Thermoelectric properties of Marcus molecular junctions

In the present work we theoretically analyze thermoelectric transport in single-molecule junctions (SMJ) characterized by strong interactions between electrons on the molecular linkers and phonons in their nuclear environments where electron hopping between the electrodes and the molecular bridge states predominates in the steady state electron transport. The analysis is based on the modified Marcus theory accounting for the lifetime broadening of the bridge's energy levels. We show that the reorganization processes in the environment accompanying electron transport may significantly affect SMJ thermoelectric properties both within and beyond linear transport regime. Specifically, we study the effect of environmental phonons on the electron conductance, the thermopower and charge current induced by the temperature gradient applied across the system.

Quantum Chemical Studies on Possible Molecular Devices Based on Electric Field-Induced Intramolecular Charge Transfer

We report quantum chemical studies on possible molecular devices working based on electric field-induced intramolecular charge transfer (EFIMCT). In the case of donor-acceptor (DA)-type molecular systems, intramolecular charge transfer (IMCT) can be induced by applying the external electric field to molecular systems along the charge transport direction, providing a possible switching mechanism which does not depend upon the electron-phonon coupling effect and is different from the negative differential resistance mechanism observed in the well-known NO2-substituted phenylene ethynylene oligomers. When the EFIMCT proceeds, the molecular systems have strong static electron correlation effects, where the standard nonequilibrium Green's function-density functional theory (DFT) approach cannot be applied to the molecular junction. As a first step toward practical switching devices, we do quantum chemical studies on the EFIMCT in such molecular systems as an isolated molecule, instead of using the electrode-junction-electrode open quantum system model. A prototype molecule P1 is designed as a tentative candidate molecule where the EFIMCT can proceed. The complete active space self-consistent field (CASSCF) molecular orbital calculations on P1 indicate that the EFIMCT can proceed at the external electric field intensity of 0.003 au, corresponding to about 2.25 V bias voltage. This calculated result strongly suggests that the development of this type of switching devices working at practically low bias voltage is feasible if the molecular system is properly designed. Broken symmetry unrestricted Hartree-Fock and spin-polarized Kohn-Sham DFT calculations also qualitatively reproduce the CASSCF results on P1, to some extent, indicating that these approaches can be employed for rough estimations on the EFIMCT such as the first screening of a large quantity of candidate molecules for this type of molecular devices. The possibility of molecular memory devices based on the EFIMCT is also discussed by analyzing the ground and excited potential energy surface model. Remaining challenges to develop practical molecular devices are discussed.

Voltage-driven control of single-molecule keto-enol equilibrium in a two-terminal junction system

Keto-enol tautomerism, describing an equilibrium involving two tautomers with distinctive structures, provides a promising platform for modulating nanoscale charge transport. However, such equilibria are generally dominated by the keto form, while a high isomerization barrier limits the transformation to the enol form, suggesting a considerable challenge to control the tautomerism. Here, we achieve single-molecule control of a keto-enol equilibrium at room temperature by using a strategy that combines redox control and electric field modulation. Based on the control of charge injection in the single-molecule junction, we could access charged potential energy surfaces with opposite thermodynamic driving forces, i.e., exhibiting a preference for the conducting enol form, while the isomerization barrier is also significantly reduced. Thus, we could selectively obtain desired and stable tautomers, which leads to significant modulation of the single-molecule conductance. This work highlights the concept of single-molecule control of chemical reactions on more than one potential energy surface.

Generic dynamic molecular devices by quantitative non-steady-state proton/water-coupled electron transport kinetics

Dynamic molecular devices operating with time- and history-dependent performance raised new challenges for the fundamental study of microscopic non-steady-state charge transport as well as functionalities that are not achievable by steady-state devices. In this study, we reported a generic dynamic mode of molecular devices by addressing the transient redox state of ubiquitous quinone molecules in the junction by proton/water transfer. The diffusion limited slow proton/water transfer-modulated fast electron transport, leading to a non-steady-state transport process, as manifested by the negative differential resistance, dynamic hysteresis, and memory-like behavior. A quantitative paradigm for the study of the non-steady-state charge transport kinetics was further developed by combining the theoretical model and transient state characterization, and the principle of the dynamic device can be revealed by the numerical simulator. On applying pulse stimulation, the dynamic device emulated the neuron synaptic response with frequency-dependent depression and facilitation, implying a great potential for future nonlinear and brain-inspired devices.

