Interpretation of Stochastic Events in Single-Molecule Measurements of Conductance and Transition Voltage Spectroscopy

Dichotomy between Level Broadening and Level Coupling to Electrodes in Large Area EGaIn Molecular Junctions

Choosing self-assembled monolayers (SAMs) of fluorine-terminated oligophenylenes adsorbed on gold as an illustration, we show that a single-level [molecular orbital (MO)] model can excellently reproduce full I-V curves measured for large area junctions fabricated with a top EGaIn contact. In addition, this model unravels a surprising dichotomy between MO coupling to electrodes and MO broadening. Importantly for the coherence of the microscopic description, the latter is found to correlate with the SAM coverage and molecular and π* orbital tilt angles.

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.

Single-molecule photoelectron tunnelling spectroscopy

Experimental mapping of transmission is essential for understanding and controlling charge transport through molecular devices and materials. Here we developed a single-molecule photoelectron tunnelling spectroscopy approach for mapping transmission beyond the HOMO-LUMO gap of the single diketopyrrolopyrrole molecule junction using an ultrafast-laser combined scanning tunnelling microscope-based break junction set-up at room temperature. Two resonant transport channels of ultrafast photocurrent are found by our photoelectron tunnelling spectroscopy, ranging from 1.31 eV to 1.77 eV, consistent with the LUMO + 1 and LUMO + 2 in the transmission spectrum obtained by density functional theory calculations. Moreover, we observed the modulation of resonant peaks by varying bias voltages, which demonstrates the ability to quantitatively characterize the effect of the electric field on frontier molecular orbitals. Our single-molecule photoelectron tunnelling spectroscopy offers an avenue that allows us to explore the nature of energy-dependent charge transport through single-molecule junctions.

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.

Controlling Charge Transport in Molecular Wires through Transannular π-π Interaction

This paper describes the influence of the transannular π-π interaction in controlling the carrier transport in molecular wires by employing the STM break junction technique. Five pentaphenylene-based molecular wires that contained [2.2]paracyclophane-1,9-dienes (PCD) as the building block were prepared as model compounds. Functional substituents with different electronic properties, ranging from strong acceptors to strong donors, were attached to the top parallel aromatic ring and used as a gate. It was found that the carrier transport features of these molecular wires, such as single-molecule conductance and a charge-tunneling barrier, can be systematically controlled through the transannular π-π interaction.

Charge Transport Characteristics of Molecular Electronic Junctions Studied by Transition Voltage Spectroscopy

The field of molecular electronics is prompted by tremendous opportunities for using a single-molecule and molecular monolayers as active components in integrated circuits. Until now, a wide range of molecular devices exhibiting characteristic functions, such as diodes, transistors, switches, and memory, have been demonstrated. However, a full understanding of the crucial factors that affect charge transport through molecular electronic junctions should yet be accomplished. Remarkably, recent advances in transition voltage spectroscopy (TVS) elucidate that it can provide key quantities for probing the transport characteristics of the junctions, including, for example, the position of the frontier molecular orbital energy relative to the electrode Fermi level and the strength of the molecule–electrode interactions. These parameters are known to be highly associated with charge transport behaviors in molecular systems and can then be used in the design of molecule-based devices with rationally tuned electronic properties. This article highlights the fundamental principle of TVS and then demonstrates its major applications to study the charge transport properties of molecular electronic junctions.

Evidence That Molecules in Molecular Junctions May Not Be Subject to the Entire External Perturbation Applied to Electrodes

Whether molecules forming molecular junctions are really subject to the entire external perturbation applied to electrodes is an important issue, but so far, it has not received adequate consideration in the literature. In this paper, we demonstrate that, out of the temperature difference ΔT_electr between electrodes applied in thermopower measurements, molecules only feel a significantly smaller temperature difference (ΔT_molec < ΔT_electr). Rephrasing, temperature drops at metal-molecule interfaces are substantial. Our theoretical analysis to address this problem of fundamental importance for surface science is based on experimental data collected via ultraviolet photoelectron spectroscopy, transition voltage spectroscopy, and Seebeck coefficient measurements. An important practical consequence of the presently reported finding is that the energetic alignment of the frontier molecular orbital (HOMO or LUMO) of the embedded molecules with respect to the metallic Fermi level position deduced from thermopower data-and this is frequently the case in current studies of molecular electronics-is substantially overestimated. Another important result presented here is that, unlike the exponential length dependence characterizing electric conduction (which is a fingerprint for quantum tunneling), thermal conduction through the molecules considered (oligophenylene thiols and alkane thiols) exhibits a length dependence compatible with classical physics.

