Nonlinear charge transport in redox molecular junctions: a Marcus perspective

Ballistic Conductance through Porphyrin Nanoribbons

The search for long molecular wires that can transport charge with maximum efficiency over many nanometers has driven molecular electronics since its inception. Single-molecule conductance normally decays with length and is typically far below the theoretical limit of G0 (77.5 μS). Here, we measure the conductances of a family of edge-fused porphyrin ribbons (lengths 1-7 nm) that display remarkable behavior. The low-bias conductance is high across the whole series. Charging the molecules in situ results in a dramatic realignment of the frontier orbitals, increasing the conductance to 1 G0 (corresponding to a current of 20 μA). This behavior is most pronounced in the longer molecules due to their smaller HOMO-LUMO gaps. The conductance-voltage traces frequently exhibit peaks at zero bias, showing that a molecular energy level is in resonance with the Fermi level. This work lays the foundations for long, perfectly transmissive, molecular wires with technological potential.

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.

Charge Transport in Conjugated and Saturated Hydrocarbons: Comparing Ballistic and Cotunneling Contributions

The comparison between electrical transport in CnH2n+2S2 alkane and CnHn+2S2 alkene (n = 4, 6, 8, 10) is studied by using a generalized Breit-Wigner approach and considering coherent transport mechanisms and eventual changes in the state of charge (i.e., cotunneling processes) for both molecules. In general, the conductance of alkanes tends to be smaller than that of similar-sized alkenes. However, cotunneling processes have an important participation in the overall transport in the case of alkanes but not for the alkene family. The progressive changes in both the eigenenergies of the relevant frontier molecular orbitals of the charged species and their spatial localization play decisive roles in the observed differences. While the molecular orbitals of the charged species of the conjugated molecules are hardly affected by the applied voltage, their saturated counterparts are quite sensitive to the external field. With this, successive avoided-crossing events between the molecular orbitals of the single-charged alkane molecules can lead to the appearance of nonballistic conduction channels that make no negligible contributions to the molecular transport.

Efficient Electron Hopping Transport through Azurin-Based Junctions

We conducted a theoretical study of electron transport through junctions of the blue-copper azurin from Pseudomonas aeruginosa. We found that single-site hopping can lead to either higher or lower current values compared to fully coherent transport. This depends on the structural details of the junctions as well as the alignment of the protein orbitals. Moreover, we show how the asymmetry of the IV curves can be affected by the position of the tip in the junction and that, under specific conditions, such a hopping mechanism is consistent with a fairly low temperature dependence of the current. Finally, we show that increasing the number of hopping sites leads to higher hopping currents. Our findings, from fully quantum calculations, provide deep insight to help guide the interpretation of experimental IV curves on highly complex systems.

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.

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.

Electron hopping heat transport in molecules

The realization of single-molecule thermal conductance measurements has driven the need for theoretical tools to describe conduction processes that occur over atomistic length scales. In macroscale systems, the principle that is typically used to understand thermal conductivity is Fourier's law. At molecular length scales, however, deviations from Fourier's law are common in part because microscale thermal transport properties typically depend on the complex interplay between multiple heat conduction mechanisms. Here, the thermal transport properties that arise from electron transfer across a thermal gradient in a molecular conduction junction are examined theoretically. We illustrate how transport in a model junction is affected by varying the electronic structure and length of the molecular bridge in the junction as well as the strength of the coupling between the bridge and its surrounding environment. Three findings are of note: First, the transport properties can vary significantly depending on the characteristics of the molecular bridge and its environment; second, the system's thermal conductance commonly deviates from Fourier's law; and third, in properly engineered systems, the magnitude of electron hopping thermal conductance is similar to what has been measured in single-molecule devices.

Hybrid molecular graphene transistor as an operando and optoelectronic platform

Lack of reproducibility hampers molecular devices integration into large-scale circuits. Thus, incorporating operando characterization can facilitate the understanding of multiple features producing disparities in different devices. In this work, we report the realization of hybrid molecular graphene field effect transistors (m-GFETs) based on 11-(Ferrocenyl)undecanethiol (FcC₁₁SH) micro self-assembled monolayers (μSAMs) and high-quality graphene (Gr) in a back-gated configuration. On the one hand, Gr enables redox electron transfer, avoids molecular degradation and permits operando spectroscopy. On the other hand, molecular electrode decoration shifts the Gr Dirac point (V_DP) to neutrality and generates a photocurrent in the Gr electron conduction regime. Benefitting from this heterogeneous response, the m-GFETs can implement optoelectronic AND/OR logic functions. Our approach represents a step forward in the field of molecular scale electronics with implications in sensing and computing based on sustainable chemicals.

