CP-AFM Molecular Tunnel Junctions with Alkyl Backbones Anchored Using Alkynyl and Thiol Groups: Microscopically Different Despite Phenomenological Similarity.

In this paper, we report results on the electronic structure and transport properties of molecular junctions fabricated via conducting probe atomic force microscopy (CP-AFM) using self-assembled monolayers (SAMs) of n-alkyl chains anchored with acetylene groups (CnA; n = 8, 9, 10, and 12) on Ag, Au, and Pt electrodes. We found that the current-voltage (I-V) characteristics of CnA CP-AFM junctions can be very accurately reproduced by the same off-resonant single-level model (orSLM) successfully utilized previously for many other junctions. We demonstrate that important insight into the energy-level alignment can be gained from experimental data of transport (processed via the orSLM) and ultraviolet photoelectron spectroscopy combined with ab initio quantum chemical information based on the many-body outer valence Green's function method. Measured conductance GAg < GAu < GPt is found to follow the same ordering as the metal work function ΦAu < ΦAu < ΦPt, a fact that points toward a transport mediated by an occupied molecular orbital (MO). Still, careful data analysis surprisingly revealed that transport is not dominated by the ubiquitous HOMO but rather by the HOMO-1. This is an important difference from other molecular tunnel junctions with p-type HOMO-mediated conduction investigated in the past, including the alkyl thiols (CnT) to which we refer in view of some similarities. Furthermore, unlike in CnT and other junctions anchored with thiol groups investigated in the past, the AFM tip causes in CnA an additional MO shift, whose independence of size (n) rules out significant image charge effects. Along with the prevalence of the HOMO-1 over the HOMO, the impact of the "second" (tip) electrode on the energy level alignment is another important finding that makes the CnA and CnT junctions different. What ultimately makes CnA unique at the microscopic level is a salient difference never reported previously, namely, that CnA's alkyne functional group gives rise to two energetically close (HOMO and HOMO-1) orbitals. This distinguishes the present CnA from the CnT, whose HOMO stemming from its thiol group is well separated energetically from the other MOs.

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.

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, 24, 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.

Gaining insight into molecular tunnel junctions with a pocket calculator without I-V data fitting. Five-thirds protocol.

The protocol put forward in the present paper is an attempt to meet the experimentalists' legitimate desire of reliably and easily extracting microscopic parameters from current-voltage measurements on molecular junctions. It applies to junctions wherein charge transport dominated by a single level (molecular orbital, MO) occurs via off-resonant tunneling. The recipe is simple. The measured current-voltage curve I = I(V) should be recast as a curve of V5/3/I versus V. This curve exhibits two maxima: one at positive bias (V = Vp+), another at negative bias (V = Vp-). The values Vp+ > 0 and Vp- < 0 at the two peaks of the curve for V5/3/I at positive and negative bias and the corresponding values Ip+ = I(Vp+) > 0 and Ip- = I(Vp-) < 0 of the current is all information needed as input. The arithmetic average of Vp+ and |Vp-| in volt provides the value in electronvolt of the MO energy offset ε0 = EMO - EF relative to the electrode Fermi level (|ε0| = e(Vp+ + |Vp-|)/2). The value of the (Stark) strength of the bias-driven MO shift is obtained as γ = (4/5)(Vp+ - |Vp-|)/(Vp+ + |Vp-|) sign (ε0). Even the low-bias conductance estimate, G = (3/8)(Ip+/Vp+ + Ip-/Vp-), can be a preferable alternative to that deduced from fitting the I-V slope in situations of noisy curves at low bias. To demonstrate the reliability and the generality of this "five-thirds" protocol, I illustrate its wide applicability for molecular tunnel junctions fabricated using metallic and nonmetallic electrodes, molecular species possessing localized σ and delocalized π electrons, and various techniques (mechanically controlled break junctions, STM break junctions, conducting probe AFM junctions, and large area junctions).

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 (GRT) and currents (IRT) measured at room temperature. On the other hand, theoretical approaches based on simplified models provide analytic formulas for the conductance (G0K) and current (I0K) 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., GRT ≈ G0K and IRT ≈ I0K) 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 Γa, 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 ≈ 3πkBT) at Γa → 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.

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.

