presents opportunities for exploring the electronic properties of coordination complexes, organometallics and metal-organic materials on the single molecule level. Recent single molecule conductance studies have shown that in situ incorporation of electrode metal atoms into coordination chains formed in the junction can occur with deprotonated, negatively charged organic ligands, such as the imidazolate (Im-) anion. However, the mechanism and chemical principles, such as the role of the charge state of the ligand, for the construction of such coordination chains are still debated. Here, we probe the role of the ligand charge state and electronic structure in single-molecule conductance and formation of metal-molecule coordination chains. We perform break junction measurements with triazole isomers, which can bridge junctions both in their neutral and charged forms, and find that prior deprotonation of the ligands is not required for coordination complex assembly, but can affect the molecular conductance and junction formation probability. Our results indicate that coordination chains can form with neutral ligands, as long as the electron density in the frontier MOs is concentrated at the binding sites and along the direction of pulling, promoting ligand binding and incorporation of gold atoms into the junction during elongation. Our findings may provide insight into design principles for in situ assembled molecular wires with transition metal atoms and open the door to electronic and spintronic studies of such materials.

Long-Range Gating in Single-Molecule One-Dimensional Topological Insulators

Single-molecule one-dimensional topological insulator (1D TI) is a class of molecular wires that exhibit increasing conductance with wire length. This unique trend is due to the coupling between the two low-lying topological edge states of 1D TIs described by the Su-Schrieffer-Heeger model. In principle, this quantum phenomenon within 1D TIs can be utilized to achieve long-range gating in molecular conductors. Here, we study electron transport through a single-edge state of doubly oxidized oligophenylene bis(triarylamine) to understand the effect of the edge state coupling on conductance. We find that conductance is elevated by approximately 1 order of magnitude compared to a control molecule with the same conductance pathway. Density function theory calculations further support that the increase in conductance is due to the interaction between the edge states of 1D TIs. This work demonstrates a new gating paradigm in molecular electronics, while also providing a deeper understanding of how edge states interact and affect electron transport within 1D TIs.

Spin-Orbit Torque in Single-Molecule Junctions from ab Initio

The use of electric fields applied across magnetic heterojunctions that lack spatial inversion symmetry has been previously proposed as a nonmagnetic means of controlling localized magnetic moments through spin-orbit torques (SOT). The implementation of this concept at the single-molecule level has remained a challenge, however. Here, we present first-principles calculations of SOT in a single-molecule junction under bias and beyond linear response. Employing a self-consistency scheme invoking density functional theory and nonequilibrium Green's function theory including spin-orbit interaction, we compute the change of the magnetization with the bias voltage and the associated current-induced SOT. Within the linear regime our quantitative estimates for the SOT in single-molecule junctions yield values similar to those known for magnetic interfaces. Our findings contribute to an improved microscopic understanding of SOT in single molecules.

Photooxidation driven formation of Fe-Au linked ferrocene-based single-molecule junctions

Metal-metal contacts, though not yet widely realized, may provide exciting opportunities to serve as tunable and functional interfaces in single-molecule devices. One of the simplest components which might facilitate such binding interactions is the ferrocene group. Notably, direct bonds between the ferrocene iron center and metals such as Pd or Co have been demonstrated in molecular complexes comprising coordinating ligands attached to the cyclopentadienyl rings. Here, we demonstrate that ferrocene-based single-molecule devices with Fe-Au interfacial contact geometries form at room temperature in the absence of supporting coordinating ligands. Applying a photoredox reaction, we propose that ferrocene only functions effectively as a contact group when oxidized, binding to gold through a formal Fe3+ center. This observation is further supported by a series of control measurements and density functional theory calculations. Our findings extend the scope of junction contact chemistries beyond those involving main group elements, lay the foundation for light switchable ferrocene-based single-molecule devices, and highlight new potential mechanistic function(s) of unsubstituted ferrocenium groups in synthetic processes.

