Redox molecular junctions are molecular conduction junctions that involve more than one oxidation state of the molecular bridge. This property is derived from the ability of the molecule to transiently localize transmitting electrons, implying relatively weak molecule-leads coupling and, in many cases, the validity of the Marcus theory of electron transfer. Here we study the implications of this property on the non-linear transport properties of such junctions. We obtain an analytical solution of the integral equations that describe molecular conduction in the Marcus kinetic regime and use it in different physical limits to predict some important features of nonlinear transport in metal-molecule-metal junctions. In particular, conduction, rectification and negative differential resistance can be obtained in different regimes of interplay between two different conduction channels associated with different localization properties of the excess molecular charge, without specific assumptions about the electronic structure of the molecular bridge. The predicted behaviors show temperature dependences typically observed in the experiment. The validity of the proposed model and ways to test its predictions and implement the implied control strategies are discussed
For defining the conductance of single molecule junctions with a redox functionality in an electrochemical cell, two conceptually different electron transport mechanisms, namely coherent tunnelling and vibrationally induced hopping compete with each other, where implicit parameters of the setup such as the length of the molecule and the applied gate voltage decide which mechanism is the dominant one. Although coherent tunnelling is most efficiently described within Landauer theory, while the common theoretical treatment of electron hopping is based on Marcus theory, both theories are adequate …
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 t…
Charge transport through molecular junctions is often described either as a purely coherent or a purely classical phenomenon, and described using the Landauer-Büttiker formalism or Marcus theory, respectively. Using a generalised quantum master equation, we here derive an expression for current through a molecular junction modelled as a single electronic level coupled to a collection of thermalised vibrational modes. We demonstrate that the aforementioned theoretical approaches can be viewed as two limiting cases of this more general expression, and present a series of approximations of this r…
We studied charge transport phenomena through a core substituted naphthalenediimide (NDI) single-molecule junctions using the electrochemical STM-based break junction technique in combination with DFT calculations. The conductance switch among three well-defined states is acquired by electrochemically controlling the redox state of the pendent diimide unit of the molecule in ionic liquid, and the conductance difference is more than one order of magnitude between di-anion states and neutral state. The potential dependent charge transport characteristics of the NDI molecules are confirmed by DFT…
In this work we present and discuss theoretical models of redox molecular junctions that account for recent observations of nonlinear charge transport phenomena, such as hysteresis and hysteretic negative differential resistance (NDR). A defining feature in such models is the involvement of at least two conduction channels - a slow channel that determines transitions between charge states of the bridge and a fast channel that dominates its conduction. Using Marcus theory of heterogeneous electron transfer (ET) at metal-molecule interfaces we identify and describe different regimes of nonlinear…
Marcus and Landauer-Buttiker 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 (HEOM) results, we demonstrate that our …
Thermoelectric energy conversion is perhaps the most promising of the potential applications of molecular electronics. Ultimately, it is desirable for this technology to operate at around room temperature, and it is therefore important to consider the role of dissipative effects in these conditions. Here, we develop a theory of thermoelectricity which accounts for the vibrational coupling within the framework of Marcus theory. We demonstrate that the inclusion of lifetime broadening is necessary in the theoretical description of this phenomenon. We further show that the Seebeck coefficient and…
There are various quantum chemical approaches for an ab initio description of transfer integrals within the framework of Marcus theory in the context of electron transfer reactions. In our article we aim to calculate transfer integrals in redox-active single molecule junctions, where we focus on the coherent tunneling limit with the metal leads taking the position of donor and acceptor and the molecule acting as a transport mediating bridge. This setup allows us to derive a conductance, which can be directly compared with recent results from a non-equilibrium Green's function approach. Compare…
For adjusting the charging state of a molecular metal complex in the context of a density functional theory description of coherent electron transport through single molecule junctions, we correct for self interaction effects by fixing the charge on a counterion, which in our calculations mimics the effect of the gate in an electrochemical STM setup, with two competing methods, namely the generalized $Δ$ SCF technique and screening with solvation shells. One would expect a transmission peak to be pinned at the Fermi energy for a nominal charge of +1 on the molecule in the junction but we find …
Two recent experimental (Li, J.~\emphj{et al}, \emph{Proc.\ Natl.\ Acad.\ Sci.\ U.~S.~A.} {\bf 2014}, 111, 1282-1287) and theoretical studies (Bâldea, I, \emph{Phys.\ Chem.\ Chem.\ Phys.}\ {\bf 2014}, 16, 25942-25949) have addressed the problem of tuning molecular charge and vibrational properties of single molecules embedded in nanojunctions. These are molecular characteristics escaping so far to an efficient experimental control in broad ranges. Here, we present a general argument demonstrating why, out of various experimental platforms possible, those wherein active molecules are asymmetric…
We demonstrate the reversible in situ photoreduction of molecular junctions of phosphomolybdate [PMo12O40]3- monolayer self-assembled on flat gold electrodes, connected by the tip of a conductive atomic force microscope. The conductance of the one electron reduced [PMo12O40]4- molecular junction is increased by ca. 10, this open-shell state is stable in the junction in air at room temperature. The analysis of a large current-voltage dataset by unsupervised machine learning and clustering algorithms reveals that the electron transport in the pristine phosphomolybdate junctions leads to symmetri…