HCnH- Anion Chains with n ≤ 8 Are Nonlinear and Their Permanent Dipole Makes Them Potential Candidates for Astronomical Observation.

To be detectable in space via radio astronomy, molecules should have a permanent dipole moment. This is the plausible reason why HCnH chains are underproportionally represented in the interstellar medium in comparison with the isoelectronically equivalent HCnN chain family, which is the most numerous homologous series astronomically observed so far. In this communication, we present results of quantum chemical calculations for the HCnH family at several levels of theory: density functional theory (DFT/B3LYP), coupled-cluster expansions (ROCCSD(T)), and G4 composite model. Contradicting previous studies, we report here that linear HCnH- anion chains with sizes of astrochemical interest are unstable (i.e., not all calculated frequencies are real). Nonlinear cis and trans HCnH- anion chains turn out to be stable both against molecular vibrations (i.e., all vibrational frequencies are real) and against electron detachment (i.e., positive electroaffinity). The fact that the cis anion conformers possess permanent dipole is the main encouraging message that this study is aiming at conveying to the astrochemical community, as this makes them observable by means of radio astronomy.

Two Theorems and Important Insight on How the Preferred Mechanism of Free Radical Scavenging Cannot Be Settled. Comment on Pandithavidana, D.R.; Jayawardana, S.B. Comparative Study of Antioxidant Potential of Selected Dietary Vitamins; Computational Insights. Molecules 2019, 24, 1646.

Totally ignoring that the five enthalpies of reaction­bond dissociation enthalpy (BDE), adiabatic ionization potential (IP), proton dissociation enthalpy (PDE), proton affinity (PA), and electron transfer enthalpy (ETE)­characterizing the three free radical scavenging mechanisms­direct hydrogen atom transfer (HAT), sequential electron transfer proton transfer (SET-PT), and stepwise proton loss electron transfer (SPLET)­are not independent of each other, a recent publication on the antioxidant activity of dietary vitamins compared various vitamins and "found" different quantities, which should be strictly equal by virtue of energy conservation. Aiming to clarify this point, as well as to avoid such mistakes in future studies and to unravel errors in the previous literature, in the present paper we formulate two theorems that any sound results on antioxidation should obey. The first theorem states that the sums of the enthalpies characterizing the individual steps of SET-PT and SPLET are equal: IP+PDE = PA+ETE (=H2). This is a mathematical identity emerging from the fact that both the reactants and the final products of SET-PT and SPLET are chemically identical. The second theorem, which is also a mathematical identity, states that H2 − BDE = IPH > 0, where IPH is the ionization potential of the H-atom in the medium (e.g., gas or solvent) considered. Due to their general character, these theorems may/should serve as necessary sanity tests for any results on antioxidant activity, whatever the method employed in their derivation. From a more general perspective, they should represent a serious word of caution regarding attempts to assign the preferred free radical scavenging pathway based merely on thermochemical descriptors.

Why Ortho- and Para-Hydroxy Metabolites Can Scavenge Free Radicals That the Parent Atorvastatin Cannot? Important Pharmacologic Insight from Quantum Chemistry.

The pharmaceutical success of atorvastatin (ATV), a widely employed drug against the "bad" cholesterol (LDL) and cardiovascular diseases, traces back to its ability to scavenge free radicals. Unfortunately, information on its antioxidant properties is missing or unreliable. Here, we report detailed quantum chemical results for ATV and its ortho- and para-hydroxy metabolites (o-ATV, p-ATV) in the methanolic phase. They comprise global reactivity indices, bond order indices, and spin densities as well as all relevant enthalpies of reaction (bond dissociation BDE, ionization IP and electron attachment EA, proton detachment PDE and proton affinity PA, and electron transfer ETE). With these properties in hand, we can provide the first theoretical explanation of the experimental finding that, due to their free radical scavenging activity, ATV hydroxy metabolites rather than the parent ATV, have substantial inhibitory effect on LDL and the like. Surprisingly (because it is contrary to the most cases currently known), we unambiguously found that HAT (direct hydrogen atom transfer) rather than SPLET (sequential proton loss electron transfer) or SET-PT (stepwise electron transfer proton transfer) is the thermodynamically preferred pathway by which o-ATV and p-ATV in methanolic phase can scavenge DPPH• (1,1-diphenyl-2-picrylhydrazyl) radicals. From a quantum chemical perspective, the ATV's species investigated are surprising because of the nontrivial correlations between bond dissociation energies, bond lengths, bond order indices and pertaining stretching frequencies, which do not fit the framework of naive chemical intuition.