Ionogel-Electrode for the Study of Protein Tunnel Junctions under Physiologically Relevant Conditions

The study of charge transport through proteins is essential for understanding complicated electrochemical processes in biological activities while the reasons for the coexistence of tunneling and hopping phenomena in protein junctions still remain unclear. In this work, a flexible and conductive ionogel electrode is synthesized and is used as a top contact to form highly reproducible protein junctions. The junctions of proteins, including human serum albumin, cytochrome C and hemoglobin, show temperature-independent electron tunneling characteristics when the junctions are in solid states while with a different mechanism of temperature-dependent electron hopping when junctions are hydrated under physiologically relevant conditions. It is demonstrated that the solvent reorganization energy plays an important role in the electron-hopping process and experimentally shown that it requires ≈100 meV for electron hopping through one heme group inside a hydrated protein molecule connected between two electrodes.

Nanoscale molecular rectifiers

The use of molecules bridged between two electrodes as a stable rectifier is an important goal in molecular electronics. Until recently, however, and despite extensive experimental and theoretical work, many aspects of our fundamental understanding and practical challenges have remained unresolved and prevented the realization of such devices. Recent advances in custom-designed molecular systems with rectification ratios exceeding 10⁵ have now made these systems potentially competitive with existing silicon-based devices. Here, we provide an overview and critical analysis of recent progress in molecular rectification within single molecules, self-assembled monolayers, molecular multilayers, heterostructures, and metal-organic frameworks and coordination polymers. Examples of conceptually important and best-performing systems are discussed, alongside their rectification mechanisms. We present an outlook for the field, as well as prospects for the commercialization of molecular rectifiers.

Empirical Parameter to Compare Molecule-Electrode Interfaces in Large-Area Molecular Junctions

This paper describes a simple model for comparing the degree of electronic coupling between molecules and electrodes across different large-area molecular junctions. The resulting coupling parameter can be obtained directly from current–voltage data or extracted from published data without fitting. We demonstrate the generalizability of this model by comparing over 40 different junctions comprising different molecules and measured by different laboratories. The results agree with existing models, reflect differences in mechanisms of charge transport and rectification, and are predictive in cases where experimental limitations preclude more sophisticated modeling. We also synthesized a series of conjugated molecular wires, in which embedded dipoles are varied systematically and at both molecule–electrode interfaces. The resulting current–voltage characteristics vary in nonintuitive ways that are not captured by existing models, but which produce trends using our simple model, providing insights that are otherwise difficult or impossible to explain. The utility of our model is its demonstrative generalizability, which is why simple observables like tunneling decay coefficients remain so widely used in molecular electronics despite the existence of much more sophisticated models. Our model is complementary, giving insights into molecule–electrode coupling across series of molecules that can guide synthetic chemists in the design of new molecular motifs, particularly in the context of devices comprising large-area molecular junctions.

Electronic Mechanism of In Situ Inversion of Rectification Polarity in Supramolecular Engineered Monolayer

This Communication describes polarity inversion in molecular rectification and the related mechanism. Using a supramolecular engineered, ultrastable, binary-mixed self-assembled monolayer (SAM) composed of an organic molecular diode (SC₁₁BIPY) and an inert reinforcement molecule (SC₈), we probed a rectification ratio (r)-voltage relationship over an unprecedentedly wide voltage range (up to |3.5 V|) with statistical significance. We observed positive polarity in rectification at |1.0 V| (r = 107), followed by disappearance of rectification at ∼|2.25 V|, and then eventual emergence of new rectification with the opposite polarity at ∼|3.5 V| (r = 0.006; 1/r = 162). The polarity inversion occurred with a span over 4 orders of magnitude in r. Low-temperature experiments, electronic structure analysis, and theoretical calculations revealed that the unusually wide voltage range permits access to molecular orbital energy levels that are inaccessible in the traditional narrow voltage regime, inducing the unprecedented in situ inversion of polarity.