Generalized Voigt broadening due to thermal fluctuations of electromechanical nanosensors and molecular electronic junctions

Graphene and other 2D materials give a platform for electromechanical sensing of biomolecules in aqueous, room temperature environments. The electronic current changes in response to mechanical deflection, indicating the presence of forces due to interactions with, e.g., molecular species. We develop illustrative models of these sensors in order to give explicit, compact expressions for the current and signal-to-noise ratio. Electromechanical structures have an electron transmission function that follows a generalized Voigt profile, with thermal fluctuations giving a Gaussian smearing analogous to thermal Doppler broadening in solution/gas-phase spectroscopic applications. The Lorentzian component of the profile comes from the contact to the electrodes. After providing an accurate approximate form of this profile, we calculate the mechanical susceptibility for a representative two-level bridge and the current fluctuations for electromechanical detection. These results give the underlying mechanics of electromechanical sensing in more complex scenarios, such as graphene deflectometry.

Why one can expect large rectification in molecular junctions based on alkane monothiols and why rectification is so modest

Many attempts to obtain high current rectification ratios (RRs) in molecular electronics are triggered by a potentiometer rule argument, which predicts that a strongly asymmetric location of the dominant molecular orbital yields large RR-values. Invoking this argument, molecular junctions based on alkane monothiols (CnT) can be expected to exhibit high RRs; the HOMO of these molecules is localized on the thiol terminal group bonded to one electrode. The extensive current-voltage (I-V) results for CP-AFM (conducting probe atomic force microscope) CnT junctions of various molecular lengths (n = 7, 8, 9, 10, and 12) and different metallic contacts (Ag, Au, and Pt) are consistent with conduction dominated by the HOMO, but the measured RR ∼ 1.5 is much smaller than that predicted by the potentiometer rule framework. Further, the linear shift in the HOMO position with applied bias, γ, which gives rise to rectification, is also smaller than expected, and critically, γ has the opposite sign from potentiometer rule predictions. Companion ab initio OVGF (outer valence Green's function) quantum chemical calculations provide important insight. Namely, a linear Stark shift γm is calculated for the HOMO of CnT molecules for electric field strengths (106-107 V cm-1) typical of molecular junctions, and the sign of γm matches the sign of the experimental γ for junctions derived from transport measurements, suggesting that the Stark effect plays an important role. However, the magnitude of the measured γ is only 10-15% of the computed value γm. We propose that this implies that the contacts are far from optimal; they substantially screen the effect of the applied bias, possibly via molecule-electrode interface states. We predict that, with optimized contacts, the rectification ratios in CnT-based junctions can reach reasonably high values (RR ≈ 500). We believe that Stark shifts and limited current rectification due to non-ideal contacts discussed here for the specific case of alkane monothiol junctions are issues of general interest for molecular electronics that deserve further consideration.

Protocol for disentangling the thermally activated contribution to the tunneling-assisted charge transport. Analytical results and experimental relevance

In this paper we present results demonstrating that the charge transport by tunneling in molecular junctions can exhibit a substantial temperature dependence.

Estimating the Landauer-Büttiker transmission function from single molecule break junction experiments

When investigating the electronic response properties of molecules, experiments often measure conductance whereas computation predicts the transmission probability. Although Landauer-Büttiker theory usually relates the two, comparison between experiment and computation remains difficult because experimental data (specifically those from break junctions) are statistical and computational results are deterministic. In this work we develop tools to quantitatively estimate-with error bars-the shape of the Landauer-Büttiker transmission function directly from experimental statistics on conductance and thermopower (if the latter is also available). We subsequently apply these tools to existing data, demonstrating a rigorous statistical comparison between experimental and computational results on molecular electron transport.

Thermoelectric effect and its dependence on molecular length and sequence in single DNA molecules

Studying the thermoelectric effect in DNA is important for unravelling charge transport mechanisms and for developing relevant applications of DNA molecules. Here we report a study of the thermoelectric effect in single DNA molecules. By varying the molecular length and sequence, we tune the charge transport in DNA to either a hopping- or tunnelling-dominated regimes. The thermoelectric effect is small and insensitive to the molecular length in the hopping regime. In contrast, the thermoelectric effect is large and sensitive to the length in the tunnelling regime. These findings indicate that one may control the thermoelectric effect in DNA by varying its sequence and length. We describe the experimental results in terms of hopping and tunnelling charge transport models.

