The relation between structure and quantum interference in single molecule junctions

Electron Transport through Linear-, Broken-, and Cross-Conjugated Polycyclic Compounds

Quantum interference (QI) effects offer unique opportunities to modulate charge transport through single molecules. In recent years, several transmission selection rules have been developed to determine constructive and destructive QIs in an intuitive and simple manner, although some of these rules fail for cross-conjugated systems. In this work, we evaluate the performance of distinct transmission rules on a broad series of anthracene and fluorene derivatives with distinctive structural features including linear-, broken-, and cross-conjugation, heteroatoms, and five-membered rings as such species affords a predictive challenge for the qualitative selection rules for QI effects. The electron transport properties and local transmission plots are first evaluated by combining DFT and the nonequilibrium Green function method allowing for an equal-footing comparison of the conductance of the different polycyclic compounds. Our findings are in line with experimental observations on the influence of the type of conjugation and the connectivity to the metallic electrodes on the transport properties. Thus, cross-conjugated systems exhibit reduced conductance values as compared to the linear-conjugated ones, although the transmission is enhanced in the meta-connected junctions. Remarkably, our study reveals that aromatic cores exhibit generally larger zero-bias conductance for a given connectivity, in contrast to the negative aromaticity-conductance relationship found in literature.

Quantum interference enhances the performance of single-molecule transistors

Quantum effects in nanoscale electronic devices promise to lead to new types of functionality not achievable using classical electronic components. However, quantum behaviour also presents an unresolved challenge facing electronics at the few-nanometre scale: resistive channels start leaking owing to quantum tunnelling. This affects the performance of nanoscale transistors, with direct source-drain tunnelling degrading switching ratios and subthreshold swings, and ultimately limiting operating frequency due to increased static power dissipation. The usual strategy to mitigate quantum effects has been to increase device complexity, but theory shows that if quantum effects can be exploited in molecular-scale electronics, this could provide a route to lower energy consumption and boost device performance. Here we demonstrate these effects experimentally, showing how the performance of molecular transistors is improved when the resistive channel contains two destructively interfering waves. We use a zinc-porphyrin coupled to graphene electrodes in a three-terminal transistor to demonstrate a >104 conductance-switching ratio, a subthreshold swing at the thermionic limit, a >7 kHz operating frequency and stability over >105 cycles. We fully map the anti-resonance interference features in conductance, reproduce the behaviour by density functional theory calculations and trace back the high performance to the coupling between molecular orbitals and graphene edge states. These results demonstrate how the quantum nature of electron transmission at the nanoscale can enhance, rather than degrade, device performance, and highlight directions for future development of miniaturized electronics.

Quantum Interference Enhancement of the Spin-Dependent Thermoelectric Response

We investigate the influence of quantum interference (QI) and broken spin-symmetry on the thermoelectric response of node-possessing junctions, finding a dramatic enhancement of the spin-thermopower (Ss), figure-of-merit (ZsT), and maximum thermodynamic efficiency (ηsmax) caused by destructive QI. Using many-body and single-particle methods, we calculate the response of 1,3-benzenedithiol and cross-conjugated molecule-based junctions subject to an applied magnetic field, finding nearly universal behavior over a range of junction parameters with Ss, ZsT, and reaching peak values of 2 π / 3 ( k / e ) , 1.51, and 28% of Carnot efficiency, respectively. We also find that the quantum-enhanced spin-response is spectrally broad, and the field required to achieve peak efficiency scales with temperature. The influence of off-resonant thermal channels (e.g., phonon heat transport) on this effect is also investigated.

Understanding Emergent Complexity from a Single-Molecule Perspective

Molecules, with structural, scaling, and interaction diversities, are crucial for the emergence of complex behaviors. Interactions are essential prerequisites for complex systems to exhibit emergent properties that surpass the sum of individual component characteristics. Tracing the origin of complex molecular behaviors from interactions is critical to understanding ensemble emergence, and requires insights at the single-molecule level. Electrical signals from single-molecule junctions enable the observation of individual molecular behaviors, as well as intramolecular and intermolecular interactions. This technique provides a foundation for bottom-up explorations of emergent complexity. This Perspective highlights investigations of various interactions via single-molecule junctions, including intramolecular orbital and weak intermolecular interactions and interactions in chemical reactions. It also provides potential directions for future single-molecule junctions in complex system research.