Energetics of the charge generation in organic donor-acceptor interfaces

Non-fullerene acceptor materials have posed new paradigms for the design of organic solar cells , whereby efficient carrier generation is obtained with small driving forces, in order to maximize the open-circuit voltage (V_OC). In this paper, we use a coarse-grained mixed quantum-classical method, which combines Ehrenfest and Redfield theories, to shed light on the charge generation process in small energy offset interfaces. We have investigated the influence of the energetic driving force as well as the vibronic effects on the charge generation and photovoltaic energy conversion. By analyzing the effects of the Holstein and Peierls vibrational couplings, we find that vibrational couplings produce an overall effect of improving the charge generation. However, the two vibronic mechanisms play different roles: the Holstein relaxation mechanism decreases the charge generation, whereas the Peierls mechanism always assists the charge generation. Moreover, by examining the electron-hole binding energy as a function of time, we evince two distinct regimes for the charge separation: the temperature independent excitonic spread on a sub-100 fs timescale and the complete dissociation of the charge-transfer state that occurs on the timescale of tens to hundreds of picoseconds, depending on the temperature. The quantum dynamics of the system exhibits the three regimes of the Marcus electron transfer kinetics as the energy offset of the interface is varied.

Electrochemical Potential-Driven High-Throughput Molecular Electronic and Spintronic Devices: From Molecules to Applications

Molecules are fascinating candidates for constructing tunable and electrically conducting devices by the assembly of either a single molecule or an ensemble of molecules between two electrical contacts followed by current-voltage (I-V) analysis, which is often termed "molecular electronics". Recently, there has been also an upsurge of interest in spin-based electronics or spintronics across the molecules, which offer additional scope to create ultrafast responsive devices with less power consumption and lower heat generation using the intrinsic spin property rather than electronic charge. Researchers have been exploring this idea of utilizing organic molecules, organometallics, coordination complexes, polymers, and biomolecules (proteins, enzymes, oligopeptides, DNA) in integrating molecular electronics and spintronics devices. Although several methods exist to prepare molecular thin-films on suitable electrodes, the electrochemical potential-driven technique has emerged as highly efficient. In this Review we describe recent advances in the electrochemical potential driven growth of nanometric various molecular films on technologically relevant substrates, including non-magnetic and magnetic electrodes to investigate the stimuli-responsive charge and spin transport phenomena.

Bias-Polarity-Dependent Direct and Inverted Marcus Charge Transport Affecting Rectification in a Redox-Active Molecular Junction

This paper describes the transition from the normal to inverted Marcus region in solid-state tunnel junctions consisting of self-assembled monolayers of benzotetrathiafulvalene (BTTF), and how this transition determines the performance of a molecular diode. Temperature-dependent normalized differential conductance analyses indicate the participation of the HOMO (highest occupied molecular orbital) at large negative bias, which follows typical thermally activated hopping behavior associated with the normal Marcus regime. In contrast, hopping involving the HOMO dominates the mechanism of charge transport at positive bias, yet it is nearly activationless indicating the junction operates in the inverted Marcus region. Thus, within the same junction it is possible to switch between Marcus and inverted Marcus regimes by changing the bias polarity. Consequently, the current only decreases with decreasing temperature at negative bias when hopping is "frozen out," but not at positive bias resulting in a 30-fold increase in the molecular rectification efficiency. These results indicate that the charge transport in the inverted Marcus region is readily accessible in junctions with redox molecules in the weak coupling regime and control over different hopping regimes can be used to improve junction performance.

Solid State Dilution Controls Marcus Inverted Transport in Rectifying Molecular Junctions

Traditional Marcus theory accounts for electron transfer reactions in solutions, and the polarity of solvent molecule matters for them. How such an environment polarity affects electron transfer reactions in solid-state devices, however, remains uncertain. This paper describes how the Marcus inverted charge transport is influenced by solid-state molecular dilution in large-area tunneling junctions. A monolayer of 2,2'-bipyridyl terminated n-alkanethiolate (SC₁₁BIPY), which rectifies currents via electron hopping within the inverted regime, is diluted with n-alkanethiolate (SC_n) of different lengths (n = 8, 10, or 18) or at different surface mole fractions. The dilution introduces nonpolar environments within the monolayer, hinders stabilization of charged BIPY species upon electron hopping, and pushes the equilibrium of BIPY ⇄ BIPY^•- process toward the reverse direction. Our work demonstrates that solid-state molecular dilution permits systematic control of the environment polarity of active component in nanoscale devices, much like solvent polarity control in solution, and their performances.