Understanding the thermoelectric effect of materials and molecules is important for understanding their charge transport properties. Here, the authors study the thermoelectric effect in single DNA molecules and show that the charge carrier properties are dependent on both the DNA length and sequence.

Counterintuitive issues in the charge transport through molecular junctions

Whether at phenomenological or microscopic levels, most theoretical approaches to charge transport through molecular junctions postulate or attempt to justify microscopically the existence of a dominant molecular orbital (MO). Within such single level descriptions, experimental current-voltage I-V curves are sometimes/often analyzed by using analytical formulas expressing the current as a cubic expansion in terms of the applied voltage V, and the possible V-driven shifts of the level energy offset relative to the metallic Fermi energy ε0 are related to the asymmetry of molecule-electrode couplings or an asymmetric location of the "center of gravity" of the MO with respect to electrodes. In this paper, we present results demonstrating the failure of these intuitive expectations. For example, we show how typical data processing based on cubic expansions yields a value of ε0 underestimated by a typical factor of about two. When compared to theoretical results of DFT approaches, which typically underestimate the HOMO-LUMO gap by a similar factor, this may create the false impression of "agreement" with experiments in situations where this is actually not the case. Furthermore, such cubic expansions yield model parameter values dependent on the bias range width employed for fitting, which is unacceptable physically. Finally, we present an example demonstrating that, counter-intuitively, the bias-induced change in the energy of an MO located much closer to an electrode can occur in a direction that is opposite to the change in the Fermi energy of that electrode. This is contrary to what one expects based on a "lever rule" argument, according to which the MO "feels" the local value of the electric potential, which is assumed to vary linearly across the junction and is closer to the potential of the closer electrode. This example emphasizes the fact that screening effects in molecular junctions can have a subtle character, contradicting common intuition.

Transition voltages respond to synthetic reorientation of embedded dipoles in self-assembled monolayers

Transition voltages respond to the collective action of dipole moments embedded in self-assembled monolayers.

We studied the influence of embedded dipole moments in self-assembled monolayers (SAMs) formed on template stripped Au surfaces with liquid eutectic Ga–In alloy as a top electrode. We designed three molecules based on a p-terphenyl structure in which the central aromatic ring is either phenyl or a dipole-inducing pyrimidyl in one of two different orientations. All three form well defined SAMs with similar thickness, packing density and tilt angle, with dipole moments embedded in the SAM, isolated from either interface. The magnitude of the current density is dominated by the tunneling distance and is not affected by the presence of dipole moments; however, transition voltages (V_T) show a clear linear correlation with the shift in the work function of Au induced by the collective action of the embedded dipoles. This observation demonstrates that V_T can be manipulated synthetically, without altering either the interfaces or electrodes and that trends in V_T can be related to experimental observables on the SAMs before installing the top contact. Calculated projected density of states of the SAMs on Au surfaces that relate HOMO-derived states to V_T further show that energy level alignment within an assembled junction can be predicted and adjusted by embedding dipoles in a SAM without altering any other properties of the junction. We therefore suggest that trends in V_T can be used analogously to β in systems for which length-dependence is physically or experimentally inaccessible.

Important issues facing model-based approaches to tunneling transport in molecular junctions

Extensive studies on thin films indicated a generic cubic current-voltage I-V dependence as a salient feature of charge transport by tunneling. A quick glance at I-V data for molecular junctions suggests a qualitatively similar behavior. This would render model-based studies almost irrelevant, since, whatever the model, its parameters can always be adjusted to fit symmetric (asymmetric) I-V curves characterized by two (three) expansion coefficients. Here, we systematically examine popular models based on tunneling barriers or tight-binding pictures and demonstrate that, for a quantitative description at biases of interest (V slightly higher than the transition voltage Vt), cubic expansions do not suffice. A detailed collection of analytical formulae as well as their conditions of applicability is presented to facilitate experimentalist colleagues to process and interpret their experimental data obtained by measuring currents in molecular junctions. We discuss in detail the limits of applicability of the various models and emphasize that uncritically adjusting the model parameters to experiment may be unjustified because the values deduced in this way may fall in ranges rendering a specific model invalid or incompatible to ab initio estimates. We exemplify with the benchmark case of oligophenylene-based junctions, for which the results of ab initio quantum chemical calculations are also reported. As a specific issue, we address the impact of the spatial potential profile and show that it is not notable up to biases V ≳ Vt, unlike at higher biases, where it may be responsible for negative differential resistance effects.