Thermoelectric Properties of Porphyrin Nano Rings: A Theoretical and Modelling Investigation

Propagation of De Broglie waves through nanomolecular junctions is greatly affected by molecular topology changes, which in turn plays a key role in determining the electronic and thermoelectric properties of source|molecule|drain junctions. The probing and realization of the constructive quantum interference (CQI) and a destructive quantum interference (DQI) are well established in this work. The critical role of quantum interference (QI) in governing and enhancing the transmission coefficient T(E), thermopower (S), power factor (P) and electronic figure of merit (ZelT) of porphyrin nanorings has been investigated using a combination of density functional theory (DFT) methods, a tight binding (Hückel) modelling (TBHM) and quantum transport theory (QTT). Remarkably, DQI not only dominates the asymmetric molecular pathways and lowering T(E), but also improves the thermoelectric properties.

Destructive quantum interference in meta-oligo(phenyleneethynylene) molecular wires with gold-graphene heterojunctions

Quantum interference (QI) is well recognised as a significant contributing factor to the magnitude of molecular conductance values in both single-molecule and large area junctions. Numerous structure-property relationship studies have shown that para-connected oligo(phenyleneethynylene) (OPE) based molecular wires exemplify the impact of constructive quantum interference (CQI), whilst destructive quantum interference (DQI) effects are responsible for the orders of magnitude lower conductance of analogous meta-contacted OPE derivatives, despite the somewhat shorter effective tunnelling distance. Since molecular conductance is related to the value of the transmission function, evaluated at the electrode Fermi energy, T(EF), which in turn is influenced by the presence and relative energy of (anti)resonances, it follows that the relative single-molecule conductance of para- and meta-contacted OPE-type molecules is tuned both by the anchor group and the nature of the electrode materials used in the construction of molecular junctions (gold|molecule|gold vs. gold|molecule|graphene). It is shown here that whilst amine-contacted junctions show little influence of the electrode material on molecular conductance due to the similar electrode-molecule coupling through this anchor group to both types of electrodes, the weaker coupling between thiomethyl and ethynyl anchors and the graphene substrate electrode results in a relative enhancement of the DQI effect. This work highlights an additional parameter space to explore QI effects and establishes a new working model based on the electrode materials and anchor groups in modulating QI effects beyond the chemical structure of the molecular backbone.

Exploring a Linear Combination Feature for Predicting the Conductance of Parallel Molecular Circuits

An accurate rule for predicting conductance is the cornerstone of developing molecular circuits and provides a promising solution for miniaturizing electric circuits. The successful prediction of series molecular circuits has proven the possibility of establishing a rule for molecular circuits under quantum mechanics. However, the quantitatively accurate prediction has not been validated by experiments for parallel molecular circuits. Here we used 1,3-dihydrobenzothiophene (DBT) to build the parallel molecular circuits. The theoretical simulation and single-molecule conductance measurements demonstrated that the conductance of the molecule containing one DBT is the unprecedented linear combination of the conductance of the two individual channels with respective contribution weights of 0.37 and 0.63. With these weights, the conductance of the molecule containing two DBTs is predicted as 1.81 nS, matching perfectly with the measured conductance (1.82 nS). This feature offers a potential rule for quantitatively predicting the conductance of parallel molecular circuits.

Controlling piezoresistance in single molecules through the isomerisation of bullvalenes

Nanoscale electro-mechanical systems (NEMS) displaying piezoresistance offer unique measurement opportunities at the sub-cellular level, in detectors and sensors, and in emerging generations of integrated electronic devices. Here, we show a single-molecule NEMS piezoresistor that operates utilising constitutional and conformational isomerisation of individual diaryl-bullvalene molecules and can be switched at 850 Hz. Observations are made using scanning tunnelling microscopy break junction (STMBJ) techniques to characterise piezoresistance, combined with blinking (current-time) experiments that follow single-molecule reactions in real time. A kinetic Monte Carlo methodology (KMC) is developed to simulate isomerisation on the experimental timescale, parameterised using density-functional theory (DFT) combined with non-equilibrium Green's function (NEGF) calculations. Results indicate that piezoresistance is controlled by both constitutional and conformational isomerisation, occurring at rates that are either fast (equilibrium) or slow (non-equilibrium) compared to the experimental timescale. Two different types of STMBJ traces are observed, one typical of traditional experiments that are interpreted in terms of intramolecular isomerisation occurring on stable tipped-shaped metal-contact junctions, and another attributed to arise from junction‒interface restructuring induced by bullvalene isomerisation.

Do quantum interference effects manifest in acyclic aliphatic molecules with anchoring groups?