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 ΔTelectr between electrodes applied in thermopower measurements, molecules only feel a significantly smaller temperature difference (ΔTmolec < ΔTelectr). 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.

Energy Level Alignment in Molecular Tunnel Junctions by Transport and Spectroscopy: Self-Consistency for the Case of Alkyl Thiols and Dithiols on Ag, Au, and Pt Electrodes.

We report here an extensive study of transport and electronic structure of molecular junctions based on alkyl thiols (CnT; n = 7, 8, 9, 10, 12) and dithiols (CnDT; n = 8, 9, 10) with various lengths contacted with different metal electrodes (Ag, Au, Pt). The dependence of the low-bias resistance (R) on contact work function indicates that transport is HOMO-assisted (p-type transport). Analysis of the current-voltage (I-V) characteristics for CnT and CnDT tunnel junctions with the analytical single-level model (SLM) provides both the HOMO-Fermi energy offset εhtrans and the average molecule-electrode coupling (Γ) as a function of molecular length (n), electrode work function (Φ), and the number of chemical contacts (one or two). The SLM analysis reveals a strong Fermi level (EF) pinning effect in all the junctions, i.e., εhtrans changes very little with n, Φ, and the number of chemical contacts, but Γ depends strongly on these variables. Significantly, independent measurements of the HOMO-Fermi level offset (εhUPS) by ultraviolet photoelectron spectroscopy (UPS) for CnT and CnDT SAMs agree remarkably well with the transport-estimated εhtrans. This result provides strong evidence for hole transport mediated by localized HOMO states at the Au-thiol interface, and not by the delocalized σ states in the C-C backbones, clarifying a long-standing issue in molecular electronics. Our results also substantiate the application of the single-level model for quantitative, unified understanding of transport in benchmark molecular junctions.

Determination of Energy-Level Alignment in Molecular Tunnel Junctions by Transport and Spectroscopy: Self-Consistency for the Case of Oligophenylene Thiols and Dithiols on Ag, Au, and Pt Electrodes.

We report detailed measurements of transport and electronic properties of molecular tunnel junctions based on self-assembled monolayers (SAMs) of oligophenylene monothiols (OPT n, n = 1-3) and dithiols (OPD n, n = 1-3) on Ag, Au, and Pt electrodes. The junctions were fabricated with the conducting probe atomic force microscope (CP-AFM) platform. Fitting of the current-voltage ( I-V) characteristics for OPT n and OPD n junctions to the analytical single-level tunneling model allows extraction of both the HOMO-to-Fermi-level offset (εh) and the average molecule-electrode coupling (Γ) as a function of molecular length ( n) and electrode work function (Φ). Significantly, direct measurements of εhUPS by ultraviolet photoelectron spectroscopy (UPS) for OPT n and OPD n SAMs on Ag, Au, and Pt agree remarkably well with the transport estimates εhtrans, providing strong support-beyond the high quality I-V simulations-for the relevance of the analytical single-level model to simple molecular tunnel junctions. Because the UPS measurements involve SAMs bonded to only one metal contact, the correspondence of εhUPS and εhtrans also indicates that the top contact has a weak effect on the HOMO energy. Corroborating ab initio calculations definitively rule out a dominant contribution of image charge effects to the magnitude of εh. Thus, the effective molecular tunnel barrier εh is determined, and essentially pinned, by the formation of a single metal-S covalent bond per OPT n or OPD n molecule.

Mechanical Deformation Distinguishes Tunneling Pathways in Molecular Junctions.