Reversal of the Direction of Rectification Induced by Fermi Level Pinning at Molecule-Electrode Interfaces in Redox-Active Tunneling Junctions

Control over the energy level alignment in molecular junctions is notoriously difficult, making it challenging to control basic electronic functions such as the direction of rectification. Therefore, alternative approaches to control electronic functions in molecular junctions are needed. This paper describes switching of the direction of rectification by changing the bottom electrode material M = Ag, Au, or Pt in M-S(CH₂)₁₁S-BTTF//EGaIn junctions based on self-assembled monolayers incorporating benzotetrathiafulvalene (BTTF) with EGaIn (eutectic alloy of Ga and In) as the top electrode. The stability of the junctions is determined by the choice of the bottom electrode, which, in turn, determines the maximum applied bias window, and the mechanism of rectification is dominated by the energy levels centered on the BTTF units. The energy level alignments of the three junctions are similar because of Fermi level pinning induced by charge transfer at the metal-thiolate interface and by a varying degree of additional charge transfer between BTTF and the metal. Density functional theory calculations show that the amount of electron transfer from M to the lowest unoccupied molecular orbital (LUMO) of BTTF follows the order Ag > Au > Pt. Junctions with Ag electrodes are the least stable and can only withstand an applied bias of ±1.0 V. As a result, no molecular orbitals can fall in the applied bias window, and the junctions do not rectify. The junction stability increases for M = Au, and the highest occupied molecular orbital (HOMO) dominates charge transport at a positive bias resulting in a positive rectification ratio of 83 at ±1.5 V. The junctions are very stable for M = Pt, but now the LUMO dominates charge transport at a negative bias resulting in a negative rectification ratio of 912 at ±2.5 V. Thus, the limitations of Fermi level pinning can be bypassed by a judicious choice of the bottom electrode material, making it possible to access selectively HOMO- or LUMO-based charge transport and, as shown here, associated reversal of rectification.

Functional Redox-Active Molecular Tunnel Junctions

Redox-active molecular junctions have attracted considerable attention because redox-active molecules provide accessible energy levels enabling electronic function at the molecular length scales, such as, rectification, conductance switching, or molecular transistors. Unlike charge transfer in wet electrochemical environments, it is still challenging to understand how redox-processes proceed in solid-state molecular junctions which lack counterions and solvent molecules to stabilize the charge on the molecules. In this minireview, we first introduce molecular junctions based on redox-active molecules and discuss their properties from both a chemistry and nanoelectronics point of view, and then discuss briefly the mechanisms of charge transport in solid-state redox-junctions followed by examples where redox-molecules generate new electronic function. We conclude with challenges that need to be addressed and interesting future directions from a chemical engineering and molecular design perspectives.

Interplay of Fermi Level Pinning, Marcus Inverted Transport, and Orbital Gating in Molecular Tunneling Junctions

This Letter examines the interplay of important tunneling mechanisms-Fermi level pinning, Marcus inverted transport, and orbital gating-in a molecular rectifier. The temperature dependence of the rectifying molecular junction containing 2,2'-bipyridyl terminated n-alkanethiolate was investigated. A bell-shaped trend of activation energy as a function of applied bias evidenced the dominant occurrence of unusual Marcus inverted transport, while retention of rectification at low temperatures implied that the rectification obeyed the resonant tunneling regime. The results allowed reconciling two separately developed transport models, Marcus-Landauer energetics and Fermi level pinning-based rectification. Our work shows that the internal orbital gating can be substituted with the pinning effect, which pushes the transport mechanism into the Marcus inverted regime.