The ability to control single molecule electronic conductance is imperative for achieving functional molecular electronics applications such as insulation, switching, and energy conversion. Quantum interference (QI) effects are generally used to control electronic transmission through single molecular junctions by tuning the molecular structure or the position of the anchoring group(s) in the molecule. While previous studies focussed on the QI between σ and/or π channels of the molecular backbone, here, we show that single molecule electronic devices can be designed based on QI effects originating from the interactions of anchoring groups. Furthermore, while previous studies have concentrated on the QI mostly in conjugated/cyclic systems, our study showcases that QI effects can be harnessed even in the simplest acyclic aliphatic systems-alkanedithiols, alkanediamines, and alkanediselenols. We identify band gap state resonances in the transmission spectrum of these molecules whose positions and intensities depend on the chain length, and anchoring group sensitive QI between the nearly degenerate molecular orbitals localized on the anchoring groups. We predict that these QI features can be harnessed through an external mechanical stimulus to tune the charge transport properties of single molecules in the break-junction experiments.

Radical Single-Molecule Junctions

Radicals are unique molecular systems for applications in electronic devices due to their open-shell electronic structures. Radicals can function as good electrical conductors and switches in molecular circuits while also holding great promise in the field of molecular spintronics. However, it is both challenging to create stable, persistent radicals and to understand their properties in molecular junctions. The goal of this Perspective is to address this dual challenge by providing design principles for the synthesis of stable radicals relevant to molecular junctions, as well as offering current insight into the electronic properties of radicals in single-molecule devices. By exploring both the chemical and physical properties of established radical systems, we will facilitate increased exploration and development of radical-based molecular systems.

Resistance saturation in semi-conducting polyacetylene molecular wires

Realizing the promises of molecular electronic devices requires an understanding of transport on the nanoscale. Here, we consider a Su-Schrieffer-Heeger model for semi-conducting trans-polyacetylene molecular wires in which we endow charge carriers with a finite lifetime. The aim of this exercise is two-fold: (i) the simplicity of the model allows an insightful numerical and analytical comparison of the Landauer and Kubo linear-response formalism; (ii) we distill the prototypical characteristics of charge transport through gapped mesoscopic systems and compare these to bulk semiconductors. We find that both techniques yield a residual differential conductance at low temperatures for contacted polyacetylene chains of arbitrary length-in line with the resistivity saturation in some correlated narrow-gap semiconductors. Quantitative agreement, however, is limited to not too long molecules. Indeed, while the Landauer transmission is suppressed exponentially with the system size, the Kubo response only decays hyperbolically. Our findings inform the choice of transport methodologies for the ab initio modelling of molecular devices.

Stereoelectronic Modulation of a Single-Molecule Junction through a Tunable Metal-Carbon dπ-pπ Hyperconjugation

Conjugated molecules play a critical role in the construction of single-molecule devices. However, most conventional conjugated molecules, such as hydrocarbons, involve only a pπ-pπ conjugation of light elements. While the metal d-orbitals can introduce abundant electronic effects to achieve novel electronic properties, it is very scarce for the charge transport study of dπ-pπ conjugated pathways with a metal involved. Here, we employed the single-molecule break junction technique to investigate the charge transport through dπ-pπ conjugated backbones with metal-carbon multiple bonds integrated into the alternative conjugated pathways. The involved dπ-pπ conjugation not only supports high conductivity comparable to that of conjugated hydrocarbons but also significantly enhances the tunable diversity in electronic properties through the metal-induced secondary interaction. Specifically, the introduction of the metal brings an unconventionally stereoelectronic effect triggered by metal-carbon dπ-pπ hyperconjugation, which can be tuned by protonation taking place on the metal-carbon multiple bonds, collectively modulating the single-molecule rectification feature and transmission mechanism. This work demonstrates the promise of utilizing the diverse electronic effect of metals to design molecular devices.

Planar aromatic anchors control the electrical conductance of gold|molecule|graphene junctions

The synthesis of a family of alkanethiol molecules with planar aromatic head groups, designed to anchor molecules effectively to graphene electrodes, is reported. Characterisation of self-assembled monolayers of these molecules on a gold surface via conductive atomic force microscopy shows that when an aromatic head group is present, the conductance G graphene obtained using a graphene coated probe is higher than the conductance G Pt obtained using a platinum (Pt) probe. For Pt probe and graphene probe junctions, the tunnelling decay constant of benzyl ether derivatives with an alkanethiol molecular backbone is determined as β = 5.6 nm-1 and 3.5 nm-1, respectively. The conductance ratio G graphene/G Pt increases as the number of rings present in the aromatic head unit, n, increases. However, as the number of rings increases, the conductance path length increases because the planar head groups lie at an angle to the plane of the electrodes. This means that overall conductance decreases as n increases. Density functional theory-based charge transport calculations support these experimental findings. This study confirms that planar aromatic head groups can function as effective anchoring units for graphene electrodes in large area molecular junctions. However, the results also indicate that the size and geometry of these head groups must be considered in order to produce effective molecular designs.

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.

