Long-range electron tunnelling in oligo-porphyrin molecular wires

Theoretical investigation of thermoelectric properties of methyl blue-based molecular junctions

Thermoelectric properties of a family of methyl blue-based molecular junctions were theoretically studied using a combination of density functional theory (DFT) methods, and quantum transport theory (QTT). Employing different numbers of amino groups not only proves itself as a powerful strategy for controlling the transport behaviour and lifting the transmission coefficient T(E) from 1.91 × 10-5 to 7.45 × 10-5 with increasing the amino groups from zero to four, but also it enhances the thermoelectric properties of these molecules, since it increases the Seebeck coefficient (S) from 106.8 to 202.4 μV K-1 and the electronic figure of merit (Z el T) has been raised from 0.15 to 0.35, making these molecules promising candidates for thermoelectric applications.

Controlling heme redox properties in peptide amphiphile fibers with sequence and heme loading ratio

Controlling the reduction midpoint potential of heme B is a key factor in many bioelectrochemical reactions, including long-range electron transport. Currently, there are a number of globular model protein systems to study this biophysical parameter; however, there are none for large polymeric protein model systems (e.g., the OmcS protein from G. sulfurreducens). Peptide amphiphiles, short peptides with a lipid tail that polymerize into fibrous structures, fill this gap. Here, we show a peptide amphiphile model system where one can tune the electrochemical potential of heme B by changing the loading ratio and peptide sequence. Changing the loading ratio resulted in the most significant increase, with values as high as -22 mV down to -224 mV. Circular dichroism spectra of certain sequences show Cotton effects at lower loading ratios that disappear as more heme B is added, indicating an ordered environment that becomes disrupted if heme B is overpacked. These findings can contribute to the design of functional self-assembling biomaterials.

Porphyrin-fused graphene nanoribbons

Graphene nanoribbons (GNRs), nanometre-wide strips of graphene, are promising materials for fabricating electronic devices. Many GNRs have been reported, yet no scalable strategies are known for synthesizing GNRs with metal atoms and heteroaromatic units at precisely defined positions in the conjugated backbone, which would be valuable for tuning their optical, electronic and magnetic properties. Here we report the solution-phase synthesis of a porphyrin-fused graphene nanoribbon (PGNR). This PGNR has metalloporphyrins fused into a twisted fjord-edged GNR backbone; it consists of long chains (>100 nm), with a narrow optical bandgap (~1.0 eV) and high local charge mobility (>400 cm2 V-1 s-1 by terahertz spectroscopy). We use this PGNR to fabricate ambipolar field-effect transistors with appealing switching behaviour, and single-electron transistors displaying multiple Coulomb diamonds. These results open an avenue to π-extended nanostructures with engineerable electrical and magnetic properties by transposing the coordination chemistry of porphyrins into graphene nanoribbons.

Organometallics in molecular junctions: conductance, functions, and reactions

Molecular junctions, which involve sandwiching molecular structures between electrodes, play a crucial role in molecular electronics. Recent advances in this field have revealed the vital role of organometallic chemistry in the investigation of molecular junctions, which has added to their well-known contributions to catalysis and materials chemistry. This review summarizes the recent examples of organometallic chemistry applications in molecular junctions, which can be categorized into three types, i.e., class I encompassing molecular junctions with bridging organometallic complexes, class II involving molecular junctions with covalent and noncovalent metal electrode-carbon bonds, and class III comprising organometallic reactions within molecular junctions.

Benzene-fused porphyrin(2.1.2.1) array: synthesis, structure, and electrocatalytic hydrogen evolution

The development of efficient molecular catalysts for the electrocatalytic hydrogen evolution reaction (HER) is very necessary and important for fuel cells. In this work, we report a new benzene-fused porphyrin(2.1.2.1) array, BPD, with a unique S-shaped molecular conformation. The electrochemistry of BPD displays multielectron donating and accepting properties owing to the two porphyrin(2.1.2.1) blocks and degenerate molecular orbitals. The electrocatalytic HER activity of BPD is remarkably higher-that is, BPD exhibited lower overpotential, faster HER kinetics, faster charge transfer kinetics, and extended catalytic stability-than that of the porphyrin(2.1.2.1) copper complex monomer.

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

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

Breakdown of Ohm's Law in Molecular Junctions with Electrodes of Single-Layer Graphene

For sufficiently low biases, Ohm's law, the cornerstone of electricity, stating that current I and voltage V are proportional, is satisfied at low biases for all known systems ranging from macroscopic conductors to nanojunctions. In this study, we predict theoretically and demonstrate experimentally that in single-molecule junctions fabricated with single-layer graphene as electrodes the current at low V scales as the cube of V, thereby invalidating Ohm's law. The absence of the ohmic regime is a direct consequence of the unique band structure of the single-layer graphene, whose vanishing density of states at the Dirac points precludes electron transfer from and to the electrodes at low biases.