Effective Gating in Single-Molecule Junctions through Fano Resonances

The successful incorporation of molecules as active circuit elements relies on the ability to tune their electronic properties through chemical design. A synthetic strategy that has been used to manipulate and gate circuit conductance involves attaching a pendant substituent along the molecular conduction pathway. However, such a chemical gate has not yet been shown to significantly modify conductance. Here, we report a novel series of triarylmethylium and triangulenium carbocations gated by different substituents coupled to the delocalized conducting orbitals on the molecular backbone through a Fano resonance. By changing the pendant substituents to modulate the position of the Fano resonance and its coupling to the conducting orbitals, we can regulate the junction conductance by a remarkable factor of 450. This work thus provides a new design principle to enable effective chemical gating of single-molecule devices toward effective molecular transistors.

Phenol is a pH-activated linker to gold: a single molecule conductance study

Single molecule conductance measurements typically rely on functional linker groups to anchor the molecule to the conductive electrodes through a donor-acceptor or covalent bond. While many linking moieties, such as thiols, amines, thiothers and phosphines have been used among others, very few involve oxygen binding directly to gold electrodes. Here, we report successful single molecule conductance measurements using hydroxy (OH)-containing phenol linkers and show that the molecule-gold attachment and electron transport are mediated by a direct O-Au bond. We find that deprotonation of the hydroxy moiety is necessary for metal-molecule binding to proceed, so that junction formation can be activated through pH control. Electronic structure and DFT+Σ transport calculations confirm our experimental findings that phenolate-terminated alkanes can anchor on the gold and show charge transport trends consistent with prior observations of alkane conductance with other linker groups. Critically, the deprotonated O--Au binding shows features similar to the thiolate-Au bond, but without the junction disruption caused by intercalation of sulfur into electrode tips often observed with thiol-terminated molecules. By comparing the conductance and binding features of O-Au and S-Au bonds, this study provides insight into the aspects of Au-linker bonding that promote reproducible and robust single molecule junction measurements.

Solvent-Mediated Modulation of the Au-S Bond in Dithiol Molecular Junctions

Gold-dithiol molecular junctions have been studied both experimentally and theoretically. However, the nature of the gold-thiolate bond as it relates to the solvent has seldom been investigated. It is known that solvents can impact the electronic structure of single-molecule junctions, but the correlation between the solvent and dithiol-linked single-molecule junction conductance is not well understood. We study molecular junctions formed with thiol-terminated phenylenes from both 1-chloronaphthalene and 1-bromonaphthalene solutions. We find that the most probable conductance and the distribution of conductances are both affected by the solvent. First-principles calculations show that junction conductance depends on the binding configurations (adatom, atop, and bridge) of the thiolate on the Au surface, as has been shown previously. More importantly, we find that brominated solvents can restrict the binding of thiols to specific Au sites. This mechanism offers new insight into the effects of the solvent environment on covalent bonding in molecular junctions.

Widening of the fundamental gap in cluster GW for metal-molecular interfaces

The GW approximation is very promising for an accurate first-principles description of charged excitations in single-molecule-metal interfaces. In the cluster approach for electronic transport across molecules, the infinite metal (with an adsorbed molecule) is replaced by a finite cluster whose volume should be incrementally increased to test the approach to the thermodynamic limit. Here we show that in GW, the approach to the thermodynamic limit will be much slower than in Kohn-Sham density-functional theory (DFT) because of the Coulomb interaction. To demonstrate this statement, we investigate spectral gaps in an ensemble of disordered sodium clusters in Kohn-Sham DFT, quasiparticle eigenvalue-self-consistent GW and Hartree-Fock. The fundamental gaps (i.e. difference between the lowest unoccupied and highest occupied level) in GW scale as N-1/3 on average, where N is the number of atoms. We demonstrate that this slow decrease artificially depletes the density of states at the Fermi level when the cluster is used to simulate a semi-infinite electrode. Therefore, the GW method cannot be taken as an out-of-the-box improvement of the DFT in cluster geometries, unless careful convergence checks are performed.