Single-molecule conductance studies on quasi- and metallaaromatic dibenzoylmethane coordination compounds and their aromatic analogs

The ability to predict the conductive behaviour of molecules, connected to macroscopic electrodes, represents a crucial prerequisite for the design of nanoscale electronic devices. In this work, we investigate whether the notion of a negative relation between conductance and aromaticity (the so-called NRCA rule) also pertains to quasi-aromatic and metallaaromatic chelates derived from dibenzoylmethane (DBM) and Lewis acids (LAs) that either do or do not contribute two extra d_π electrons to the central resonance-stabilised β-ketoenolate binding pocket. We therefore synthesised a family of methylthio-functionalised DBM coordination compounds and subjected them, along with their truly aromatic terphenyl and 4,6-diphenylpyrimidine congeners, to scanning tunneling microscope break-junction (STM-BJ) experiments on gold nanoelectrodes. All molecules share the common motif of three π-conjugated, six-membered, planar rings with a meta-configuration at the central ring. According to our results, their molecular conductances fall within a factor of ca. 9 in an ordering aromatic < metallaaromatic < quasi-aromatic. The experimental trends are rationalised by quantum transport calculations based on density functional theory (DFT).

Quantum interference effects elucidate triplet-pair formation dynamics in intramolecular singlet-fission molecules

Quantum interference (QI)-the constructive or destructive interference of conduction pathways through molecular orbitals-plays a fundamental role in enhancing or suppressing charge and spin transport in organic molecular electronics. Graphical models were developed to predict constructive versus destructive interference in polyaromatic hydrocarbons and have successfully estimated the large conductivity differences observed in single-molecule transport measurements. A major challenge lies in extending these models to excitonic (photoexcited) processes, which typically involve distinct orbitals with different symmetries. Here we investigate how QI models can be applied as bridging moieties in intramolecular singlet-fission compounds to predict relative rates of triplet pair formation. In a series of bridged intramolecular singlet-fission dimers, we found that destructive QI always leads to a slower triplet pair formation across different bridge lengths and geometries. A combined experimental and theoretical approach reveals the critical considerations of bridge topology and frontier molecular orbital energies in applying QI conductance principles to predict rates of multiexciton generation.

Learning Conductance: Gaussian Process Regression for Molecular Electronics

Experimental studies of charge transport through single molecules often rely on break junction setups, where molecular junctions are repeatedly formed and broken while measuring the conductance, leading to a statistical distribution of conductance values. Modeling this experimental situation and the resulting conductance histograms is challenging for theoretical methods, as computations need to capture structural changes in experiments, including the statistics of junction formation and rupture. This type of extensive structural sampling implies that even when evaluating conductance from computationally efficient electronic structure methods, which typically are of reduced accuracy, the evaluation of conductance histograms is too expensive to be a routine task. Highly accurate quantum transport computations are only computationally feasible for a few selected conformations and thus necessarily ignore the rich conformational space probed in experiments. To overcome these limitations, we investigate the potential of machine learning for modeling conductance histograms, in particular by Gaussian process regression. We show that by selecting specific structural parameters as features, Gaussian process regression can be used to efficiently predict the zero-bias conductance from molecular structures, reducing the computational cost of simulating conductance histograms by an order of magnitude. This enables the efficient calculation of conductance histograms even on the basis of computationally expensive first-principles approaches by effectively reducing the number of necessary charge transport calculations, paving the way toward their routine evaluation.

Quantum Interference in Mixed-Valence Complexes: Tuning Electronic Coupling Through Substituent Effects

Whilst 2- or 5-OMe groups on the bridging phenylene ring in [{Cp*(dppe)RuC≡C}₂ (μ-1,3-C₆ H₄ )]⁺ have little influence on the electronic structure of this weakly coupled mixed-valence complex, a 4-OMe substituent enhances ground state electron delocalization, and increases the intensity of the IVCT transition. Vibrational frequency and TDDFT calculations (LH20t-D3(BJ), def2-SVP, COSMO (CH₂ Cl₂ )) on ([{Cp*(dppe)RuC≡C}₂ (μ-1,3-C₆ H₃ -n-OMe)]⁺ (n=2, 4, 5) models are in excellent agreement with the experimental results. The stronger ground state coupling is attributed to the change in composition of the β-HOSO brought about by the 4-OMe group, which is ortho or para to each of the metal fragments. The intensity of the IVCT transition increases with the greater overlap of the β-HOSO and β-LUSO, whilst the relative phases of the β-HOSO and β-LUSO in the 4-OMe substituted complex are consistent with predictions of constructive quantum interference from molecular circuit rules.