Carbon Nanohoops: Multiple Molecular Templates for Exploring Spectroscopic, Electronic, and Thermoelectric Properties

A combination of density functional theory (DFT) methods and quantum transport theory (QTT) has been used to investigate the spectroscopic, electronic, and thermoelectric properties of carbon nanohoop molecules with different molecular templates. The connectivity type, along with inherent strain, impacts the transport behavior and creates a destructive quantum interference (DQI), which proves itself to be a powerful strategy to enhance the thermoelectric properties of these molecules, making them promising candidates for thermoelectric applications.

Reply to the 'Comment on "A single level tunneling model for molecular junctions: evaluating the simulation methods"' by I Baldea, Phys. Chem. Chem. Phys., 2024, , D2CP05110A (http://D2CP05110A)

We respond to the recent comment by Dr. Ion Bâldea concerning our work, "A single level tunneling model for molecular junctions: evaluating the simulation methods [E. M. Opodi et al.,Phys. Chem. Chem. Phys., 2022, 24, 11958]". Dr. Bâldea has raised concerns about the applicability map we developed based on the comparison study of the 3 analytical models used in the study of molecular electronics. In our response, we have dissected Dr. Bâldea's critique into four primary points. For each, we have provided comprehensive replies that address and rectify the misinterpretations of our initial study. We'd like to thank Dr. Ion Bâldea for his comments, which have resulted in further clarification of the applicability of the analytical models for the study of molecular electronics.

Comment on "A single level tunneling model for molecular junctions: evaluating the simulation methods" by E. M. Opodi, X. Song, X. Yu and W. Hu, Phys. Chem. Chem. Phys., 2022, , 11958"

The present Comment demonstrates important flaws of the paper Opodi et al. Phys. Chem. Chem. Phys., 2022, 24, 11958 Their crown result ("applicability map") aims at indicating parameter ranges wherein two approximate methods (called method 2 and 3) apply. My calculations reveal that the applicability map is a factual error. Deviations of I2 from the exact current I1 do not exceed 3% for model parameters where Opodi et al. claimed that method 2 is inapplicable. As for method 3, the parameter range of the applicability map is beyond its scope, as stated in papers cited by Opodi et al. themselves.

Can tunneling current in molecular junctions be so strongly temperature dependent to challenge a hopping mechanism? Analytical formulas answer this question and provide important insight into large area junctions

Analytical equations like Richardson-Dushman's or Shockley's provided a general, if simplified conceptual background, which was widely accepted in conventional electronics and made a fundamental contribution to advances in the field. In the attempt to develop a (highly desirable, but so far missing) counterpart for molecular electronics, in this work, we deduce a general analytical formula for the tunneling current through molecular junctions mediated by a single level that is valid for any bias voltage and temperature. Starting from this expression, which is exact and obviates cumbersome numerical integration, in the low and high temperature limits we also provide analytical formulas expressing the current in terms of elementary functions. They are accurate for broad model parameter ranges relevant for real molecular junctions. Within this theoretical framework we show that: (i) by varying the temperature, the tunneling current can vary by several orders of magnitude, thus debunking the myth that a strong temperature dependence of the current is evidence for a hopping mechanism, (ii) real molecular junctions can undergo a gradual (Sommerfeld-Arrhenius) transition from a weakly temperature dependent to a strongly ("exponential") temperature dependent current that can be tuned by the applied bias, and (iii) important insight into large area molecular junctions with eutectic gallium indium alloy (EGaIn) top electrodes can be gained. E.g., merely based on transport data, we estimate that the current carrying molecules represent only a fraction of f ≈ 4 × 10-4 out of the total number of molecules in a large area Au-S-(CH2)13-CH3/EGaIn junction.

Seebeck Effect in Molecular Wires Facilitating Long-Range Transport

The study of molecular wires facilitating long-range charge transport is of fundamental interest for the development of various technologies in (bio)organic and molecular electronics. Defining the nature of long-range charge transport is challenging as electrical characterization does not offer the ability to distinguish a tunneling mechanism from the other. Here, we show that investigation of the Seebeck effect provides the ability. We examine the length dependence of the Seebeck coefficient in electrografted bis-terpyridine Ru(II) complex films. The Seebeck coefficient ranges from 307 to 1027 μV/K, with an increasing rate of 95.7 μV/(K nm) as the film thickness increases to 10 nm. Quantum-chemical calculations unveil that the nearly overlapped molecular-orbital energy level of the Ru complex with the Fermi level accounts for the giant thermopower. Landauer-Büttiker probe simulations indicate that the significant length dependence evinces the Seebeck effect dominated by coherent near-resonant tunneling rather than thermal hopping. This study enhances our comprehension of long-range charge transport, paving the way for efficient electronic and thermoelectric materials.