Single-Molecule Conductance of Intramolecular Hydrogen Bonding in Histamine on Gold

We perform single-molecule conductance measurements and DFT calculations on histamine, a biogenic amine that contains a flexible aliphatic linker and several nitrogen moieties with a potential for hydrogen bonding. Our study determines that junctions containing the free-base form of histamine can bridge through a molecular structure containing an intramolecular hydrogen bond. Conductance of this structure is higher than that through the saturated aliphatic linker. Flicker noise analysis of junction conductance confirms that transport occurs through the hydrogen bond and establishes a benchmark for noise measurements in hydrogen-bonded junctions. Overall, our work provides insights into the formation and conduction of intramolecular hydrogen bonding in single-molecule conductance measurements and into the conformations of the neurotransmitter histamine on noble metal surfaces.

An Updated Review on Developing Small Molecule Kinase Inhibitors Using Computer-Aided Drug Design Approaches

Small molecule kinase inhibitors (SMKIs) are of heightened interest in the field of drug research and development. There are 79 (as of July 2023) small molecule kinase inhibitors that have been approved by the FDA and hundreds of kinase inhibitor candidates in clinical trials that have shed light on the treatment of some major diseases. As an important strategy in drug design, computer-aided drug design (CADD) plays an indispensable role in the discovery of SMKIs. CADD methods such as docking, molecular dynamic, quantum mechanics/molecular mechanics, pharmacophore, virtual screening, and quantitative structure-activity relationship have been applied to the design and optimization of small molecule kinase inhibitors. In this review, we provide an overview of recent advances in CADD and SMKIs and the application of CADD in the discovery of SMKIs.

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.

Resonant transport in a highly conducting single molecular junction via metal-metal covalent bond

Achieving highly transmitting molecular junctions through resonant transport at low bias is key to the next-generation low-power molecular devices. Although resonant transport in molecular junctions was observed by connecting a molecule between the metal electrodes via chemical anchors by applying a high source-drain bias (>1 V), the conductance was limited to <0.1G0, G0 being the quantum of conductance. Herein, we report electronic transport measurements by directly connecting a ferrocene molecule between Au electrodes under ambient conditions in a mechanically controllable break junction setup (MCBJ), revealing a conductance peak at ∼0.2G0 in the conductance histogram. A similar experiment was repeated for ferrocene terminated with amine (-NH2) and cyano (-CN) anchors, where conductance histograms exhibit an extended low conductance feature, including the sharp high conductance peak, similar to pristine ferrocene. The statistical analysis of the data and density functional theory-based transport calculation suggest a possible molecular conformation with a strong hybridization between the Au electrodes, and that the Fe atom of ferrocene is responsible for a near-perfect transmission in the vicinity of the Fermi energy, leading to the resonant transport at a small applied bias (<0.5 V). Moreover, calculations including van der Waals/dispersion corrections reveal a covalent-like organometallic bonding between Au and the central Fe atom of ferrocene, having bond energies of ∼660 meV. Overall, our study not only demonstrates the realization of an air-stable highly transmitting molecular junction, but also provides important insights about the nature of chemical bonding at the metal/organo-metallic interface.

Electric fields drive bond homolysis

Electric fields have been used to control and direct chemical reactions in biochemistry and enzymatic catalysis, yet directly applying external electric fields to activate reactions in bulk solution and to characterize them ex situ remains a challenge. Here we utilize the scanning tunneling microscope-based break-junction technique to investigate the electric field driven homolytic cleavage of the radical initiator 4-(methylthio)benzoic peroxyanhydride at ambient temperatures in bulk solution, without the use of co-initiators or photochemical activators. Through time-dependent ex situ quantification by high performance liquid chromatography using a UV-vis detector, we find that the electric field catalyzes the reaction. Importantly, we demonstrate that the reaction rate in a field increases linearly with the solvent dielectric constant. Using density functional theory calculations, we show that the applied electric field decreases the dissociation energy of the O-O bond and stabilizes the product relative to the reactant due to their different dipole moments.