Experimental and Theoretical Analysis of Nanotransport in Oligophenylene Dithiol Junctions as a Function of Molecular Length and Contact Work Function

We report the results of an extensive investigation of metal-molecule-metal tunnel junctions based on oligophenylene dithiols (OPDs) bound to several types of electrodes (M1-S-(C6H4)n-S-M2, with 1 ≤ n ≤ 4 and M1,2 = Ag, Au, Pt) to examine the impact of molecular length (n) and metal work function (Φ) on junction properties. Our investigation includes (1) measurements by scanning Kelvin probe microscopy of electrode work function changes (ΔΦ = ΦSAM - Φ) caused by chemisorption of OPD self-assembled monolayers (SAMs), (2) measurements of junction current-voltage (I-V) characteristics by conducting probe atomic force microscopy in the linear and nonlinear bias ranges, and (3) direct quantitative analysis of the full I-V curves. Further, we employ transition voltage spectroscopy (TVS) to estimate the energetic alignment εh = EF - EHOMO of the dominant molecular orbital (HOMO) relative to the Fermi energy EF of the junction. Where photoelectron spectroscopy data are available, the εh values agree very well with those determined by TVS. Using a single-level model, which we justify via ab initio quantum chemical calculations at post-density functional theory level and additional UV-visible absorption measurements, we are able to quantitatively reproduce the I-V measurements in the whole bias range investigated (∼1.0-1.5 V) and to understand the behavior of εh and Γ (contact coupling strength) extracted from experiment. We find that Fermi level pinning induced by the strong dipole of the metal-S bond causes a significant shift of the HOMO energy of an adsorbed molecule, resulting in εh exhibiting a weak dependence with the work function Φ. Both of these parameters play a key role in determining the tunneling attenuation factor (β) and junction resistance (R). Correlation among Φ, ΔΦ, R, transition voltage (Vt), and εh and accurate simulation provide a remarkably complete picture of tunneling transport in these prototypical molecular junctions.

Quantitative Interpretations of Break Junction Conductance Histograms in Molecular Electron Transport

We develop theoretical and computational tools for extracting quantitative molecular information from experimental conductance histograms for electron transport through single-molecule break junctions. These experimental setups always measure a combination of molecular conductance and direct electrode-electrode tunneling; our derivations explicitly incorporate the effects of such background tunneling. Validation of our models to simulated data shows that background tunneling is crucial for quantitative analyses (even in cases where it appears to be qualitatively negligible), and comparison to experimental data is favorable. Finally, we generalize these ideas to the case of molecules with a destructive interference feature and discuss potential signatures for interference in a conductance histogram.

Electronic transport in benzodifuran single-molecule transistors

Benzodifuran (BDF) single-molecule transistors have been fabricated in electromigration break junctions for electronic measurements. The inelastic electron tunneling spectrum validates that the BDF molecule is the pathway of charge transport. The gating effect is analyzed in the framework of a single-level tunneling model combined with transition voltage spectroscopy (TVS). The analysis reveals that the highest occupied molecular orbital (HOMO) of the thiol-terminated BDF molecule dominates the charge transport through Au-BDF-Au junctions. Moreover, the energy shift of the HOMO caused by the gate voltage is the main reason for conductance modulation. In contrast, the electronic coupling between the BDF molecule and the gold electrodes, which significantly affects the low-bias junction conductance, is only influenced slightly by the applied gate voltage. These findings will help in the design of future molecular electronic devices.

An important impact of the molecule–electrode coupling asymmetry on the efficiency of bias-driven redox processes in molecular junctions

An almost full reduction driven by applied bias can be achieved in cases of molecules asymmetrically coupled to two-electrodes. For symmetric coupling, reduction cannot exceed 50%.