Quantum Interference-Controlled Conductance Enhancement in Stacked Graphene-like Dimers

Stacking interactions are of significant importance in the fields of chemistry, biology, and material optoelectronics because they determine the efficiency of charge transfer between molecules and their quantum states. Previous studies have proven that when two monomers are π-stacked in series to form a dimer, the electrical conductance of the dimer is significantly lower than that of the monomer. Here, we present a strong opposite case that when two anthanthrene monomers are π-stacked to form a dimer in a scanning tunneling microscopic break junction, the conductance increases by as much as 25 in comparison with a monomer, which originates from a room-temperature quantum interference. Remarkably, both theory and experiment consistently reveal that this effect can be reversed by changing the connectivity of external electrodes to the monomer core. These results demonstrate that synthetic control of connectivity to molecular cores can be combined with stacking interactions between their π systems to modify and optimize charge transfer between molecules, opening up a wide variety of potential applications ranging from organic optoelectronics and photovoltaics to nanoelectronics and single-molecule electronics.

Single-molecule nano-optoelectronics: insights from physics

Single-molecule optoelectronic devices promise a potential solution for miniaturization and functionalization of silicon-based microelectronic circuits in the future. For decades of its fast development, this field has made significant progress in the synthesis of optoelectronic materials, the fabrication of single-molecule devices and the realization of optoelectronic functions. On the other hand, single-molecule optoelectronic devices offer a reliable platform to investigate the intrinsic physical phenomena and regulation rules of matters at the single-molecule level. To further realize and regulate the optoelectronic functions toward practical applications, it is necessary to clarify the intrinsic physical mechanisms of single-molecule optoelectronic nanodevices. Here, we provide a timely review to survey the physical phenomena and laws involved in single-molecule optoelectronic materials and devices, including charge effects, spin effects, exciton effects, vibronic effects, structural and orbital effects. In particular, we will systematically summarize the basics of molecular optoelectronic materials, and the physical effects and manipulations of single-molecule optoelectronic nanodevices. In addition, fundamentals of single-molecule electronics, which are basic of single-molecule optoelectronics, can also be found in this review. At last, we tend to focus the discussion on the opportunities and challenges arising in the field of single-molecule optoelectronics, and propose further potential breakthroughs.

Edge magnetization and thermally induced spin current in nanostructured graphene

In this work, the magnetic states and thermally induced spin currents in graphene nanoflake sizes with different sizes and shapes have been investigated using Hubbard model combined with non-equilibrium Green's function method. In addition to the antiferromagnetic (AFM) state governed by the sizes, shapes, armchair bond densities, and Coulomb energy, our calculations have also pointed out the emergence of ferromagnetic (FM) and complex magnetic states when the gate voltage is invoked in the graphene nanoflakes. More prominently, by exploiting the geometric symmetry of the nanoflakes without external fields, a pure spin current and zero charge current are generated in spin caloritronic device when the graphene nanoflakes are both in the AFM and FM states. The formation of pure spin currents driven by temperature difference depends on the graphene nanoflakes' size, shape, temperature and gate voltage as well. The study also shows the outstanding advantages of diamond-shaped graphene nanoflakes in both magnetic properties and spin currents. This result paves the way for the possibility of practical applications of graphene materials in spintronics and spin caloritronics.

Substituent Control of σ-Interference Effects in the Transmission of Saturated Molecules

The single-molecule conductance of saturated molecules can potentially be fully suppressed by destructive quantum interference in their σ-system. However, only few molecules with σ-interference have been identified, and the structure-property relationship remains to be elucidated. Here, we explore the role of substituents in modulating the electronic transmission of saturated molecules. In functionalized bicyclo[2.2.2]octanes, the transmission is suppressed by σ-interference when fluorine substituents are applied. For bicyclo[2.2.2]octasilane and -octagermanes, the transmission is suppressed when carbon-based substituents are used, and such molecules are likely to be highly insulating. For the carbon-based substituents, we find a strong correlation between the appropriate Hammett constants and the transmission. The substituent effect enables systematic optimization of the insulating properties of saturated molecular cores.

Nonequilibrium Green's function method for phonon heat transport in quantum system

Phonon heat transport property in quantum devices is of great interesting since it presents significant quantum behaviors. In the past few decades, great efforts have been devoted to establish the theoretical method for phonon heat transport simulation in nanostructures. However, modeling phonon heat transport from wavelike coherent regime to particlelike incoherent regime remains a challenging task. The widely adopted theoretical approach, such as molecular dynamics, semiclassical Boltzmann transport equation, captures quantum mechanical effects within different degrees of approximation. Among them, Non-equilibrium Green's function (NEGF) method has attracted wide attention, as its ability to perform full quantum simulation including many-body interactions. In this review, we summarized recent theoretical advances of phonon NEGF method and the applications on the numerical simulation for phonon heat transport in nanostructures. At last, the challenges of numerical simulation are discussed.