Topological Radical Pairs Produce Ultrahigh Conductance in Long Molecular Wires

Molecular one-dimensional topological insulators (1D TIs), which conduct through energetically low-lying topological edge states, can be extremely highly conducting and exhibit a reversed conductance decay, affording them great potential as building blocks for nanoelectronic devices. However, these properties can only be observed at the short length limit. To extend the length at which these anomalous effects can be observed, we design topological oligo[n]emeraldine wires using short 1D TIs as building blocks. As the wire length increases, the number of topological states increases, enabling an increased electronic transmission along the wire; specifically, we show that we can drive over a microampere current through a single ∼5 nm molecular wire, appreciably more than what has been observed in other long wires reported to date. Calculations and experiments show that the longest oligo[7]emeraldine with doped topological states has over 10⁶ enhancements in the transmission compared to its pristine form. The discovery of these highly conductive, long organic wires helps overcome a fundamental hurdle to implementing molecules in complex, nanoscale circuitry: their structures become too insulating at lengths that are useful in designing nanoscale circuits.

Voltage-Modulated van der Waals Interaction in Single-Molecule Junctions

Understanding how molecular geometry affects the electronic properties of single-molecule junctions experimentally has been challenging. Typically, metal-molecule-metal junctions are measured using a break-junction method where electrode separation is mechanically evolving during measurement. Here, to probe the impact of the junction geometry on conductance, we apply a sinusoidal modulation to the molecular junction electrode position. Simultaneously, we probe the nonlinearity of the current-voltage characteristics of each junction through a modulation in the applied bias at a different frequency. In turn, we show that junctions formed with molecules that have different molecule-electrode interfaces exhibit statistically distinguishable Fourier-transformed conductances. In particular, we find a marked bias dependence for the modulation of junctions where transmission is mediated thorough the van der Waals (vdW) interaction. We attribute our findings to voltage-modulated vdW interactions at the single-molecule level.

Atomically precise binding conformations of adenine and its variants on gold using single molecule conductance signatures

We demonstrate single molecule conductance as a sensitive and atomically precise probe of binding configurations of adenine and its biologically relevant variants on gold. By combining experimental measurements and density functional theory (DFT) calculations of single molecule-metal junction structures in aqueous conditions, we determine for the first time that robust binding of adenine occurs in neutral or basic pH when the molecule is deprotonated at the imidazole moiety. The molecule binds through the donation of the electron lone pairs from the imidazole nitrogen atoms, N7 and N9, to the gold electrodes. In addition, the pyrimidine ring nitrogen, N3, can bind concurrently and strengthen the overall metal-molecule interaction. The amine does not participate in binding to gold in contrast to most other amine-terminated molecular wires due to the planar geometry of the nucleobase. DFT calculations reveal the importance of interface charge transfer in stabilizing the experimentally observed binding configurations. We demonstrate that biologically relevant variants of adenine, 6-methyladenine and 2'-deoxyadenosine, have distinct conductance signatures. These results lay the foundation for biosensing on gold using single molecule conductance readout.

Highly conducting single-molecule topological insulators based on mono- and di-radical cations

Single-molecule topological insulators are promising candidates as conducting wires over nanometre length scales. A key advantage is their ability to exhibit quasi-metallic transport, in contrast to conjugated molecular wires which typically exhibit a low conductance that decays as the wire length increases. Here, we study a family of oligophenylene-bridged bis(triarylamines) with tunable and stable mono- or di-radicaloid character. These wires can undergo one- and two-electron chemical oxidations to the corresponding mono-cation and di-cation, respectively. We show that the oxidized wires exhibit reversed conductance decay with increasing length, consistent with the expectation for Su-Schrieffer-Heeger-type one-dimensional topological insulators. The 2.6-nm-long di-cation reported here displays a conductance greater than 0.1G₀, where G₀ is the conductance quantum, a factor of 5,400 greater than the neutral form. The observed conductance-length relationship is similar between the mono-cation and di-cation series. Density functional theory calculations elucidate how the frontier orbitals and delocalization of radicals facilitate the observed non-classical quasi-metallic behaviour.