Developing a clearer understanding of electron tunneling through molecules is a central challenge in molecular electronics. Here we demonstrate the use of mechanical stretching to distinguish orbital pathways that facilitate tunneling in molecular junctions. Our experiments employ junctions based on self-assembled monolayers (SAMs) of homologous alkanethiols (C nT) and oligophenylene thiols (OPT n), which serve as prototypical examples of σ-bonded and π-bonded backbones, respectively. Surprisingly, molecular conductances ( Gmolecule) for stretched C nT SAMs have exactly the same length dependence as unstretched C nT SAMs in which molecular length is tuned by the number of CH2 repeat units, n. In contrast, OPT n SAMs exhibit a 10-fold-greater decrease in Gmolecule with molecular length for stretched versus unstretched cases. Experiment and theory show that these divergent results are explained by the dependence of the molecule-electrode electronic coupling Γ on strain and the spatial extent of the principal orbital facilitating tunneling. In particular, differences in the strain sensitivity of Γ versus the repeat-length ( n) sensitivity can be used to distinguish tunneling via delocalized orbitals versus localized orbitals. Angstrom-level tuning of interelectrode separation thus provides a strategy for examining the relationship between orbital localization or delocalization and electronic coupling in molecular junctions and therefore for distinguishing tunneling pathways.

A sui generis electrode-driven spatial confinement effect responsible for strong twisting enhancement of floppy molecules in closely packed self-assembled monolayers.

At present, it is widely accepted that properties (e.g., molecular conformation) of molecules adsorbed to form self-assembled monolayers (SAMs) on electrodes can be very different from isolated species because of a substantial charge transfer or specific chemical bonding at the interface. Contrary to this view, the theoretical results presented here predict that the strong twisting angle (φ) enhancement of floppy molecules adsorbed to form densely packed SAMs on most common electrodes (Pt, Au, Ag, and Cu) is neither due to charge transfer nor to specific bonding but rather to a sui generis electrode-driven spatial confinement effect that can be quantitatively described within an electrode-free two-dimensional model. We predict a logistic ("Fermi-Dirac") growth pattern of φ as the coverage approaches the value characteristic of a herringbone arrangement, which is twice the value for isolated molecules or low-coverage SAMs.

Exceptionally Small Statistical Variations in the Transport Properties of Metal-Molecule-Metal Junctions Composed of 80 Oligophenylene Dithiol Molecules.

Strong stochastic fluctuations witnessed as very broad resistance (R) histograms with widths comparable to or even larger than the most probable values characterize many measurements in the field of molecular electronics, particularly those measurements based on single molecule junctions at room temperature. Here we show that molecular junctions containing 80 oligophenylene dithiol molecules (OPDn, 1 ≤ n ≤ 4) connected in parallel display small relative statistical deviations-δR/R ≈ 25% after only ∼200 independent measurements-and we analyze the sources of these deviations quantitatively. The junctions are made by conducting probe atomic force microscopy (CP-AFM) in which an Au-coated tip contacts a self-assembled monolayer (SAM) of OPDs on Au. Using contact mechanics and direct measurements of the molecular surface coverage, the tip radius, tip-SAM adhesion force (F), and sample elastic modulus (E), we find that the tip-SAM contact area is approximately 25 nm2, corresponding to about 80 molecules in the junction. Supplementing this information with I-V data and an analytic transport model, we are able to quantitatively describe the sources of deviations δR in R: namely, δN (deviations in the number of molecules in the junction), δε (deviations in energetic position of the dominant molecular orbital), and Î´Γ (deviations in molecule-electrode coupling). Our main results are (1) direct determination of N; (2) demonstration that δN/N for CP-AFM junctions is remarkably small (≤2%) and that the largest contributions to δR are δε and δΓ; (3) demonstration that δR/R after only ∼200 measurements is substantially smaller than most reports based on >1000 measurements for single molecule break junctions. Overall, these results highlight the excellent reproducibility of junctions composed of tens of parallel molecules, which may be important for continued efforts to build robust molecular devices.

A surprising way to control the charge transport in molecular electronics: the subtle impact of the coverage of self-assembled monolayers of floppy molecules adsorbed on metallic electrodes.