Mechanoresistive single-molecule junctions

Single-molecule junctions - devices fabricated by electrically connecting a single molecule to two electrodes - can respond to a variety of stimuli, that include electrostatic/electrochemical gating, light, other chemical species, and mechanical forces. When the latter is used, the device becomes mechanoresistive which means that its electrical resistance/conductance changes upon application of a mechanical stress. The mechanoresistive phenomenon can arise at the metal-molecule interface or it can be embedded in the molecular backbone, and several strategies to attain high reproducibility, high sensitivity and reversible behaviour have been developed over the years. These devices offer a unique insight on the process of charge transfer/transport at the metal/molecule interface, and have potential for applications as nanoelectromechanical systems, integrating electrical and mechanical functionality at the nanoscale. In this review, the status of the field is presented, with a focus on those systems that proved to have reversible behaviour, along with a discussion on the techniques used to fabricate and characterise mechanoresistive devices.

Multiple heteroatom substitution effect on destructive quantum interference in tripodal single-molecule junctions

Destructive quantum interference manipulating the electron transport in tripodal meta-linked phenyl derivatives can be modulated by adjusting the number and the position of the substituted heteroatom(s) inside the molecular core.

Magnetic Exchange Coupling through the Nonalternant Cyclopentadienyl π-System of Ferrocene

Electronic and magnetic coupling through nonalternant π-systems is an area of intense interest in photonics and molecular electronics research, yet relatively little is known regarding coupling through nonalternant π-systems. Herein we present magnetic exchange coupling in two semiquinone-based biradicals: 1,3-SQ₂Fc has two semiquinone radicals attached to the one- and three-positions of the same cyclopentadienyl ligand (a nonalternant π-system) of ferrocene, whereas 1,1'-SQ₂Fc has one semiquinone radical attached to each of the two cyclopentadienyl ligands of ferrocene.

Rules for Magnetic Exchange in Azulene-Bridged Biradicals: Quo Vadis?

Electronic coupling through organic bridges facilitates magnetic exchange interactions and controls electron transfer and single-molecule device electron transport. Electronic coupling through alternant π-systems (e.g., benzene) is better understood than the corresponding coupling through nonalternant π-systems (e.g., azulene). Herein, we examine the structure, spectroscopy, and magnetic exchange coupling in two biradicals (1,3-SQ₂Az and 1,3-SQ-Az-NN; SQ = the zinc(II) complex of spin-1/2 semiquinone radical anion, NN = spin-1/2 nitronylnitroxide; Az = azulene) that possess nonalternant azulene π-system bridges. The SQ radical spin density in both molecules is delocalized into the Az π-system, while the NN spin is effectively localized onto the five-atom ONCNO π-system of NN radical. The spin distributions and interactions are probed by EPR spectroscopy and magnetic susceptibility measurements. We find that J = +38 cm^-1 for 1,3-SQ₂Az and J = +9 cm^-1 for 1,3-SQ-Az-NN (H=-2JS^SQ·S^SQorNN). Our results highlight the differences in exchange coupling mediated by azulene compared to exchange coupling mediated by alternant π-systems.

Quantum Circuit Rules for Molecular Electronic Systems: Where Are We Headed Based on the Current Understanding of Quantum Interference, Thermoelectric, and Molecular Spintronics Phenomena?

In this minireview, we discuss important aspects of the various quantum phenomena (such as quantum interference, spin-dependent charge transport, and thermoelectric effects) relevant in single-molecule charge transport and list some of the basic circuit rules devised for different molecular systems. These quantum phenomena, in conjunction with the existing empirical circuit rules, can help in predicting some of the structure-property relationships in molecular circuits. However, a universal circuit law that predicts the charge transport properties of a molecular circuit has not been derived yet. Having such law(s) will help to design and build a complex molecular device leading to exciting unique applications that are not possible with the traditional silicon-based technologies. Based on the existing knowledge in the literature, here we open the discussion on the possible future research directions for deriving unified circuit law(s) to predict the charge transport in complex single-molecule circuits.

Electrode effects on the observability of destructive quantum interference in single-molecule junctions

Destructive quantum interference (QI) has been a source of interest as a new paradigm for molecular electronics as the electronic conductance is widely dependent on the occurrence or absence of destructive QI effects. In order to interpret experimentally observed transmission features, it is necessary to understand the effects of all components of the junction on electron transport. We perform non-equilibrium Green's function calculations within the framework of density functional theory to assess the structure-function relationship of transport through pyrene molecular junctions with distinct QI properties. The chemical nature of the anchor groups and the electrodes controls the Fermi level alignment, which determines the observability of destructive QI. A thorough analysis allows to disentangle the transmission features arising from the molecule and the electrodes. Interestingly, graphene electrodes introduce features in the low-bias regime, which can either mask or be misinterpreted as QI effects, while instead originating from the topological properties of the edges. Thus, this first principles analysis provides clear indications to guide the interpretation of experimental studies, which cannot be obtained from simple Hückel model calculations.