Break-junctions for investigating transport at the molecular scale

Break-junctions (BJs) enable a pair of atomic-sized electrodes to be created and the relative position between them to be controlled with sub-nanometer accuracy by mechanical means-a level of microscopic control that is not yet achievable by top-down fabrication. Locally, a BJ consists of a single-atom contact, an arrangement that is ideal not only to study various types of quantum point contacts, but also to investigate transport through an individual molecule that can bridge such a junction. In this topical review, we will provide a broad overview on the field of single-molecule electronics, in which BJs serve as the main tool of investigation. To correlate the molecular structure and transport properties to gain a fundamental understanding of the underlying transport mechanisms at the molecular scale, basic experiments that systematically cover all aspects of transport by rational chemical design and tailored experiments are needed. The variety of fascinating transport mechanisms and intrinsic molecular functionalities discovered in the past range from nonlinear transport over conductance switching to quantum interference effects observable even at room temperature. Beside discussing these results, we also look at novel directions and the most recent advances in molecular electronics investigating simultaneously electronic transport and also the mechanical and thermal properties of single-molecule junctions as well as the interaction between molecules and light. Finally, we will describe the requirements for a stepwise transition from fundamental BJ experiments towards technology-relevant architectures for future nanoelectronics applications based on ultimately-scaled molecular building blocks.

Quantifying the relative molecular orbital alignment for molecular junctions with similar chemical linkage to electrodes

Estimating the relative alignment between the frontier molecular orbitals (MOs) that dominates the charge transport through single-molecule junctions represents a challenge for theory. This requires approaches beyond the widely employed framework provided by the density functional theory, wherein the Kohn-Sham 'orbitals' are treated as if they were real MOs, which is not the case. In this paper, we report results obtained by means of quantum chemical calculations, including the equation-of-motion coupled-cluster singles and doubles, which is the state-of-the-art of quantum chemistry for medium-size molecules like those considered here. These theoretical results are validated against data on the MO energy offset relative to the electrodes' Fermi energy extracted from experiments for junctions based on 4,4'-bipyridine and 1,4-dicyanobenzene.

A quantum chemical study from a molecular transport perspective: ionization and electron attachment energies for species often used to fabricate single-molecule junctions

The accurate determination of the lowest electron attachment (EA) and ionization (IP) energies for molecules embedded in molecular junctions is important for correctly estimating, for example, the magnitude of the currents (I) or the biases (V) where an I-V curve exhibits significant non-Ohmic behavior. Benchmark calculations for the lowest electron attachment and ionization energies of several typical molecules utilized to fabricate single-molecule junctions characterized by n-type conduction (4,4'-bipyridine, 1,4-dicyanobenzene and 4,4'-dicyano-1,1'-biphenyl) and p-type conduction (benzenedithiol, biphenyldithiol, hexanemonothiol and hexanedithiol) based on the EOM-CCSD (equation-of-motion coupled-cluster singles and doubles) state-of-the-art method of quantum chemistry are presented. They indicate significant differences from the results obtained within current approaches to molecular transport. The present study emphasizes that, in addition to a reliable quantum chemical method, basis sets much better than the ubiquitous double-zeta set employed for transport calculations are needed. The latter is a particularly critical issue for correctly determining EAs, which is impossible without including sufficient diffuse basis functions. The spatial distribution of the dominant molecular orbitals (MOs) is another important issue, on which the present study draws attention, because it sensitively affects the MO energy shifts Φ due to image charges formed in electrodes. The present results cannot substantiate the common assumption of a point-like MO midway between electrodes, which substantially affects the actual Φ-values.

Quantitative interpretation of the transition voltages in gold-poly(phenylene) thiol-gold molecular junctions

The transition voltage of three different asymmetric Au∕poly(phenylene) thiol∕Au molecular junctions in which the central molecule is either benzene thiol, biphenyl thiol, or terphenyl thiol is investigated by first-principles quantum transport simulations. For all the junctions, the calculated transition voltage at positive polarity is in quantitative agreement with the experimental values and shows weak dependence on alterations of the Au-phenyl contact. When compared to the strong coupling at the Au-S contact, which dominates the alignment of various molecular orbitals with respect to the electrode Fermi level, the coupling at the Au-phenyl contact produces only a weak perturbation. Therefore, variations of the Au-phenyl contact can only have a minor influence on the transition voltage. These findings not only provide an explanation to the uniformity in the transition voltages found for π-conjugated molecules measured with different experimental methods, but also demonstrate the advantage of transition voltage spectroscopy as a tool for determining the positions of molecular levels in molecular devices.