Electronic Transport in Molecular Wires of Precisely Controlled Length Built from Modular Proteins

DNA molecular wires have been studied extensively because of the ease with which molecules of controlled length and composition can be synthesized. The same has not been true for proteins. Here, we have synthesized and studied a series of consensus tetratricopeptide repeat (CTPR) proteins, spanning 4 to 20 nm in length, in increments of 4 nm. For lengths in excess of 6 nm, their conductance exceeds that of the canonical molecular wire, oligo(phenylene-ethylenene), because of the more gradual decay of conductance with length in the protein. We show that, while the conductance decay fits an exponential (characteristic of quantum tunneling) and not a linear increase of resistance with length (characteristic of hopping transport), it is also accounted for by a square-law dependence on length (characteristic of weakly driven hopping). Measurements of the energy dependence of the decay length rule out the quantum tunneling case. A resonance in the carrier injection energy shows that allowed states in the protein align with the Fermi energy of the electrodes. Both the energy of these states and the long-range of hopping suggest that the reorganization induced by hole formation is greatly reduced inside the protein. We outline a model for calculating the molecular-electronic properties of proteins.

Mechanism of Side Chain-Controlled Proton Conductivity in Bioinspired Peptidic Nanostructures

Bioinspired peptide assemblies are promising candidates for use as proton-conducting materials in electrochemical devices and other advanced technologies. Progress toward applications requires establishing foundational structure-function relationships for transport in these materials. This experimental-theoretical study sheds light on how the molecular structure and proton conduction are linked in three synthetic cyclic peptide nanotube assemblies that comprise the three canonical basic amino acids (lysine, arginine, and histidine). Experiments find an order of magnitude higher proton conductivity for lysine-containing peptide assemblies compared to histidine and arginine containing assemblies. The simulations indicate that, upon peptide assembly, the basic amino acid side chains are close enough to enable direct proton transfer. The proton transfer kinetics is determined in the simulations to be governed by the structure and flexibility of the side chains. Together, experiments and theory indicate that the proton mobility is the main determinant of proton conductivity, critical for the performance of peptide-based devices.

Classical master equations and broadened classical master equations: Some analytical results

Some analytical results for the steady-state properties of the single-molecule tunneling junction are obtained with the use of the broadened classical master equations and classical master equations. The case of the one electronic level of the bridge molecule coupled to a single classical harmonic oscillator is considered within the spin-less model. Based on these equations, we establish some relations between different average values of interest, considering the large bias limit and the limit of the weak electron-oscillator coupling. We derive the analytical expressions for a number of characteristic properties of the tunneling junction in these limiting cases, compare our results with those obtained by the numerically exact calculations, and find that our expressions work very well. In the diabatic regime, the approximate solutions of the classical master equations are suggested, which permit us to introduce the effective temperature T_eff and perform rather simple calculations of the average vibrational excitations N and the tunnel current I. It is shown that in the adiabatic regime, the properties of the tunneling junction depend essentially on the effective temperature T_{eff ad}. We obtain the analytical expressions for T_{eff ad} using different approaches for the treatment of the adiabatic regime. For both the diabatic and adiabatic regimes, we calculate T_eff, T_{eff ad}, N, and I, compare our results with those available in the literature, and confirm well agreement. The dependence of N and I on the reorganization energy and the position of the electronic level of the bridge molecule is discussed.

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.

Quantum Algorithm for Simulating Single-Molecule Electron Transport

An accurate description of electron transport at a molecular level requires a precise treatment of quantum effects. These effects play a crucial role in determining the electron transport properties of single molecules, which can be challenging to simulate classically. Here we introduce a quantum algorithm to efficiently calculate electronic current through single-molecule junctions in the weak-coupling regime. We show that a quantum computer programmed to simulate vibronic transitions between different charge states of a molecule can be used to compute electron-transfer rates and electronic current. In the harmonic approximation, the algorithm can be implemented using Gaussian boson sampling devices, which are a near-term platform for photonic quantum computing. We apply the algorithm to simulate the current and conductance of a magnesium porphine molecule. The algorithm provides a means for better understanding the mechanism of electron transport at a molecular level, which paves the way for building practical molecular electronic devices.