Single-Electron Currents in Designer Single-Cluster Devices

Atomically precise clusters can be used to create single-electron devices wherein a single redox-active cluster is connected to two macroscopic electrodes via anchoring ligands. Unlike single-electron devices comprising nanocrystals, these cluster-based devices can be fabricated with atomic precision. This affords an unprecedented level of control over the device properties. Herein, we design a series of cobalt chalcogenide clusters with varying ligand geometries and core nuclearities to control their current-voltage (I-V) characteristics in a scanning tunneling microscope-based break junction (STM-BJ) device. First, the device geometry is modified by precisely positioning junction-anchoring ligands on the surface of the cluster. We show that the I-V characteristics are independent of ligand placement, confirming a sequential, single-electron tunneling mechanism. Next, we chemically fuse two clusters to realize a larger cluster dimer that behaves as a single electronic unit, possessing a smaller reorganization energy and more accessible redox states than the monomeric analogues. As a result, dimer-based devices exhibit significantly higher currents and can even be pushed to current saturation at high bias. Owing to these controllable properties, single-cluster junctions serve as an excellent platform for exploring incoherent charge transport processes at the nanoscale. With this understanding, as well as properties such as nonlinear I-V characteristics and rectification, these molecular clusters may function as conductive inorganic nodes in new devices and materials.

Systematic Modulation of Charge Transport in Molecular Devices through Facile Control of Molecule-Electrode Coupling Using a Double Self-Assembled Monolayer Nanowire Junction

We report a novel solid-state molecular device structure based on double self-assembled monolayers (D-SAM) incorporated into the suspended nanowire architecture to form a "Au|SAM-1||SAM-2|Au" junction. Using commercially available thiol molecules that are devoid of synthetic difficulty, we constructed a "Au|S-(CH2)6-ferrocene||SAM-2|Au" junction with various lengths and chemical structures of SAM-2 to tune the coupling between the ferrocene conductive molecular orbital and electrode of the junction. Combining low noise and a wide temperature range measurement, we demonstrated systematically modulated conduction depending on the length and chemical nature of SAM-2. Meanwhile, the transport mechanism transition from tunneling to hopping and the intermediate state accompanied by the current fluctuation due to the coexistence of the hopping and tunneling transport channels were observed. Considering the versatility of this solid-state D-SAM in modulating the electrode-molecule interface and electroactive groups, this strategy thus provides a novel facile strategy for tailorable nanoscale charge transport studies and functional molecular devices.

Energy, Work, Entropy, and Heat Balance in Marcus Molecular Junctions

We present a consistent theory of energy balance and conversion in a single-molecule junction with strong interactions between electrons on the molecular linker (dot) and phonons in the nuclear environment where the Marcus-type electron hopping processes predominate in the electron transport. It is shown that the environmental reorganization and relaxation that accompany electron hopping energy exchange between the electrodes and the nuclear (molecular and solvent) environment may bring a moderate local cooling of the latter in biased systems. The effect of a periodically driven dot level on the heat transport and power generated in the system is analyzed, and energy conservation is demonstrated both within and beyond the quasistatic regime. Finally, a simple model of atomic scale engine based on a Marcus single-molecule junction with a driven electron level is suggested and discussed.

Charge Transfer through Redox Molecular Junctions in Nonequilibrated Solvents

Molecular conduction operating in dielectric solvent environments is often described using kinetic rates based on the Marcus theory of electron transfer at a molecule-metal electrode interface. However, the successive nature of charge transfer in such a system implies that the solvent does not necessarily reach equilibrium in such processes. Here we generalize the theory to account for solvent nonequilibrium and consider a molecular junction consisting of an electronic donor-acceptor system coupled to two metallic electrodes and placed in a polarizable solvent. We determine the nonequilbrium distribution of the solvent by solving diffusion equations in the strong- and weak-friction limits and calculate the charge current and its fluctuating behavior. In extreme limits, the absence of the solvent or fast solvent relaxation, the charge-transfer statistics is Poissonian, while it becomes correlated by the dynamic solvent between these limits. A Kramers-like turnover of the nonequilibrium current as a function of the solvent damping is found. Finally, we propose a way to tune the solvent-induced damping using geometrical control of the solvent dielectric response in nanostructured solvent channels.