Molecular Graphene Nanoribbon Junctions

One of the challenges for the realization of molecular electronics is the design of nanoscale molecular wires displaying long-range charge transport. Graphene nanoribbons are an attractive platform for the development of molecular wires with long-range conductance owing to their unique electrical properties. Despite their potential, the charge transport properties of single nanoribbons remain underexplored. Herein, we report a synthetic approach to prepare N-doped pyrene-pyrazinoquinoxaline molecular graphene nanoribbons terminated with diamino anchoring groups at each end. These terminal groups allow for the formation of stable molecular graphene nanoribbon junctions between two metal electrodes that were investigated by scanning tunneling microscope-based break-junction measurements. The experimental and computational results provide evidence of long-range tunneling charge transport in these systems characterized by a shallow conductance length dependence and electron tunneling through >6 nm molecular backbone.

Conductive Covalent Organic Frameworks of Polymetallophthalocyanines as a Tunable Platform for Electrocatalysis

Developing an electrocatalyst platform that can control the interplay among activity, selectivity, and stability at atomic precision remains a grand challenge. Here, we have synthesized highly crystalline polymetallophthalocyanines (pMPcs, M = Fe, Co, Ni, and Cu) through the annulation of tetracyanobenzene in the presence of transition metals. The conjugated, conductive, and stable backbones with precisely installed metal sites render pMPcs a unique platform in electrochemical catalysis, where tunability emerges from long-range interactions. The construction of pCoNiPc with a Co and Ni dual-site integrates the advantageous features of pCoPc and pNiPc in electrocatalytic CO2 reduction through electronic communication of the dual-site with an unprecedented long atomic separation of ≥14 chemical bonds. This integration provides excellent activity (current density, j = -16.0 and -100 mA cm-2 in H-type and flow cell, respectively), selectivity (CO Faraday efficiency, FECO = 94%), and stability (>10 h), making it one of the best-performing reticular materials.

The impact of spin-orbit coupling on fine-structure and spin polarisation in photoexcited porphyrin triplet states

The photoexcited triplet states of porphyrins show great promise for applications in the fields of opto-electronics, photonics, molecular wires, and spintronics. The magnetic properties of porphyrin triplet states are most conveniently studied by time-resolved continuous wave and pulse electron spin resonance (ESR). This family of techniques is singularly able to probe small yet essential details of triplet states: zero-field splittings, g-anisotropy, spin polarisation, and hyperfine interactions. These characteristics are linked to spin-orbit coupling (SOC) which is known to have a strong influence on photophysical properties such as intersystem crossing rates. The present study explores SOC effects induced by the presence of Pd2+ in various porphyrin architectures. In particular, the impact of this relativistic interaction on triplet state fine-structure and spin polarisation is investigated. These properties are probed using time-resolved ESR complemented by electron-nuclear double resonance. The findings of this study could influence the future design of molecular spintronic devices. The Pd2+ ion may be incorporated into porphyrin molecular wires as a way of controlling spin polarisation.

Can room-temperature data for tunneling molecular junctions be analyzed within a theoretical framework assuming zero temperature?

Routinely, experiments on tunneling molecular junctions report values of conductances (G_RT) and currents (I_RT) measured at room temperature. On the other hand, theoretical approaches based on simplified models provide analytic formulas for the conductance (G_0K) and current (I_0K) valid at zero temperature. Therefore, interrogating the applicability of the theoretical results deduced in the zero-temperature limit to real experimental situations at room temperature (i.e., G_RT ≈ G_0K and I_RT ≈ I_0K) is a relevant aspect. Quantifying the pertaining temperature impact on the transport properties computed within the ubiquitous single-level model with Lorentzian transmission is the specific aim of the present work. Comprehensive results are presented for broad ranges of the relevant parameters (level's energy offset ε₀ and width Γ_a, and applied bias V) that safely cover values characterizing currently fabricated junctions. They demonstrate that the strongest thermal effects occur at biases below resonance (2|ε₀| - δε₀ - 0.3 ≲ |eV| - 0.3 ≲ 2|ε₀|). At fixed V, they affect an ε₀-range whose largest width δε₀ is about nine times larger than the thermal energy (δε₀ ≈ 3πk_BT) at Γ_a → 0. The numerous figures included aim to convey a quick overview on the applicability of the zero-temperature limit to a specific real junction. In quantitative terms, the conditions of applicability are expressed as mathematical inequalities involving elementary functions. They constitute the basis of a proposed interactive data-fitting procedure, which aims to guide experimentalists interested in data processing in a specific case.