Long-lived charged states of single porphyrin-tape junctions under ambient conditions

The ability to control the charge state of individual molecules wired in two-terminal single-molecule junctions is a key challenge in molecular electronics, particularly in relation to the development of molecular memory and other computational componentry. Here we demonstrate that single porphyrin molecular junctions can be reversibly charged and discharged at elevated biases under ambient conditions due to the presence of a localised molecular eigenstate close to the Fermi edge of the electrodes. In particular, we can observe long-lived charge-states with lifetimes upwards of 1-10 seconds after returning to low bias and large changes in conductance, in excess of 100-fold at low bias. Our theoretical analysis finds charge-state lifetimes within the same time range as the experiments. The ambient operation demonstrates that special conditions such as low temperatures or ultra-high vacuum are not essential to observe hysteresis and stable charged molecular junctions.

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.

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.

Sharp Negative Differential Resistance from Vibrational Mode Softening in Molecular Junctions

We unravel the critical role of vibrational mode softening in single-molecule electronic devices at high bias. Our theoretical analysis is carried out with a minimal model for molecular junctions, with mode softening arising due to quadratic electron-vibration couplings, and by developing a mean-field approach. We discover that the negative sign of the quadratic electron-vibration coupling coefficient can realize, at high voltage, a sharp negative differential resistance (NDR) effect with a large peak-to-valley ratio. Calculated current-voltage characteristics, obtained based on physical parameters for a nitro-substituted oligo(phenylene ethynylene) junction, agree very well with the measurements. Our results establish that vibrational mode softening is a crucial effect at high voltage, underlying NDR, a substantial diode effect, and the breakdown of current-carrying molecular junctions.

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.

Beyond Marcus theory and the Landauer-Büttiker approach in molecular junctions. II. A self-consistent Born approach

Marcus and Landauer-Büttiker approaches to charge transport through molecular junctions describe two contrasting mechanisms of electronic conduction. In previous work, we have shown how these charge transport theories can be unified in the single-level case by incorporating lifetime broadening into the second-order quantum master equation. Here, we extend our previous treatment by incorporating lifetime broadening in the spirit of the self-consistent Born approximation. By comparing both theories to numerically converged hierarchical-equations-of-motion results, we demonstrate that our novel self-consistent approach rectifies shortcomings of our earlier framework, which are present especially in the case of relatively strong electron-vibrational coupling. We also discuss circumstances under which the theory developed here simplifies to the generalized theory developed in our earlier work. Finally, by considering the high-temperature limit of our new self-consistent treatment, we show how lifetime broadening can also be self-consistently incorporated into Marcus theory. Overall, we demonstrate that the self-consistent approach constitutes a more accurate description of molecular conduction while retaining most of the conceptual simplicity of our earlier framework.

2'-Deoxy-2'-fluoro-arabinonucleic acid: a valid alternative to DNA for biotechnological applications using charge transport

The non-biological 2'-deoxy-2'-fluoro-arabinonucleic acid (2'F-ANA) may be used as a valid alternative to DNA in biomedical and electronic applications because of its higher resistance to hydrolysis and nuclease degradation. However, the advantage of using 2'F-ANA in such applications also depends on its charge-transfer properties compared to DNA. In this study, we compare the charge conduction properties of model 2'F-ANA and DNA double-strands, using structural snapshots from MD simulations to calculate the electronic couplings and reorganization energies associated with the hole transfer steps between adjacent nucleobase pairs. Inserting these charge-transfer parameters into a kinetic model for charge conduction, we find similar conductive properties for DNA and 2'F-ANA. Moreover, we find that 2'F-ANA's enhanced chemical stability does not correspond to a reduction in the nucleobase π-stack structural flexibility relevant to both electronic couplings and reorganization free energies. Our results promote the use of 2'F-ANA in applications that can be based on charge transport, such as biosensing and chip technology, where its chemical stability and conductivity can advantageously combine.

Understanding resonant charge transport through weakly coupled single-molecule junctions

Off-resonant charge transport through molecular junctions has been extensively studied since the advent of single-molecule electronics and is now well understood within the framework of the non-interacting Landauer approach. Conversely, gaining a qualitative and quantitative understanding of the resonant transport regime has proven more elusive. Here, we study resonant charge transport through graphene-based zinc-porphyrin junctions. We experimentally demonstrate an inadequacy of non-interacting Landauer theory as well as the conventional single-mode Franck–Condon model. Instead, we model overall charge transport as a sequence of non-adiabatic electron transfers, with rates depending on both outer and inner-sphere vibrational interactions. We show that the transport properties of our molecular junctions are determined by a combination of electron–electron and electron-vibrational coupling, and are sensitive to interactions with the wider local environment. Furthermore, we assess the importance of nuclear tunnelling and examine the suitability of semi-classical Marcus theory as a description of charge transport in molecular devices.