Electronic Communication as a Transferable Property of Molecular Bridges?

Electronic communication through molecular bridges is important for different types of experiments, such as single-molecule conductance, electron transfer, superexchange spin coupling, and intramolecular singlet fission. In many instances, the chemical structure of the bridge determines how the two parts it is connecting communicate, and does so in ways that are transferable between these different manifestations (for example, high conductance often correlates with strong antiferromagnetic spin coupling, and low conductance due to destructive quantum interference correlates with ferromagnetic coupling). Defining electronic communication as a transferable property of the bridge can help transfer knowledge between these different areas of research. Examples and limits of such transferability are discussed here, along with some possible directions for future research, such as employing spin-coupled and mixed-valence systems as structurally well-controlled proxies for understanding molecular conductance and for validating first-principles theoretical methodologies, building conceptual understanding for the growing experimental work on intramolecular singlet fission, and developing measures for the transferability of electronic communication as a bridge property.

Tuning the charge flow between Marcus regimes in an organic thin-film device

Marcus’s theory of electron transfer, initially formulated six decades ago for redox reactions in solution, is now of great importance for very diverse scientific communities. The molecular scale tunability of electronic properties renders organic semiconductor materials in principle an ideal platform to test this theory. However, the demonstration of charge transfer in different Marcus regions requires a precise control over the driving force acting on the charge carriers. Here, we make use of a three-terminal hot-electron molecular transistor, which lets us access unconventional transport regimes. Thanks to the control of the injection energy of hot carriers in the molecular thin film we induce an effective negative differential resistance state that is a direct consequence of the Marcus Inverted Region.

To demonstrate charge transfer in different Marcus regimes in an organic semiconductor, precise tuning of the material’s electronic properties is required. Here, the authors use a three-terminal hot-electron technique to access the Marcus regimes for electronic transport in organic thin films.

Peptides as Bio-Inspired Electronic Materials: An Electrochemical and First-Principles Perspective

Molecular electronics is at the forefront of interdisciplinary research, offering a significant extension of the capabilities of conventional silicon-based technology as well as providing a possible stand-alone alternative. Bio-inspired molecular electronics is a particularly intriguing paradigm, as charge transfer in proteins/peptides, for example, plays a critical role in the energy storage and conversion processes for all living organisms. However, the structure and conformation of even the simplest protein is extremely complex, and therefore, synthetic model peptides comprising well-defined geometry and predetermined functionality are ideal platforms to mimic nature for the elucidation of fundamental biological processes while also enhancing the design and development of single-peptide electronic components. In this Account, we first present intramolecular electron transfer within two synthetic peptides, one with a well-defined helical conformation and the other with a random geometry, using electrochemical techniques and computational simulations. This study reveals two definitive electron transfer pathways (mechanisms), the natures of which are dependent on secondary structure. Following on from this, electron transfer within a series of well-defined helical peptides, constrained by either Huisgen cycloaddition, ring-closing metathesis, or a lactam bridge, was determined. The electrochemical results indicate that each constrained peptide, in contrast to a linear counterpart, exhibits a remarkable shift of the formal potential to the positive (>460 mV) and a significant reduction of the electron transfer rate constant (up to 15-fold), which represent two distinct electronic "on/off" states. High-level calculations demonstrate that the additional backbone rigidity provided by the side-bridge constraints leads to an increased reorganization energy barrier, which impedes the vibrational fluctuations necessary for efficient intramolecular electron transfer through the peptide backbone. Further calculations reveal a clear mechanistic transition from hopping to superexchange (tunneling) stemming from side-bridge gating. We then extended our research to fine-tuning of the electronic properties of peptides through both structural and chemical manipulation, to reveal an interplay between electron-rich side chains and backbone rigidity on electron transfer. Further to this, we explored the possibility that the side-bridge constraints present in our synthetic peptides provide an additional electronic transport pathway, which led to the discovery of two distinct forms of quantum interferometer. The effects of destructive quantum interference appear essentially through both the backbone and an alternative tunneling pathway provided by the side bridge in the constrained β-strand peptide, as evidenced by a correlation between electrochemical measurements and conductance simulations for both linear and constrained β-strand peptides. In contrast, an interplay between quantum interference effects and vibrational fluctuations is revealed in the linear and constrained 3₁₀-helical peptides. Collectively, these exciting findings augment our fundamental knowledge of charge transfer dynamics and kinetics in peptides and also open up new avenues to design and develop functional bio-inspired electronic devices, such as on/off switches and quantum interferometers, for practical applications in molecular electronics.