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.

Advances in single-molecule junctions as tools for chemical and biochemical analysis

The development of miniaturized electronics has led to the design and construction of powerful experimental platforms capable of measuring electronic properties to the level of single molecules, along with new theoretical concepts to aid in the interpretation of the data. A new area of activity is now emerging concerned with repurposing the tools of molecular electronics for applications in chemical and biological analysis. Single-molecule junction techniques, such as the scanning tunnelling microscope break junction and related single-molecule circuit approaches have a remarkable capacity to transduce chemical information from individual molecules, sampled in real time, to electrical signals. In this Review, we discuss single-molecule junction approaches as emerging analytical tools for the chemical and biological sciences. We demonstrate how these analytical techniques are being extended to systems capable of probing chemical reaction mechanisms. We also examine how molecular junctions enable the detection of RNA, DNA, and traces of proteins in solution with limits of detection at the zeptomole level.

Anti-ohmic nanoconductors: myth, reality and promise

The recent accomplishment in the design of molecular nanowires characterized by increasing conductance with length has led to the origin of an extraordinary new family of molecular junctions referred to as "anti-ohmic" wires. Herein, this highly desirable, non-classical behavior, has been examined for molecules long-enough to exhibit pronounced diradical character in their ground state within the unrestricted DFT formalism with spin symmetry breaking. We demonstrate that highly conjugated acenes signal higher resistance in an open-shell singlet (OSS) configuration as compared to their closed-shell counterparts. This anomaly has been further proven for experimentally certified cumulene wires, which reveals phenomenal modulation in the transport characteristics such that an increasing conductance is observed in the closed-shell limit, while higher cumulenes in the OSS ground state yield regular decay of conductance.

Topological Radical Pairs Produce Ultrahigh Conductance in Long Molecular Wires

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

Self-Assembled Monolayers of Molecular Conductors with Terpyridine-Metal Redox Switching Elements: A Combined AFM, STM and Electrochemical Study

Self-assembled monolayers (SAMs) of terpyridine-based transition metal (ruthenium and osmium) complexes, anchored to gold substrate via tripodal anchoring groups, have been investigated as possible redox switching elements for molecular electronics. An electrochemical study was complemented by atomic force microscopy (AFM) and scanning tunneling microscopy (STM) methods. STM was used for determination of the SAM conductance values, and computation of the attenuation factor β from tunneling current-distance curves. We have shown that SAMs of Os-tripod molecules contain larger adlayer structures compared with SAMs of Ru-tripod molecules, which are characterized by a large number of almost evenly distributed small islands. Furthermore, upon cyclic voltammetric experimentation, Os-tripod films rearrange to form a smaller number of even larger islands, reminiscent of the Ostwald ripening process. Os-tripod SAMs displayed a higher surface concentration of molecules and lower conductance compared with Ru-tripod SAMs. The attenuation factor of Os-tripod films changed dramatically, upon electrochemical cycling, to a higher value. These observations are in accordance with previously reported electron transfer kinetics studies.

Estimating the Number of Molecules in Molecular Junctions Merely Based on the Low Bias Tunneling Conductance at Variable Temperature

Temperature (T) dependent conductance G=G(T) data measured in molecular junctions are routinely taken as evidence for a two-step hopping mechanism. The present paper emphasizes that this is not necessarily the case. A curve of lnG versus 1/T decreasing almost linearly (Arrhenius-like regime) and eventually switching to a nearly horizontal plateau (Sommerfeld regime), or possessing a slope gradually decreasing with increasing 1/T is fully compatible with a single-step tunneling mechanism. The results for the dependence of G on T presented include both analytical exact and accurate approximate formulas and numerical simulations. These theoretical results are general, also in the sense that they are not limited, e.g., to the (single molecule electromigrated (SET) or large area EGaIn) fabrication platforms, which are chosen for exemplification merely in view of the available experimental data needed for analysis. To be specific, we examine in detail transport measurements for molecular junctions based on ferrocene (Fc). As a particularly important finding, we show how the present analytic formulas for G=G(T) can be utilized to compute the ratio f=Aeff/An between the effective and nominal areas of large area Fc-based junctions with an EGaIn top electrode. Our estimate of f≈0.6×10-4 is comparable with previously reported values based on completely different methods for related large area molecular junctions.