Formation and Evolution of Metallocene Single-Molecule Circuits with Direct Gold-π Links

Single-molecule circuits with group 8 metallocenes are formed without additional linker groups in scanning tunneling microscope-based break junction (STMBJ) measurements at cryogenic and room-temperature conditions with gold (Au) electrodes. We investigate the nature of this direct gold-π binding motif and its effect on molecular conductance and persistence characteristics during junction evolution. The measurement technique under cryogenic conditions tracks molecular plateaus through the full cycle of extension and compression. Analysis reveals that junction persistence when the metal electrodes are pushed together correlates with whether electrodes are locally sharp or blunt, suggesting distinct scenarios for metallocene junction formation and evolution. The top and bottom surfaces of the "barrel"-shaped metallocenes present the electron-rich π system of cyclopentadienyl rings, which interacts with the gold electrodes in two distinct ways. An undercoordinated gold atom on a sharp tip forms a donor-acceptor bond to a specific carbon atom in the ring. However, a small, flat patch on a dull tip can bind more strongly to the ring as a whole through van der Waals interactions. Density functional theory (DFT)-based calculations of model electrode structures provide an atomic-scale picture of these scenarios, demonstrating the role of these bonding motifs during junction evolution and showing that the conductance is relatively independent of tip atomic-scale structure. The nonspecific interaction of the cyclopentadienyl rings with the electrodes enables extended conductance plateaus, a mechanism distinct from that identified for the more commonly studied, rod-shaped organic molecular wires.

Single cycloparaphenylene molecule devices: Achieving large conductance modulation via tuning radial π-conjugation

Conjugated macrocycles cycloparaphenylenes (CPPs) have unusual size-dependent electronic properties because of their unique radially π-conjugated structures. Contrary to linearly π-conjugated molecules, their highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap shrinks as the molecular size reduces, and this feature can, in principle, be leveraged to achieve unexpected size-dependent transport properties. Here, we examine charge transport characteristics of [n]CPPs (n = 5 to 12) at the single molecule level using the scanning tunneling microscope–break junction technique. We find that the [n]CPPs have a much higher conductance than their linear oligoparaphenylene counterparts at small ring size and at the same time show a large tunneling attenuation coefficient comparable to saturated alkane series. These results show that the radially π-conjugated molecular systems can offer much larger conductance modulation range than standard linear molecules and can be a new platform for building molecular devices with highly tunable transport behaviors.

Hard-Soft Chemistry Design Principles for Predictive Assembly of Single Molecule-Metal Junctions

The achievement of atomic control over the organic-inorganic interface is key to engineering electronic and spintronic properties of molecular devices. We leverage insights from inorganic chemistry to create hard-soft acid-base (HSAB) theory-derived design principles for incorporation of single molecules onto metal electrodes. A single molecule circuit is assembled via a bond between an organic backbone and an under-coordinated metal atom of the electrode surface, typically Au. Here, we study molecular composition factors affecting the junction assembly of coordination complexes containing transition metals atoms on Au electrodes. We employ hetero- and homobimetallic lantern complexes and systematically change the coordination environment to vary the character of the intramolecular bonds relative to the electrode-molecule interaction. We observe that trends in the robustness and chemical selectivity of single molecule junctions formed with a range of linkers correlate with HSAB principles, which have traditionally been used to guide atomic arrangements in the synthesis of coordination complexes. We find that this similarity between the intermolecular electrode-molecule bonding in a molecular circuit and the intramolecular bonds within a coordination complex has implications for the design of metal-containing complexes compatible with electrical measurements on metal electrodes. Our results here show that HSAB principles determine which intramolecular interactions can be compromised by inter molecule-electrode coordination; in particular on Au electrodes, soft-soft metal-ligand bonding is vulnerable to competition from soft-soft Au-linker bonding in the junction. Neutral donor-acceptor intramolecular bonds can be tuned by the Lewis acidity of the transition metal ion, suggesting future synthetic routes toward incorporation of transition metal atoms into molecular junctions for increased functionality of single molecule devices.