The mechanism of nonadiabatic electron transfer in molecular systems is an important research topic for understanding various chemical reactions. Thomas et al. quantify resonant charge transport through single-molecule junctions as a model system for examining quantum and Marcus theories.

Electron Transfer Methods in Open Systems

Utilization of electron transfer methods for description of quantum transport is popular due to simplicity of the formulation and its ability to account for basic physics of electron exchange between the system and baths. At the same time, the necessity to go beyond simple golden rule-type expressions for rates was indicated in the literature and ad hoc formulations were proposed. Similarly, kinetic schemes for quantum transport beyond the usual second-order Lindblad/Redfield considerations were discussed. Here we utilize recently introduced the nonequilibrium Hubbard Green's function diagrammatic technique to analyze the construction of rates in open systems. We show that previous considerations for rates of second and fourth order can be obtained as a particular case of zero- and second-order Green's function diagrammatic series with bare diagrams. We discuss limitations of previous considerations, stress advantages of the Hubbard Green's function approach in constructing the rates, and indicate that standard dressing of the diagrams is a natural way to account for additional baths/degrees of freedom in the formulation of generalized expressions for the rates.

Mapping hole hopping escape routes in proteins

A recently proposed oxidative damage protection mechanism in proteins relies on hole hopping escape routes formed by redox-active amino acids. We present a computational tool to identify the dominant charge hopping pathways through these residues based on the mean residence times of the transferring charge along these hopping pathways. The residence times are estimated by combining a kinetic model with well-known rate expressions for the charge-transfer steps in the pathways. We identify the most rapid hole hopping escape routes in cytochrome P450 monooxygenase, cytochrome c peroxidase, and benzylsuccinate synthase (BSS). This theoretical analysis supports the existence of hole hopping chains as a mechanism capable of providing hole escape from protein catalytic sites on biologically relevant timescales. Furthermore, we find that pathways involving the [4Fe4S] cluster as the terminal hole acceptor in BSS are accessible on the millisecond timescale, suggesting a potential protective role of redox-active cofactors for preventing protein oxidative damage.

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.

Breaking Down Resonance: Nonlinear Transport and the Breakdown of Coherent Tunneling Models in Single Molecule Junctions

The promise of the field of single-molecule electronics is to reveal a new class of quantum devices that leverages the strong electronic interactions inherent to subnanometer scale systems. Here, we form Au-molecule-Au junctions using a custom scanning tunneling microscope and explore charge transport through current-voltage measurements. We focus on the resonant tunneling regime of two molecules, one that is primarily an electron conductor and one that conducts primarily holes. We find that in the high bias regime, junctions that do not rupture demonstrate reproducible and pronounced negative differential resistance (NDR)-like features followed by hysteresis with peak-to-valley ratios exceeding 100 in some cases. Furthermore, we show that both junction rupture and NDR are induced by charging of the molecular orbital dominating transport and find that the charging is reversible at lower bias and with time with kinetic time scales on the order of hundreds of milliseconds. We argue that these results cannot be explained by existing models of charge transport and likely require theoretical advances describing the transition from coherent to sequential tunneling. Our work also suggests new rules for operating single-molecule devices at high bias to obtain highly nonlinear behavior.

Charge Transfer between [4Fe4S] Proteins and DNA Is Unidirectional: Implications for Biomolecular Signaling

Recent experiments suggest that DNA-mediated charge transport might enable signaling between the [4Fe4S] clusters in the C-terminal domains of human DNA primase and polymerase α, as well as the signaling between other replication and repair high-potential [4Fe4S] proteins. Our theoretical study demonstrates that the redox signaling cannot be accomplished exclusively by DNA-mediated charge transport because part of the charge transfer chain has an unfavorable free energy profile. We show that hole or excess electron transfer between a [4Fe4S] cluster and a nucleic acid duplex through a protein medium can occur within microseconds in one direction, while it is kinetically hindered in the opposite direction. We present a set of signaling mechanisms that may occur with the assistance of oxidants or reductants, using the allowed charge transfer processes. These mechanisms would enable the coordinated action of [4Fe4S] proteins on DNA, engaging the [4Fe4S] oxidation state dependence of the protein-DNA binding affinity.

Kinetic Schemes in Open Interacting Systems

We discuss utilization of kinetic schemes for description of open interacting systems, focusing on vibrational energy relaxation for an oscillator coupled to a nonequilibirum electronic bath. Standard kinetic equations with constant rate coefficients are obtained under the assumption of time scale separation between the system and bath, with the bath dynamics much faster than that of the system of interest. This assumption may break down in certain limits, and we show that ignoring this may lead to qualitatively wrong predictions. Connection with more general, nonequilibrium Green's function (NEGF) analysis is demonstrated. Our considerations are illustrated within generic molecular junction models with electron-vibration coupling.