Temperature-Dependent Coherent Tunneling across Graphene-Ferritin Biomolecular Junctions

Understanding the mechanisms of charge transport (CT) across biomolecules in solid-state devices is imperative to realize biomolecular electronic devices in a predictive manner. Although it is well-accepted that biomolecule-electrode interactions play an essential role, it is often overlooked. This paper reveals the prominent role of graphene interfaces with Fe-storing proteins in the net CT across their tunnel junctions. Here, ferritin (AfFtn-AA) is adsorbed on the graphene by noncovalent amine-graphene interactions confirmed with Raman spectroscopy. In contrast to junctions with metal electrodes, graphene has a vanishing density of states toward its intrinsic Fermi level ("Dirac point"), which increases away from the Fermi level. Therefore, the amount of charge carriers is highly sensitive to temperature and electrostatic charging (induced doping), as deduced from a detailed analysis of CT as a function of temperature and iron loading. Remarkably, the temperature dependence can be fully explained within the coherent tunneling regime due to excitation of hot carriers. Graphene is not only demonstrated as an alternative platform to study CT across biomolecular tunnel junctions, but it also opens rich possibilities in employing interface electrostatics in tuning CT behavior.

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

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

Exploring seebeck-coefficient fluctuations in endohedral-fullerene, single-molecule junctions

For the purpose of creating single-molecule junctions, which can convert a temperature difference ΔT into a voltage ΔV via the Seebeck effect, it is of interest to screen molecules for their potential to deliver high values of the Seebeck coefficient S = -ΔV/ΔT. Here we demonstrate that insight into molecular-scale thermoelectricity can be obtained by examining the widths and extreme values of Seebeck histograms. Using a combination of experimental scanning-tunnelling-microscopy-based transport measurements and density-functional-theory-based transport calculations, we study the electrical conductance and Seebeck coefficient of three endohedral metallofullerenes (EMFs) Sc₃N@C₈₀, Sc₃C₂@C₈₀, and Er₃N@C₈₀, which based on their structures, are selected to exhibit different degrees of charge inhomogeneity and geometrical disorder within a junction. We demonstrate that standard deviations in the Seebeck coefficient σ_S of EMF-based junctions are correlated with the geometric standard deviation σ and the charge inhomogeneity σ_q. We benchmark these molecules against C₆₀ and demonstrate that both σ_q, σ_S are the largest for Sc₃C₂@C₈₀, both are the smallest for C₆₀ and for the other EMFs, they follow the order Sc₃C₂@C₈₀ > Sc₃N@C₈₀ > Er₃N@C₈₀ > C₆₀. A large value of σ_S is a sign that a molecule can exhibit a wide range of Seebeck coefficients, which means that if orientations corresponding to high values can be selected and controlled, then the molecule has the potential to exhibit high-performance thermoelectricity. For the EMFs studied here, large values of σ_S are associated with distributions of Seebeck coefficients containing both positive and negative signs, which reveals that all these EMFs are bi-thermoelectric materials.

Electrochemical gating for single-molecule electronics with hybrid Au|graphene contacts

The single-molecular conductance of a redox active viologen molecular bridge between Au|graphene electrodes has been studied in an electrochemical gating configuration in an ionic liquid medium. A clear "off-on-off" conductance switching behaviour has been achieved through gating of the redox state when the electrochemical potential is swept. The Au|viologen|graphene junctions show single-molecule conductance maxima centred close to the equilibrium redox potentials for both reduction steps. The peak conductance of Au|viologen|graphene junctions during the first reduction is significantly higher than that of previously measured Au|viologen|Au junctions. This shows that even though the central viologen moiety is not directly linked to the enclosing electrodes, substituting one gold contact for a graphene one nevertheless has a significant impact on junction conductance values. The experimental data was compared against two theoretical models, namely a phase coherent tunnelling and an incoherent "hopping" model. The former is a simple gating monoelectronic model within density functional theory (DFT) which discloses the charge state evolution of the molecule with electrode potential. The latter model is the collective Kuznetsov Ulstrup model for 2-step sequential charge transport through the redox centre in the adiabatic limit. The comparison of both models to the experimental data is discussed for the first time. This work opens perspectives for graphene-based molecular transistors with more effective gating and fundamental understanding of electrochemical electron transfer at the single molecular level.