Highly nonlinear transport across single-molecule junctions via destructive quantum interference

To rival the performance of modern integrated circuits, single-molecule devices must be designed to exhibit extremely nonlinear current-voltage (I-V) characteristics^1-4. A common approach is to design molecular backbones where destructive quantum interference (QI) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) produces a nonlinear energy-dependent tunnelling probability near the electrode Fermi energy (E_F)^5-8. However, tuning such systems is not straightforward, as aligning the frontier orbitals to E_F is hard to control⁹. Here, we instead create a molecular system where constructive QI between the HOMO and LUMO is suppressed and destructive QI between the HOMO and strongly coupled occupied orbitals of opposite phase is enhanced. We use a series of fluorene oligomers containing a central benzothiadiazole¹⁰ unit to demonstrate that this strategy can be used to create highly nonlinear single-molecule circuits. Notably, we are able to reproducibly modulate the conductance of a 6-nm molecule by a factor of more than 10⁴.

Cumulene Wires Display Increasing Conductance with Increasing Length

One-dimensional sp-hybridized carbon wires, including cumulenes and polyynes, can be regarded as finite versions of carbynes. They are likely to be good candidates for molecular-scale conducting wires as they are predicted to have a high-conductance. In this study, we first characterize the single-molecule conductance of a series of cumulenes and polyynes with a backbone ranging in length from 4 to 8 carbon atoms, including [7]cumulene, the longest cumulenic carbon wire studied to date for molecular electronics. We observe different length dependence of conductance when comparing these two forms of carbon wires. Polyynes exhibit conductance decays with increasing molecular length, while cumulenes show a conductance increase with increasing molecular length. Their distinct conducting behaviors are attributed to their different bond length alternation, which is supported by theoretical calculations. This study confirms the long-standing theoretical predictions on sp-hybridized carbon wires and demonstrates that cumulenes can form highly conducting molecular wires.

Mechanically Tunable Quantum Interference in Ferrocene-Based Single-Molecule Junctions

Ferrocenes are ubiquitous organometallic building blocks that comprise a Fe atom sandwiched between two cyclopentadienyl (Cp) rings that rotate freely at room temperature. Of widespread interest in fundamental studies and real-world applications, they have also attracted some interest as functional elements of molecular-scale devices. Here we investigate the impact of the configurational degrees of freedom of a ferrocene derivative on its single-molecule junction conductance. Measurements indicate that the conductance of the ferrocene derivative, which is suppressed by 2 orders of magnitude as compared to a fully conjugated analogue, can be modulated by altering the junction configuration. Ab initio transport calculations show that the low conductance is a consequence of destructive quantum interference effects of the Fano type that arise from the hybridization of localized metal-based d-orbitals and the delocalized ligand-based π-system. By rotation of the Cp rings, the hybridization, and thus the quantum interference, can be mechanically controlled, resulting in a conductance modulation that is seen experimentally.

Gold-Carbon Contacts from Oxidative Addition of Aryl Iodides

Aryl halides are ubiquitous functional groups in organic chemistry, yet despite their obvious appeal as surface-binding linkers and as precursors for controlled graphene nanoribbon synthesis, they have seldom been used as such in molecular electronics. The confusion regarding the bonding of aryl iodides to Au electrodes is a case in point, with ambiguous reports of both dative Au-I and covalent Au-C contacts. Here we form single-molecule junctions with a series of oligophenylene molecular wires terminated asymmetrically with iodine and thiomethyl to show that the dative Au-I contact has a lower conductance than the covalent Au-C interaction, which we propose occurs via an in situ oxidative addition reaction at the Au surface. Furthermore, we confirm the formation of the Au-C bond by measuring an analogous series of molecules prepared ex situ with the complex Au^I(PPh₃) in place of the iodide. Density functional theory-based transport calculations support our experimental observations that Au-C linkages have higher conductance than Au-I linkages. Finally, we demonstrate selective promotion of the Au-C bond formation by controlling the bias applied across the junction. In addition to establishing the different binding modes of aryl iodides, our results chart a path to actively controlling oxidative addition on an Au surface using an applied bias.