Single molecules are nanoscale thermodynamic systems with few degrees of freedom. Thus, the knowledge of their entropy can reveal the presence of microscopic electron transfer dynamics, that are difficult to observe otherwise. Here, we apply thermocurrent spectroscopy to directly measure the entropy of a single free radical molecule in a magnetic field. Our results allow us to uncover the presence of a singlet to triplet transition in one of the redox states of the molecule, not detected by conventional charge transport measurements. This highlights the power of thermoelectric measurements whi…
Experimental studies on single-molecule junctions are typically in need of a simple theoretical approach that can reproduce or be fitted to experimentally measured transport data. In this context, the single-level variant of the Landauer approach is most commonly used but methods based on Marcus theory are also gaining in popularity. Recently, a generalized theory unifying these two approaches has also been developed. In the present work, we extend this theory so that it includes entropic effects (which can be important when polar solvents are involved, but are likely minor for solid-state sys…
Embedding a magnetic electroactive molecule in a three-terminal junction allows for the fast and local electric field control of magnetic properties desirable in spintronic devices and quantum gates. Here, we provide an example of this control through the reversible and stable charging of a single all-organic neutral diradical molecule. By means of inelastic electron tunnel spectroscopy (IETS) we show that the added electron occupies a molecular orbital distinct from those containing the two radical electrons, forming a spin system with three antiferromagnetically-coupled spins. Changing the r…
Charge transport through single molecules can be influenced by the charge and spin states of redox-active metal centres placed in the transport pathway. These molecular intrinsic properties are usually addressed by varying the molecules electrochemical and magnetic environment, a procedure that requires complex setups with multiple terminals. Here we show that oxidation and reduction of organometallic compounds containing either Fe, Ru or Mo centres can solely be triggered by the electric field applied to a two-terminal molecular junction. Whereas all compounds exhibit bias-dependent hysteresi…
Polyoxometalates (POMs) are redox-active molecular oxides, which attract growing interest for their integration into nano-devices, such as high-density data storage non-volatile memories. In this work, we investigated the electrostatic deposition of the negatively charged [H7P8W48O184]33- POM onto positively charged 8-amino-1-octanethiol self-assembled monolayers (SAMs) preformed onto gold substrates or onto an array of gold nanodots. The ring-shaped [H7P8W48O184]33- POM was selected as an example of large POMs with high charge storage capacity. To avoid the formation of POM aggregates onto th…
Quantum Thermodynamics of Electron Transport along Chains of Redox Centers
University of Lille（里尔大学）；Institut d’Électronique, de Microélectronique et de Nanotechnologie (IEMN CNRS UMR8520)（电子、微电子和纳米技术研究所）；Department of Chemical Systems Engineering, University of Tokyo（东京大学化学系统工程系）；Unité de Glycobiologie Structurale et Fonctionnelle (UGSF CNRS UMR8576)（结构与功能糖生物学单元）；CNRS（法国国家科学研究中心）；Centrale Lille（里尔中央理工学院）；Univ. Polytechnique Hauts-de-France（上法兰西工业大学）
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 g…
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…
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 lev…
We determine the zero-frequency charge current noise in a metal-molecule-metal junction embedded in a thermal environment, e.g., a solvent, dominated by sequential charge transmission described by a classical master equation, and study its dependence of specific model parameters, i.e., the environmental reorganization energy and relaxation behavior. Interestingly, the classical current noise term has the same structure as its quantum analog which reflects a charge correlation due to the bridging molecule. We further determine the thermodynamic uncertainty relation (TUR) which defines a bound o…
Off-resonant charge transport through molecular junctions has been extensively studied since the advent of single-molecule electronics and it 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 the non-interacting Landauer theory as well as the conventional single-mode Franck-Condon model. Instead, we mod…
Molecular electronics is a fascinating area of research with the ability to tune device properties by a chemical tailoring of organic molecules. However, molecular electronics devices often suffer from dispersion and lack of reproducibility of their electrical performances. Here, we show that water molecules introduced during the fabrication process or coming from the environment can strongly modify the electrical transport properties of molecular junctions made on hydrogen-terminated silicon. We report an increase in conductance by up to three orders of magnitude, as well as an induced asymme…
Sequential tunneling model is used to study electron transport in molecular rectifiers based on structures of donor-bridge-acceptor type. The device is made of two metallic electrodes connected by a molecule, which contains acceptor and donor subunits, separated by insulating bridge. Both subunits are modeled as quantum dots with discrete energy levels, isolated from each other by potential barrier and weakly coupled to both electrodes through tunnel junctions. Intervalence donor-acceptor tunneling process is treated as a superexchange mechanism or equivalently through the use of Marcus theory…
The Wiedemann-Franz (WF) law is a fundamental result in solid-state physics that relates the thermal and electrical conductivity of a metal. It is derived from the predominant origin of energy conversion in metals: the motion of quasi-free charge-carrying particles. Here, an equivalent WF relationship is developed for molecular systems in which charge carriers are moving not as free particles but instead hop between redox sites. We derive a concise analytical relationship between the electrical and thermal conductivity generated by electron hopping in molecular systems and find that the linear…