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.

Reassessment of the Four-Point Approach to the Electron-Transfer Marcus-Hush Theory

The Marcus-Hush theory has been successfully applied to describe and predict the activation barriers and hence the electron-transfer (ET) rates in several physicochemical and biological systems. This theory assumes that in the ET reaction, the geometry of the free Gibbs energy landscape is parabolic, with equal curvature near the local minimum for both reactants and products. In spite of its achievements, more realistic models have included the assumption of the two parabolas having not the same curvature. This situation is analyzed by the Nelsen's four-point method. As a benchmark to compare the Marcus-Hush approximation to a precise calculation of the excitation energy, we studied the non-ET process of the electronic excitation of the aluminum dimer that has two local minima (³∑_g ^- and ³∏_u electronic states) and allows to obtain analytically the Marcus-Hush nonsymmetric parameters. We appraise the ability of the Marcus-Hush formula to approximate the analytical results by using several averages of the two reorganization energies associated with the forward and backward transitions and analyze the error. It is observed that the geometric average minimizes the relative error and that the analytical case is recovered. The main results of this paper are obtained by the application of the Nelsen's four-point method to compute the reorganization energies of a large set of potential π-conjugated molecules proposed for organic photovoltaic devices using the above-mentioned averages for the Marcus-Hush formula. The activation energies obtained with the geometric average are significantly larger for some donor-acceptor pairs in comparison with the previously employed arithmetic average, their differences being suitable for experimental testing.

Analytical expression for the tunnel current through the redox-mediated tunneling contact in the case of the adiabatic electron transfer at one of the working electrodes and any possible type of the electron transfer at the other electrode

We study the tunnel current through a one-level redox molecule immersed into the electrolyte solution for the case when the coupling of the molecule to one of the working electrodes is strong while it is arbitrary to the other electrode. Using the Feynman-Vernon influence functional theory and the perturbation expansion of the effective action of the classical oscillator coupled both to the valence level of the redox molecule and to the thermal bath representing the classical fluctuations of the polarization of the solvent, we obtain, following the canonical way, the Langevin equation for the oscillator. It is found that for the aqueous electrolyte solution, the damping and the stochastic forces which arise due to the tunnel current are much smaller than those due to the thermal bath and therefore can be neglected. We estimate the higher-order corrections to the effective action and show that the Langevin dynamics takes place in this case for arbitrary parameters of the tunneling junction under the condition of the strong coupling of the redox molecule to one of the working electrodes. Then the steady-state coordinate distribution function of the oscillator resulting from the corresponding Fokker-Planck equation is the Boltzmann distribution function which is determined by the adiabatic free energy surface arising from the mean current-induced force. It enables us to obtain the expression for the tunnel current in the case when the coupling of the redox molecule to one of the working electrodes is strong while it is arbitrary to the other electrode.

Modulation and Control of Charge Transport Through Single-Molecule Junctions

The ability to modulate and control charge transport though single-molecule junction devices is crucial to achieving the ultimate goal of molecular electronics: constructing real-world-applicable electronic components from single molecules. This review aims to highlight the progress made in single-molecule electronics, emphasizing the development of molecular junction electronics in recent years. Among many techniques that attempt to wire a molecule to metallic electrodes, the single-molecule break junction (SMBJ) technique is one of the most reliable and tunable experimental platforms for achieving metal-molecule-metal configurations. It also provides great freedom to tune charge transport through the junction. Soon after the SMBJ technique was introduced, it was extensively used to measure the conductances of individual molecules; however, different conductances were obtained for the same molecule, and it proved difficult to interpret this wide distribution of experimental data. This phenomenon was later found to be mainly due to a lack of precise experimental control and advanced data analysis methods. In recent years, researchers have directed considerable effort into advancing the SMBJ technique by gaining a deeper physical understanding of charge transport through single molecules and thus enhancing its potential applicability in functional molecular-scale electronic devices, such as molecular diodes and molecular transistors. In parallel with that research, novel data analysis methods and approaches that enable the discovery of hidden yet important features in the data are being developed. This review discusses various aspects of molecular junction electronics, from the initial goal of molecular electronics, the development of experimental techniques for creating single-molecule junctions and determining single-molecule conductance, to the characterization of functional current-voltage features and the investigation of physical properties other than charge transport. In addition, the development of advanced data analysis methods is considered, as they are critical to gaining detailed physical insight into the underlying transport mechanisms.