Chemical self-assembly strategies for designing molecular electronic circuits

Design principles are demonstrated for fabricating molecular electronic circuits using the inherently self-limiting growth of molecular wires between gold nanoparticles from the oligomerization of 1,4-phenylene diisocyanide.

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.

Near Length-Independent Conductance in Polymethine Molecular Wires

Polymethine dyes are linear π-conjugated compounds with an odd number of carbons that display a much greater delocalization in comparison to polyenes that have an even number of carbon atoms in their main chain. Herein, we perform scanning tunneling microscope based break-junction measurements on a series of three cyanine dyes of increasing length. We demonstrate, at the single molecule level, that these short chain polymethine systems exhibit a substantially smaller decay in conductance with length (attenuation factor β = 0.04 Å^-1) compared to traditional polyenes (β ≈ 0.2 Å^-1). Furthermore, we show that by changing solvent we are able to shift the β value, demonstrating a remarkable negative β value, with conductance increasing with molecular length. First principle calculations provide support for the experimentally observed near-uniform length dependent conductance and further suggest that the variations in β with solvent are due to solvent-induced changes in the alignment of the frontier molecular orbitals relative to the Fermi energy of the leads. A simplified Hückel model suggests that the smaller decay in conductance correlates with the smaller degree of bond order alternation present in polymethine compounds compared to polyenes. These findings may enable the design of molecular wires without a length-dependent decay for efficient electron transport at the nanoscale.

Conductance saturation in a series of highly transmitting molecular junctions

Revealing the mechanisms of electronic transport through metal-molecule interfaces is of central importance for a variety of molecule-based devices. A key method for understanding these mechanisms is based on the study of conductance versus molecule length in molecular junctions. However, previous works focused on transport governed either by coherent tunnelling or hopping, both at low conductance. Here, we study the upper limit of conductance across metal-molecule-metal interfaces. Using highly conducting single-molecule junctions based on oligoacenes with increasing length, we find that the conductance saturates at an upper limit where it is independent of molecule length. With the aid of two prototype systems, in which the molecules are contacted by either Ag or Pt electrodes, we find two different possible origins for conductance saturation. The results are explained by an intuitive model, backed by ab initio calculations. Our findings shed light on the mechanisms that constrain the conductance of metal-molecule interfaces at the high-transmission limit.

Steady-State Density Functional Theory for Finite Bias Conductances

In the framework of density functional theory, a formalism to describe electronic transport in the steady state is proposed which uses the density on the junction and the steady current as basic variables. We prove that, in a finite window around zero bias, there is a one-to-one map between the basic variables and both local potential on as well as bias across the junction. The resulting Kohn-Sham system features two exchange-correlation (xc) potentials, a local xc potential, and an xc contribution to the bias. For weakly coupled junctions the xc potentials exhibit steps in the density-current plane which are shown to be crucial to describe the Coulomb blockade diamonds. At small currents these steps emerge as the equilibrium xc discontinuity bifurcates. The formalism is applied to a model benzene junction, finding perfect agreement with the orthodox theory of Coulomb blockade.

Impact of Electrode Density of States on Transport through Pyridine-Linked Single Molecule Junctions

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.

Spin transition in arrays of gold nanoparticles and spin crossover molecules

We investigate if the functionality of spin crossover molecules is preserved when they are assembled into an interfacial device structure. Specifically, we prepare and investigate gold nanoparticle arrays, into which room-temperature spin crossover molecules are introduced, more precisely, [Fe(AcS-BPP)2](ClO4)2, where AcS-BPP = (S)-(4-{[2,6-(dipyrazol-1-yl)pyrid-4-yl]ethynyl}phenyl)ethanethioate (in short, Fe(S-BPP)2). We combine three complementary experiments to characterize the molecule-nanoparticle structure in detail. Temperature-dependent Raman measurements provide direct evidence for a (partial) spin transition in the Fe(S-BPP)2-based arrays. This transition is qualitatively confirmed by magnetization measurements. Finally, charge transport measurements on the Fe(S-BPP)2-gold nanoparticle devices reveal a minimum in device resistance versus temperature, R(T), curves around 260-290 K. This is in contrast to similar networks containing passive molecules only that show monotonically decreasing R(T) characteristics. Backed by density functional theory calculations on single molecular conductance values for both spin states, we propose to relate the resistance minimum in R(T) to a spin transition under the hypothesis that (1) the molecular resistance of the high spin state is larger than that of the low spin state and (2) transport in the array is governed by a percolation model.