Substitution Pattern Controlled Quantum Interference in [2.2]Paracyclophane-Based Single-Molecule Junctions

Quantum interference (QI) of electron waves passing through a single-molecule junction provides a powerful means to influence its electrical properties. Here, we investigate the correlation between substitution pattern, conductance, and mechanosensitivity in [2.2]paracyclophane (PCP)-based molecular wires in a mechanically controlled break junction experiment. The effect of the meta versus para connectivity in both the central PCP core and the phenyl ring connecting the terminal anchoring group is studied. We find that the meta-phenyl-anchored PCP yields such low conductance levels that molecular features cannot be resolved; in the case of para-phenyl-coupled anchoring, however, large variations in conductance values for modulations of the electrode separation occur for the pseudo-para-coupled PCP core, while this mechanosensitivity is absent for the pseudo-meta-PCP core. The experimental findings are interpreted in terms of QI effects between molecular frontier orbitals by theoretical calculations based on density functional theory and the Landauer formalism.

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.

Interacting resonances and antiresonances in conjugated hydrocarbons: exceptional points and bound states in the continuum

Quantum interference dramatically modulates electron transport that provides exciting prospects for molecular electronics. We develop a holistic picture of quantum interference phenomena in molecular conductors based on conjugated hydrocarbons taking into account the interaction of resonances and antiresonances (AR). This interaction can result in the coalescence of resonances and ARs accompanied by a significant quantum transparency change. As such a change results from a small variation of the system parameters, it is essential for reducing power consumption in electronics. We establish that the coalescence of ARs is intimately connected with the exceptional point of an underlying non-Hermitian Hamiltonian. The coalescence of ARs cannot be explained considering only the LUMO and HOMO without orbitals beyond them. Cyclobutadiene is discussed as an example. We show that the interaction of resonances and ARs can also result in the formation of a bound state in the continuum (BIC). Our formalism accounting for separate descriptions of resonances and ARs is especially suitable for describing BICs, which can be considered as either a resonance or an AR with zero width. In particular, we show that benzene in the para-configuration possesses BICs, which can be revealed as narrow Fano resonances (FRs) in the transmission spectrum by perturbing the molecule symmetry. Any BIC can be turned into an FR by a proper change of the system parameters, but the reverse is not true. We demonstrate that BICs are related to such chemical concepts as non-bonding orbitals, radicals, and diradicals. Our analytical results within the Hückel formalism are closely reproduced by ab initio simulations. Therefore, experimentally revealing these phenomena looks quite probable.

Origin of the Electron Transport Properties of Aromatic and Antiaromatic Single Molecule Circuits

Antiaromatic molecules have been predicted to exhibit increased electron transport properties when placed between two nanoelectrodes compared to their aromatic analogues. While some studies have demonstrated this relationship, others have found no substantial increase. We use atomistic simulations to establish a general relationship between the electronic spectra of aromatic, antiaromatic, and quinoidal molecules and illustrate its implications for electron transport. We compare the electronic properties of a series of aromatic-antiaromatic counterparts and show that antiaromaticity effectively p-dopes the aromatic electronic spectra. As a consequence, the conducting properties of aromatic-antiaromatic analogues are closely related. For similar attachment points to the electrodes, an interference feature is expected in the HOMO-LUMO gap of one whenever it is absent in the other one. We demonstrate how the relative conductance of aromatic-antiaromatic pairs can be tuned and even reversed through the choice of chemical linker groups. Our work provides a general picture relating connectivity, (anti)aromaticity, and quantum interference and establishes new design rules for single molecule circuits.