Generalized Breit-Wigner treatment of molecular transport: Charging effects in a single decanedithiol molecule

We examine the relative contribution of ballistic and elastic cotunneling mechanisms to the charge transport through a single decanedithiol molecule linked to two terminal clusters of gold atoms. For this, we first introduced a conceptual model that permits a generalization of the Breit-Wigner scattering formalism where the cation, anion, and neutral forms of the molecule can participate with different probabilities of the charge transfer process, but in a simultaneous manner. We used a density functional theory treatment and considered the fixed geometry of each charge state to calculate the corresponding eigenvalues and eigenvectors of the extended system for different values of the external electric field. We have found that for the ballistic transport the HOMO and LUMO of the neutral species play a key role, while the charged states give a negligible contribution. On the other hand, an elastic cotunneling charge transfer can occur whenever a molecular orbital (MO) of the cation or anion species, even if localized in just one side of the molecule-gold clusters complex, has energy close to that of a delocalized MO of the neutral species. Under these conditions, a conduction channel is formed throughout the entire system, in a process that is controlled by the degree of resonance between the MOs involved. Our results indicate that while different charge transfer mechanisms contribute to the overall charge transport, quantum effects such as avoided-crossing situations between relevant frontier MOs can be of special importance. In these specific situations, the interchange of spatial localization of two MOs involved in the crossing can open a new channel of charge transfer that otherwise would not be available.

Transition from direct to inverted charge transport Marcus regions in molecular junctions via molecular orbital gating

Solid-state molecular tunnel junctions are often assumed to operate in the Landauer regime, which describes essentially activationless coherent tunnelling processes. In solution, on the other hand, charge transfer is described by Marcus theory, which accounts for thermally activated processes. In practice, however, thermally activated transport phenomena are frequently observed also in solid-state molecular junctions but remain poorly understood. Here, we show experimentally the transition from the Marcus to the inverted Marcus region in a solid-state molecular tunnel junction by means of intra-molecular orbital gating that can be tuned via the chemical structure of the molecule and applied bias. In the inverted Marcus region, charge transport is incoherent, yet virtually independent of temperature. Our experimental results fit well to a theoretical model that combines Landauer and Marcus theories and may have implications for the interpretation of temperature-dependent charge transport measurements in molecular junctions.

Bias-induced conductance switching in single molecule junctions containing a redox-active transition metal complex

ABSTRACT

The paper provides a comprehensive theoretical description of electron transport through transition metal complexes in single molecule junctions, where the main focus is on an analysis of the structural parameters responsible for bias-induced conductance switching as found in recent experiments, where an interpretation was provided by our simulations. The switching could be theoretically explained by a two-channel model combining coherent electron transport and electron hopping, where the underlying mechanism could be identified as a charging of the molecule in the junction made possible by the presence of a localized electronic state on the transition metal center. In this article, we present a framework for the description of an electron hopping-based switching process within the semi-classical Marcus-Hush theory, where all relevant quantities are calculated on the basis of density functional theory (DFT). Additionally, structural aspects of the junction and their respective importance for the occurrence of irreversible switching are discussed.

GRAPHICAL ABSTRACT

Covalently bonded single-molecule junctions with stable and reversible photoswitched conductivity

Through molecular engineering, single diarylethenes were covalently sandwiched between graphene electrodes to form stable molecular conduction junctions. Our experimental and theoretical studies of these junctions consistently show and interpret reversible conductance photoswitching at room temperature and stochastic switching between different conductive states at low temperature at a single-molecule level. We demonstrate a fully reversible, two-mode, single-molecule electrical switch with unprecedented levels of accuracy (on/off ratio of ~100), stability (over a year), and reproducibility (46 devices with more than 100 cycles for photoswitching and ~10(5) to 10(6) cycles for stochastic switching).