Inspired by earlier attempts in organic electronics aiming at controlling charge injection from metals into organic materials by manipulating the Schottky energy barrier using self-assembled monolayers (SAMs), recent experimental and theoretical work in molecular electronics showed that metal-organic interfaces can be controlled via changes in the metal work function that are induced by SAMs. In this paper we indicate a different route to achieve interface-driven control over the charge transfer/transport at the molecular scale. It is based on the fact that, in floppy molecule based SAMs, the molecular conformation can be tuned by varying the coverage of the adsorbate. We demonstrate this effect with the aid of benchmark molecules that are often used to fabricate nanojunctions and consist of two rings that can easily rotate relative to each other. We show that, by varying the coverage of the SAM, the twisting angle φ of the considered molecular species can be modified by a factor of two. Given the fact that the low bias conductance G scales as cos2 φ, this results in a change in G of over one order of magnitude for the considered molecular species. Tuning the twisting angle by controlling the SAM coverage may be significant, e.g., for current efforts to fabricate molecular switches. Conversely, the lack of control over the local SAM coverage may be problematic for the reproducibility and interpretation of the STM (scanning tunneling microscope) measurements on repeatedly forming single molecule break junctions.

Floppy molecules as candidates for achieving optoelectronic molecular devices without skeletal rearrangement or bond breaking.

Molecular species investigated as possible candidates for molecular photoswitches often toggle between two (low and high conductance) conformations implying skeletal rearrangement, bond breaking, and substantial changes of molecular length. All these represent shortcomings that impede the switching speed and straightforward incorporation in nanodevices. In the present paper we propose a mechanism wherein the photoinduced switching is from a nonplanar conformation to a planar conformation, and involves neither skeletal rearrangement nor bond breaking or significant molecular length changes. Specifically, by choosing typical floppy molecules consisting of two benzene or benzene-like rings that can easily rotate relative to each other, we present results of both ab initio and DFT quantum chemical calculations demonstrating that the lowest electronic excitation corresponds to a planar molecular conformation (φ = 0), in contrast to the nonplanar ground state characterized by φ ≠ 0. Because the low bias conductance scales as G ∝ cos2 φ, the planar conformation has a higher conductance than the non-planar conformation, acting therefore as ON and OFF states of the molecular switch, respectively. We analyze recent experimental data on illuminated single-molecule junctions (E.-D. Fung et al., Nano Lett., 2017, 17, 1255) and show that the measured photoinduced conductance enhancement is consistent with the presently proposed mechanism. Furthermore, based on recent results demonstrating the substantial impact of the SAM coverage on the twisting angle (I. Bâldea, Faraday Discuss., 2017, 204, 35) we show that a photoinduced conductance enhancement can be much stronger than the rather modest enhancement obtained in the aforementioned experiment.

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. We deduce an accurate analytical interpolation formula for the low bias conductance G enabling disentangling into a temperature independent contribution and a thermally activated contribution. The latter is found to have a temperature dependence more general than the ubiquitous Arrhenius form, which it recovers as a limiting case, and permits to extract the energy offset of the molecular orbital that dominates the charge transport. Importantly, the interpolation formula is general; it can be utilized for fitting experimental conductance data for any form of transmission (e.g., Lorentzian, Gaussian, generalized exponential or else). Furthermore, from the fitting parameters thus obtained, valuable information on the energy dependence of the transmission function can be gathered, which is hard to obtain from other methods. For illustration, available experimental transport data at variable temperature for molecular junctions are analyzed within the present theoretical framework. From a more general perspective, the results reported here are important because they attempt to give a constructive answer to the question of discriminating between the (single-step) tunneling and (two-step) hopping mechanisms based on the temperature dependence of the conductance. Namely, they suggest performing variable temperature G-measurements on nanojunctions fabricated by contacting a given molecular species to different electrodes and monitoring the metal dependence of the activation energy.

Vibrational Frequencies of Fractionally Charged Molecular Species: Benchmarking DFT Results against ab Initio Calculations.

Recent advances in nano/molecular electronics and electrochemistry made it possible to continuously tune the fractional charge q of single molecules and to use vibrational spectroscopic methods to monitor such changes. Approaches to compute vibrational frequencies ω(q) of fractionally charged species based on the density functional theory (DFT) are faced with an important issue: the basic quantity used in these calculations, the total energy, should exhibit piecewise linearity with respect to the fractional charge, but approximate, commonly utilized exchange correlation functionals do not obey this condition. In this paper, with the aid of a simple and representative example, we benchmark results for ω(q) obtained within the DFT against ab initio methods, namely, coupled cluster singles and doubles and also second- and third-order Møller-Plesset perturbation) expansions. These results indicate that, in spite of missing the aforementioned piecewise linearity, DFT-based values ω(q) can reasonably be trusted.

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.