Side-group-mediated thermoelectric properties of anthracene single-molecule junction with anchoring groups

Charge transfer characteristics of single-molecule junctions at the nanoscale, and consequently, their thermoelectric properties can be dramatically tuned by chemical or conformational modification of side groups or anchoring groups. In this study, we used density functional theory (DFT) combined with the non-equilibrium Green's function (NEGF) formalism in the linear response regime to examine the thermoelectric properties of a side-group-mediated anthracene molecule coupled to gold (Au) electrodes via anchoring groups. In order to provide a comparative inspection three different side groups, i.e. amine, nitro and methyl, in two different positions were considered for the functionalization of the molecule terminated with thiol or isocyanide anchoring groups. We showed that when the anchored molecule is perturbed with side group, the peaks of the transmission spectrum were shifted relative to the Fermi energy in comparison to the unperturbed molecule (i.e. without side group) leading to modified thermoelectric properties of the system. Particularly, in the thiol-terminated molecule the amine side group showed the greatest figure of merit in both positions which was suppressed by the change of side group position. However, in the isocyanide-terminated molecule the methyl side group attained the greatest thermoelectric efficiency where its magnitude was relatively robust to the change of side group position. In this way, different combinations of side groups and anchoring groups can improve or suppress thermopower and the figure of merit of the molecular junction depending on the interplay between charge donating/accepting nature of the functionals or their position.

Nonexponential Length Dependence of Molecular Conductance in Acene-Based Molecular Wires

In the nonresonant regime, molecular conductance decays exponentially with distance, limiting the fabrication of efficient molecular semiconductors at the nanoscale. In this work, we calculate the conductance of a series of acene derivatives connected to gold electrodes using density functional theory (DFT) combined with the nonequilibrium Green's function (NEGF) formalism. We show that these systems have near length-independent conductance and can exhibit a conductance increase with molecular length depending on the connection to the electrodes. The analysis of the molecular orbital energies and transmission functions attribute this behavior to the dramatic decrease of the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap with length, which shifts the transmission peaks near the Fermi level. These results demonstrate that the anchoring configuration determines the conductance behavior of acene derivatives, which are optimal building blocks to fabricate single-molecule devices with tunable charge transport properties.

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.

Quantum interference enhances rectification behavior of molecular devices

A theoretical and computational study of the effect of quantum interference on the rectification behavior of unimolecular devices.

Smart local orbitals for efficient calculations within density functional theory and beyond

Localized basis sets in the projector augmented wave formalism allow for computationally efficient calculations within density functional theory (DFT). However, achieving high numerical accuracy requires an extensive basis set, which also poses a fundamental problem for the interpretation of the results. We present a way to obtain a reduced basis set of atomic orbitals through the subdiagonalization of each atomic block of the Hamiltonian. The resulting local orbitals (LOs) inherit the information of the local crystal field. In the LO basis, it becomes apparent that the Hamiltonian is nearly block-diagonal, and we demonstrate that it is possible to keep only a subset of relevant LOs that provide an accurate description of the physics around the Fermi level. This reduces to some extent the redundancy of the original basis set, and at the same time, it allows one to perform post-processing of DFT calculations, ranging from the interpretation of electron transport to extracting effective tight-binding Hamiltonians, very efficiently and without sacrificing the accuracy of the results.

Intermolecular Effects on Tunneling through Acenes in Large-Area and Single-Molecule Junctions

This paper describes the conductance of single-molecules and self-assembled monolayers comprising an oligophenyleneethynylene core, functionalized with acenes of increasing length that extend conjugation perpendicular to the path of tunneling electrons. In the Mechanically Controlled Break Junction (MCBJ) experiment, multiple conductance plateaus were identified. The high conductance plateau, which we attribute to the single molecule conformation, shows an increase of conductance as a function of acene length, in good agreement with theoretical predictions. The lower plateau is attributed to multiple molecules bridging the junctions with intermolecular interactions playing a role. In junctions comprising a self-assembled monolayer with eutectic Ga-In top-contacts (EGaIn), the pentacene derivative exhibits unusually low conductance, which we ascribe to the inability of these molecules to pack in a monolayer without introducing significant intermolecular contacts. This hypothesis is supported by the MCBJ data and theoretical calculations showing suppressed conductance through the PC films. These results highlight the role of intermolecular effects and junction geometries in the observed fluctuations of conductance values between single-molecule and ensemble junctions, and the importance of studying molecules in both platforms.

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.

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.

Understanding the Role of Parallel Pathways via In-Situ Switching of Quantum Interference in Molecular Tunneling Junctions

This study describes the modulation of tunneling probabilities in molecular junctions by switching one of two parallel intramolecular pathways. A linearly conjugated molecular wire provides a rigid framework that allows a second, cross-conjugated pathway to be effectively switched on and off by protonation, affecting the total conductance of the junction. This approach works because a traversing electron interacts with the entire quantum-mechanical circuit simultaneously; Kirchhoff's rules do not apply. We confirm this concept by comparing the conductances of a series of compounds with single or parallel pathways in large-area junctions using EGaIn contacts and single-molecule break junctions using gold contacts. We affect switching selectively in one of two parallel pathways by converting a cross-conjugated carbonyl carbon into a trivalent carbocation, which replaces destructive quantum interference with a symmetrical resonance, causing an increase in transmission in the bias window.