Coherent and incoherent contributions to molecular electron transport

We numerically isolate the limits of validity of the Landauer approximation to describe charge transport along molecular junctions in condensed phase environments. To do so, we contrast Landauer with exact time-dependent non-equilibrium Green’s function quantum transport computations in a two-site molecular junction subject to exponentially correlated noise. Under resonant transport conditions, we find Landauer accuracy to critically depend on intramolecular interactions. By contrast, under nonresonant conditions, the emergence of incoherent transport routes that go beyond Landauer depends on charging and discharging processes at the electrode–molecule interface. In both cases, decreasing the rate of charge exchange between the electrodes and molecule and increasing the interaction strength with the thermal environment cause Landauer to become less accurate. The results are interpreted from a time-dependent perspective where the noise prevents the junction from achieving steady-state and from a fully quantum perspective where the environment introduces dephasing in the dynamics. Using these results, we analyze why the Landauer approach is so useful to understand experiments, isolate regimes where it fails, and propose schemes to chemically manipulate the degree of transport coherence.

Thermally activated delayed fluorescence materials as organic photosensitizers

Photosensitizer molecules play a crucial role in materials and life sciences. Efforts to improve their performance and reduce the associated costs are therefore vital for advancing environmentally friendly light-driven technologies. In this Feature Article, we describe the use of photosensitizers that make use of thermally activated delayed fluorescence (TADF), their benefits compared to conventional fluorescent and phosphorescent sensitizers, and the efforts of our group and others to develop emitters with application-tailored properties. The key feature is the diversity of accessible excited state pathways, which may be tuned by molecular and supramolecular approaches to suit a particular problem. This unique property has allowed TADF emitters to become competitive for applications including TADF-sensitized fluorescence in light emitting diodes and chemical sensing, organic long persistent luminescence, photodynamic therapy, and non-coherent photon upconversion.

Transition between Nonresonant and Resonant Charge Transport in Molecular Junctions

Efficient long-range charge transport is required for high-performance molecular electronic devices. Resonant transport is thought to occur in single molecule junctions when molecular frontier orbital energy levels align with electrode Fermi levels, thereby enabling efficient transport without molecular or environmental relaxation. Despite recent progress, we lack a systematic understanding of the transition between nonresonant and resonant transport for molecular junctions with different chemical compositions. In this work, we show that molecular junctions undergo a reversible transition from nonresonant tunneling to resonant transport as a function of applied bias. Transient bias-switching experiments show that the nonresonant to resonant transition is reversible with the applied bias. We determine a general quantitative relationship that describes the transition voltage as a function of the molecular frontier orbital energies and electrode Fermi levels. Overall, this work highlights the importance of frontier orbital energy alignment in achieving efficient charge transport in molecular devices.

Porphyrins as building blocks for single-molecule devices

Direct measurement of single-molecule electrical transparency by break junction experiments has become a major field of research over the two last decades. This review specifically and comprehensively highlights the use of porphyrins as molecular components and discusses their potential use for the construction of future devices. Throughout the review, the features provided by porphyrins, such as low level misalignments and very low attenuation factors, are shown with numerous examples, illustrating the potential and limitations of these molecular junctions, as well as differences emerging from applied integration/investigation techniques.

Single-Molecule Junctions with Highly Improved Stability

Single-molecule junctions (SMJs) have been fabricated using layers generated by diazonium electroreduction. This process creates a C-Au covalent bond between the molecule and the electrode. Rigid oligomers of variable length, based on porphyrin derivatives in their free base or cobalt complex forms, have been grafted on the surface. The conductance of the oligomers has been studied by a scanning tunneling microscopy break junction (STM-bj) technique and G(t) measurements, and the lifetime of the SMJs has been investigated. The conductance histograms indicate that charge transport in the porphyrins is relatively efficient and influenced by the presence of the cobalt center. With both systems, random telegraph G(t) signals are easily recorded, showing SMJ on/off states. The SMJs then stabilize and exhibit a surprisingly long lifetime around 10 s, and attenuation plots, obtained by both G(t) and STM-bj measurements, give identical values. This work shows that highly stable SMJs can be prepared using a diazonium grafting approach.

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.

Bottom-up Fabrication and Atomic-Scale Characterization of Triply Linked, Laterally π-Extended Porphyrin Nanotapes*

Porphyrin nanotapes (Por NTs) are promising structures for their use as molecular wires thanks to a high degree of π‐conjugation, low HOMO—LUMO gaps, and exceptional conductance. Such structures have been prepared in solution, but their on‐surface synthesis remains unreported. Here, meso–meso triply fused Por NTs have been prepared through a two‐step synthesis on Au(111). The diradical character of the on‐surface formed building block PorA₂, a phenalenyl π‐extended Zn^IIPor, facilitates intermolecular homocoupling and allows for the formation of laterally π‐extended tapes. The structural and electronic properties of individual Por NTs are addressed, both on Au(111) and on a thin insulating NaCl layer, by high‐resolution scanning probe microscopy/spectroscopy complemented by DFT calculations. These Por NTs carry one unpaired electron at each end, which leads to magnetic end states. Our study provides a versatile route towards Por NTs and the atomic‐scale characterization of such tapes.