A Single-Level Tunnel Model to Account for Electrical Transport through Single Molecule- and Self-Assembled Monolayer-based Junctions

We present a theoretical analysis aimed at understanding electrical conduction in molecular tunnel junctions. We focus on discussing the validity of coherent versus incoherent theoretical formulations for single-level tunneling to explain experimental results obtained under a wide range of experimental conditions, including measurements in individual molecules connecting the leads of electromigrated single-electron transistors and junctions of self-assembled monolayers (SAM) of molecules sandwiched between two macroscopic contacts. We show that the restriction of transport through a single level in solid state junctions (no solvent) makes coherent and incoherent tunneling formalisms indistinguishable when only one level participates in transport. Similar to Marcus relaxation processes in wet electrochemistry, the thermal broadening of the Fermi distribution describing the electronic occupation energies in the electrodes accounts for the exponential dependence of the tunneling current on temperature. We demonstrate that a single-level tunnel model satisfactorily explains experimental results obtained in three different molecular junctions (both single-molecule and SAM-based) formed by ferrocene-based molecules. Among other things, we use the model to map the electrostatic potential profile in EGaIn-based SAM junctions in which the ferrocene unit is placed at different positions within the molecule, and we find that electrical screening gives rise to a strongly non-linear profile across the junction.

Electrostatic control over temperature-dependent tunnelling across a single-molecule junction

Understanding how the mechanism of charge transport through molecular tunnel junctions depends on temperature is crucial to control electronic function in molecular electronic devices. With just a few systems investigated as a function of bias and temperature so far, thermal effects in molecular tunnel junctions remain poorly understood. Here we report a detailed charge transport study of an individual redox-active ferrocene-based molecule over a wide range of temperatures and applied potentials. The results show the temperature dependence of the current to vary strongly as a function of the gate voltage. Specifically, the current across the molecule exponentially increases in the Coulomb blockade regime and decreases at the charge degeneracy points, while remaining temperature-independent at resonance. Our observations can be well accounted for by a formal single-level tunnelling model where the temperature dependence relies on the thermal broadening of the Fermi distributions of the electrons in the leads.

Negative differential conductance in molecular junctions: an overview of experiment and theory

One of the ultimate goals of molecular electronics is to create technologies that will complement-and eventually supersede-Si-based microelectronics technologies. To reach this goal, electronic properties that mimic at least some of the electrical behaviors of today's semiconductor components must be recognized and characterized. An outstanding example for one such behavior is negative differential conductance (NDC), in which an increase in the voltage across the device terminals results in a decrease in the electric current passing through the device. This overview focuses on the NDC phenomena observed in metal-single molecule-metal molecular junctions, and is roughly divided into two parts. In the first part, the central experiments which demonstrate NDC in single-molecule junctions are critically reviewed, with emphasis on the main observations and their possible physical origins. The second part is devoted to the theory of NDC in single-molecule junctions, where simple models are employed to shed light on the different possible mechanisms leading to NDC.

Quantum transport with two interacting conduction channels

The transport properties of a conduction junction model characterized by two mutually coupled channels that strongly differ in their couplings to the leads are investigated. Models of this type describe molecular redox junctions (where a level that is weakly coupled to the leads controls the molecular charge, while a strongly coupled one dominates the molecular conduction), and electron counting devices in which the current in a point contact is sensitive to the charging state of a nearby quantum dot. Here we consider the case where transport in the strongly coupled channel has to be described quantum mechanically (covering the full range between sequential tunneling and co-tunneling), while conduction through the weakly coupled channel is a sequential process that could by itself be described by a simple master equation. We compare the result of a full quantum calculation based on the pseudoparticle non-equilibrium Green function method to that obtained from an approximate mixed quantum-classical calculation, where correlations between the channels are taken into account through either the averaged rates or the averaged energy. We find, for the steady state current, that the approximation based on the averaged rates works well in most of the voltage regime, with marked deviations from the full quantum results only at the threshold for charging the weekly coupled level. These deviations are important for accurate description of the negative differential conduction behavior that often characterizes redox molecular junctions in the neighborhood of this threshold.