Break-junctions for investigating transport at the molecular scale

Break-junctions (BJs) enable a pair of atomic-sized electrodes to be created and the relative position between them to be controlled with sub-nanometer accuracy by mechanical means-a level of microscopic control that is not yet achievable by top-down fabrication. Locally, a BJ consists of a single-atom contact, an arrangement that is ideal not only to study various types of quantum point contacts, but also to investigate transport through an individual molecule that can bridge such a junction. In this topical review, we will provide a broad overview on the field of single-molecule electronics, in which BJs serve as the main tool of investigation. To correlate the molecular structure and transport properties to gain a fundamental understanding of the underlying transport mechanisms at the molecular scale, basic experiments that systematically cover all aspects of transport by rational chemical design and tailored experiments are needed. The variety of fascinating transport mechanisms and intrinsic molecular functionalities discovered in the past range from nonlinear transport over conductance switching to quantum interference effects observable even at room temperature. Beside discussing these results, we also look at novel directions and the most recent advances in molecular electronics investigating simultaneously electronic transport and also the mechanical and thermal properties of single-molecule junctions as well as the interaction between molecules and light. Finally, we will describe the requirements for a stepwise transition from fundamental BJ experiments towards technology-relevant architectures for future nanoelectronics applications based on ultimately-scaled molecular building blocks.

Current patterns and orbital magnetism in mesoscopic dc transport

We present ab initio calculations of the local current density j(r) as it arises in dc-transport measurements. We discover pronounced patterns in the local current density, ring currents ("eddies"), that go along with orbital magnetism. Importantly, the magnitude of the ring currents can exceed the (average) transport current by orders of magnitude. We find associated magnetic fields that exhibit drastic fluctuations with field gradients reaching 1  T nm⁻¹ V⁻¹. The relevance of our observations for spin relaxation in systems with very weak spin-orbit interaction, such as organic semiconductors, is discussed. In such systems, spin relaxation induced by bias driven orbital magnetism competes with relaxation induced by the hyperfine interaction and appears to be of similar strength. We propose a NMR-type experiment in the presence of dc-current flow to observe the spatial fluctuations of the induced magnetic fields.

Transport properties of individual C60-molecules

Electrical and thermal transport properties of C60 molecules are investigated with density-functional-theory based calculations. These calculations suggest that the optimum contact geometry for an electrode terminated with a single-Au atom is through binding to one or two C-atoms of C60 with a tendency to promote the sp(2)-hybridization into an sp(3)-type one. Transport in these junctions is primarily through an unoccupied molecular orbital that is partly hybridized with the Au, which results in splitting the degeneracy of the lowest unoccupied molecular orbital triplet. The transmission through these junctions, however, cannot be modeled by a single Lorentzian resonance, as our results show evidence of quantum interference between an occupied and an unoccupied orbital. The interference results in a suppression of conductance around the Fermi energy. Our numerical findings are readily analyzed analytically within a simple two-level model.

The dark side of DFT based transport calculations

We compare the conductance of an interacting ring with six lattice sites threaded by flux π in a two terminal setup with the conductance of the corresponding Kohn-Sham particles. Based on symmetry considerations we can show that even within (lattice) Density Functional Theory employing the exact Kohn-Sham exchange-correlation functional the conductance of the Kohn-Sham particles is exactly zero, while the conductance of the physical system is close to the unitary limit. We provide a clear demonstration that the linear conductance is not given by the conductance of the Kohn-Sham particles. We show that this fundamental problem might be solved by extending the standard DFT scheme.