A single atom change turns insulating saturated wires into molecular conductors

We present an efficient strategy to modulate tunnelling in molecular junctions by changing the tunnelling decay coefficient, β, by terminal-atom substitution which avoids altering the molecular backbone. By varying X = H, F, Cl, Br, I in junctions with S(CH₂)_(10-18)X, current densities (J) increase >4 orders of magnitude, creating molecular conductors via reduction of β from 0.75 to 0.25 Å⁻¹. Impedance measurements show tripled dielectric constants (ε_r) with X = I, reduced HOMO-LUMO gaps and tunnelling-barrier heights, and 5-times reduced contact resistance. These effects alone cannot explain the large change in β. Density-functional theory shows highly localized, X-dependent potential drops at the S(CH₂)_nX//electrode interface that modifies the tunnelling barrier shape. Commonly-used tunnelling models neglect localized potential drops and changes in ε_r. Here, we demonstrate experimentally that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta \propto 1/\sqrt{{\varepsilon }_{r}}$$\end{document}β∝1/εr, suggesting highly-polarizable terminal-atoms act as charge traps and highlighting the need for new charge transport models that account for dielectric effects in molecular tunnelling junctions.

In molecular junctions, where a molecule is placed between two electrodes, the current passed decays exponentially as a function of length. Here, Chen et al. show that this exponentially attenuation can be controlled by changing a single atom at the end of the molecular wire.

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

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

Molecular Structure-(Thermo)electric Property Relationships in Single-Molecule Junctions and Comparisons with Single- and Multiple-Parameter Models

The most probable single-molecule conductance of each member of a series of 12 conjugated molecular wires, 6 of which contain either a ruthenium or platinum center centrally placed within the backbone, has been determined. The measurement of a small, positive Seebeck coefficient has established that transmission through these molecules takes place by tunneling through the tail of the HOMO resonance near the middle of the HOMO-LUMO gap in each case. Despite the general similarities in the molecular lengths and frontier-orbital compositions, experimental and computationally determined trends in molecular conductance values across this series cannot be satisfactorily explained in terms of commonly discussed "single-parameter" models of junction conductance. Rather, the trends in molecular conductance are better rationalized from consideration of the complete molecular junction, with conductance values well described by transport calculations carried out at the DFT level of theory, on the basis of the Landauer-Büttiker model.

Achieving Ultralow, Zero, and Inverted Tunneling Attenuation Coefficients in Molecular Wires with Extended Conjugation

Molecular tunnel junctions are organic devices miniaturized to the molecular scale. They serve as a versatile toolbox that can systematically examine charge transport behaviors at the atomic level. The electrical conductance of the molecular wire that bridges the two electrodes in a junction is significantly influenced by its chemical structure, and an intrinsically poor conductance is a major barrier for practical applications toward integrating individual molecules into electronic circuitry. Therefore, highly conjugated molecular wires are attractive as active components for the next-generation electronic devices, owing to the narrow highest occupied molecular orbital-lowest occupied molecular orbital gaps provided by their extended π-building blocks. This article aims to highlight the significance of highly conductive molecular wires in molecular electronics, the structures of which are inspired from conductive organic polymers, and presents a body of discussion on molecular wires exhibiting ultralow, zero, or inverted attenuation of tunneling probability at different lengths, along with future directions.

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

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

Temperature-Dependent Tunneling in Furan Oligomer Single-Molecule Junctions

Two commonly observed charge transport mechanisms in single-molecule junctions are coherent tunneling and incoherent hopping. It has been generally believed that tunneling processes yield temperature-independent conductance behavior and hopping processes exhibit increasing conductance with increasing temperature. However, it has recently been proposed that tunneling can also yield temperature-dependent transport due to the thermal broadening of the Fermi energy of the contacts. In this work, we examine a series of rigid, planar furan oligomers that are free from a rotational internal degree of freedom to examine the temperature dependence of tunneling transport directly over a wide temperature range (78-300 K). Our results demonstrate conductance transition from a temperature-independent regime to a temperature-dependent regime. By examining various hopping and tunneling models and the correlation between the temperature dependence of conductance and molecular orbital energy offset from the Fermi level, we conclude thermally assisted tunneling is the dominant cause for the onset of temperature-dependent conductance in these systems.