Transition voltage spectroscopy reveals significant solvent effects on molecular transport and settles an important issue in bipyridine-based junctions

Results of a seminal study (B. Xu and N. J. Tao, Science, 2003, 301, 1221) on the single-molecule junctions based on bipyridine placed in a solvent have been challenged recently (S. Y. Quek et al., Nat. Nano, 2009, 4, 230) by implicitly assuming a negligible solvent impact on the molecular transport and by merely considering low bias conductance data. In this paper we demonstrate that solvent effects on the molecular transport are important, and to show this we focus our attention on the energy offset ε(0) of the dominant molecular orbital (LUMO) relative to the electrode Fermi level. To estimate the energy offset ε(0)(sol) from the full I-V curves presented by Xu and Tao for wet junctions, we resort to the recently proposed transition voltage spectroscopy (TVS). TVS, which plays a key role in the present analysis, emphasizes that data beyond the ohmic conductance regime are needed to reveal the solvent impact. We show that ε(0)(sol) significantly differs from the energy offset ε(0)(0)deduced for dry junctions (J. R. Widawsky et al., Nano Lett., 2012, 12, 354). The present work demonstrates that solvent effects on molecular transport are important and can be understood quantitatively. Results of ab initio calculations with and without solvent are reported that excellently explain the difference δε(0) = ε(0)(sol)-ε(0)(0). δε(0) = ΔΔG + δΦ + δW can be disentangled in contributions with a clear physical content: solvation energies (ΔΔG), image charges (δΦ), and work functions (δW). Accurate analytical formulae for ΔΔG and δΦ are reported, which provide experimentalists with a convenient framework to quantify solvent effects obviating demanding numerical efforts.

Single molecule conductance, thermopower, and transition voltage

We have measured the thermopower as well as other important charge transport quantities, including conductance, current-voltage characteristics, and transition voltage of single molecules. The thermopower has little correlation with the conductance, but it decreases with the transition voltage, which is consistent with a theory based on Landauer's formula. Since the transition voltage reflects the molecular energy level alignment, our finding also shows that the thermopower provides valuable information about the relative alignment between the molecular energy levels and the electrodes' Fermi energy level.

Rethinking transition voltage spectroscopy within a generic Taylor expansion view

Transition voltage spectroscopy (TVS) has become an accepted quantification tool for molecular transport characteristics, due to its simplicity and reproducibility. Alternatively, the Taylor expansion view, TyEx, of transport by tunneling suggests that conductance-voltage curves have approximately a generic parabolic shape, regardless of whether the tunneling model is derived from an average medium view (e.g., WKB) or from a scattering view (e.g., Landauer). Comparing TVS and TyEx approaches reveals that TVS is closely related to a bias-scaling factor, V(0), which is directly derived from the third coefficient of TyEx, namely, the second derivative of the conductance with respect to bias at 0 V. This interpretation of TVS leads to simple expressions that can be compared easily across primarily different tunneling models. Because the basic curve shape is mostly generic, the quality of model fitting is not informative on the actual tunneling model. However internal correlation between the conductance near 0 V and V(0) (TVS) provides genuine indication on fundamental tunneling features. Furthermore, we show that the prevailing concept that V(0) is proportional to the barrier height holds only in the case of resonant tunneling, while for off-resonant or deep tunneling, V(0) is proportional to the ratio of barrier height to barrier width. Finally, considering TVS as a measure of conductance nonlinearity, rather than as an indicator for energy level spectroscopy, explains the very low TVS values observed with a semiconducting (instead of metal) electrode, where transport is highly nonlinear due to the relatively small, bias-dependent density of states of the semiconducting electrode.

Single molecule bridging between metal electrodes

Single molecular junctions, in which a single molecule bridges between metal electrodes, have attracted wide attention as novel properties can appear due to their peculiar geometrical and electronic characters. The single molecular junction has also attracted attention due to its potential application in ultrasmall single molecular electronic devices, where single molecules are utilized as active electronic components. Thus, fabrication of single molecular junctions as well as understanding and controlling their properties (e.g. conductance, optical and magnetic properties) have become long-standing goals of scientists and engineers. This review article focuses on the experimental aspects of single molecular junctions, with primary focus on the electron transport mechanism.