Single-molecule junctions of multinuclear organometallic wires: long-range carrier transport brought about by metal-metal interaction

Here, we report multinuclear organometallic molecular wires having (2,5-diethynylthiophene)diyl-Ru(dppe)₂ repeating units. Despite the molecular dimensions of 2–4 nm the multinuclear wires show high conductance (up to 10⁻² to 10⁻³G₀) at the single-molecule level with small attenuation factors (β) as revealed by STM-break junction measurements. The high performance can be attributed to the efficient energy alignment between the Fermi level of the metal electrodes and the HOMO levels of the multinuclear molecular wires as revealed by DFT–NEGF calculations. Electrochemical and DFT studies reveal that the strong Ru–Ru interaction through the bridging ligands raises the HOMO levels to access the Fermi level, leading to high conductance and small β values.

Multinuclear organometallic molecular wires having (diethynylthiophene)diyl-Ru(dppe)₂ repeating units show high conductance with small attenuation factors. The strong Ru–Ru interaction is the key for the long-range carrier transport.

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.

Weak Distance Dependence of Hot-Electron-Transfer Rates at the Interface between Monolayer MoS2 and Gold

Electron transport across the transition-metal dichalcogenide (TMD)/metal interface plays an important role in determining the performance of TMD-based optoelectronic devices. However, the robustness of this process against structural heterogeneities remains unexplored, to the best of our knowledge. Here, we employ a combination of time-resolved photoemission electron microscopy (TR-PEEM) and atomic force microscopy to investigate the spatially resolved hot-electron-transfer dynamics at the monolayer (1L) MoS₂/Au interface. A spatially heterogeneous distribution of 1L-MoS₂/Au gap distances, along with the sub-80 nm spatial- and sub-60 fs temporal resolution of TR-PEEM, permits the simultaneous measurement of electron-transfer rates across a range of 1L-MoS₂/Au distances. These decay exponentially as a function of distance, with an attenuation coefficient β ∼ 0.06 ± 0.01 Å^-1, comparable to molecular wires. Ab initio simulations suggest that surface plasmon-like states mediate hot-electron-transfer, hence accounting for its weak distance dependence. The weak distance dependence of the interfacial hot-electron-transfer rate indicates that this process is insensitive to distance fluctuations at the TMD/metal interface, thus motivating further exploration of optoelectronic devices based on hot carriers.

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.

Tuning Single-Molecule Conductance in Metalloporphyrin-Based Wires via Supramolecular Interactions

Nature has developed supramolecular constructs to deliver outstanding charge-transport capabilities using metalloporphyrin-based supramolecular arrays. Herein we incorporate simple, naturally inspired supramolecular interactions via the axial complexation of metalloporphyrins into the formation of a single-molecule wire in a nanoscale gap. Small structural changes in the axial coordinating linkers result in dramatic changes in the transport properties of the metalloporphyrin-based wire. The increased flexibility of a pyridine-4-yl-methanethiol ligand due to an extra methyl group, as compared to a more rigid 4-pyridinethiol linker, allows the pyridine-4-yl-methanethiol ligand to adopt an unexpected highly conductive stacked structure between the two junction electrodes and the metalloporphyrin ring. DFT calculations reveal a molecular junction structure composed of a shifted stack of the two pyridinic linkers and the metalloporphyrin ring. In contrast, the more rigid 4-mercaptopyridine ligand presents a more classical lifted octahedral coordination of the metalloporphyrin metal center, leading to a longer electron pathway of lower conductance. This works opens to supramolecular electronics, a concept already exploited in natural organisms.

Long-range electron transport in Prussian blue analog nanocrystals

We report electron transport measurements through nano-scale devices consisting of 1 to 3 Prussian blue analog (PBA) nanocrystals connected between two electrodes. We compare two types of cubic nanocrystals, CsCoIIIFeII (15 nm) and CsNiIICrIII (6 nm), deposited on highly oriented pyrolytic graphite and contacted by conducting-AFM. The measured currents show an exponential dependence with the length of the PBA nano-device (up to 45 nm), with low decay factors β, in the range 0.11-0.18 nm-1 and 0.25-0.34 nm-1 for the CsCoFe and the CsNiCr nanocrystals, respectively. From the theoretical analysis of the current-voltage curve for the nano-scale device made of a single nanoparticle, we deduce that the electron transport is mediated by the localized d bands at around 0.5 eV from the electrode Fermi energy in the two cases. By comparison with previously reported ab initio calculations, we tentatively identify the involved orbitals as the filled Fe(ii)-t2g d band (HOMO) for CsCoFe and the half-filled Ni(ii)-eg d band (SOMO) for CsNiCr. Conductance values measured for multi-nanoparticle nano-scale devices (2 and 3 nanocrystals between the electrodes) are consistent with a multi-step coherent tunneling in the off-resonance regime between adjacent PBAs, a simple model gives a strong coupling (around 0.1-0.25 eV) between the adjacent PBA nanocrystals, mediated by electrostatic interactions.