Relating energy level alignment and amine-linked single molecule junction conductance

Interpretation of molecular electron transport in ab initio many-electron framework incorporating zero-point nuclear motion effects

A computational methodology, founded on chemical concepts, is presented for interpreting the role of nuclear motion in the electron transport through single-molecule junctions (SMJ) using many-electron ab initio quantum chemical calculations. Within this approach the many-electron states of the system, computed at the SOS-ADC(2) level, are followed along the individual normal modes of the encapsulated molecules. The inspection of the changes in the partial charge distribution of the many-electron states allows the quantification of the electron transport and the estimation of transmission probabilities. This analysis improves the understanding of the relationship between internal motions and electron transport. Two SMJ model systems are studied for validation purposes, constructed from a conductor (BDA, benzene-1,4-diamine) and an insulator molecule (DABCO, 1,4-diazabicyclo[2.2.2]octane). The trends of the resulting transmission probabilities are in agreement with the experimental observations, demonstrating the capability of the approach to distinguish between conductor and insulator type systems, thereby offering a straightforward and cost-effective tool for such classifications via quantum chemical calculations.

Thermopower in Underpotential Deposition-Based Molecular Junctions

Underpotential deposition (UPD) is an intriguing means for tailoring the interfacial electronic structure of an adsorbate at a substrate. Here we investigate the impact of UPD on thermoelectricity occurring in molecular tunnel junctions based on alkyl self-assembled monolayers (SAMs). We observed noticeable enhancements in the Seebeck coefficient of alkanoic acid and alkanethiol monolayers, by up to 2- and 4-fold, respectively, upon replacement of a conventional Au electrode with an analogous bimetallic electrode, Cu UPD on Au. Quantum transport calculations indicated that the increased Seebeck coefficients are due to the UPD-induced changes in the shape or position of transmission resonances corresponding to gateway orbitals, which depend on the choice of the anchor group. Our work unveils UPD as a potent means for altering the shape of the tunneling energy barrier at the molecule-electrode contact of alkyl SAM-based junctions and hence enhancing thermoelectric performance.

Constrained DFT for Molecular Junctions

We have explored the use of constrained density functional theory (cDFT) for molecular junctions based on benzenediamine. By elongating the junction, we observe that the energy gap between the ionization potential and the electronic affinity increases with the stretching distance. This is consistent with the trend expected from the electrostatic screening. A more detailed analysis shows how this influences the charge distribution of both the individual metal layers and the molecular atoms. Overall, our work shows that constrained DFT is a powerful tool for studying screening effects in molecular junctions.

Determination of the valence band edge of Fe oxide nanoparticles dispersed in aqueous solution through resonant photoelectron spectroscopy from a liquid microjet

We use X-ray photoemission and a near ambient pressure with a liquid microjet setup to investigate the electronic structure of FeOOH nanoparticles dispersed in aqueous solution. In particular, we show that by using X-ray resonant photoemission in dilute solutions, we can overcome the limits of conventional photoemission such as low nanoparticle-to-solvent signal ratio, and local nanoparticle charging and measure the valence band structure of FeOOH nanoparticles in aqueous solution with chemical specificity. The resonant photoemission signal across the Fe 2p_3/2 absorption edge is measured for 2 wt% aqueous solutions of FeOOH nanoparticles (NPs) and the valence band maximum (VBM) of the hydrated FeOOH nanoparticles is determined. We compare the obtained VBM value in aqueous solution to that of FeOOH NPs in the dry phase. We show that the valence band edge position of NPs in the liquid phase can be accurately predicted from the values obtained in the dry phase provided that a simple potential shift due to solution chemistry is applied. Our results demonstrate the suitability of resonant photoemission in measuring the electronic structure of strongly diluted nanosystems where the conventional non-resonant photoemission technique fails.

Role of the Binding Motifs in the Energy Level Alignment and Conductance of Amine-Gold Linked Molecular Junctions within DFT and DFT + Σ

We investigate, using density functional theory (DFT), the electronic and conducting properties of benzenediamine connected to gold electrodes via different tip structures. We examine a series of binding motifs to the electrodes and calculate the junction spectral properties. We consider corrections to the position of molecular resonances at the junction and discuss different approaches to the calculation of these shifts. We relate the magnitude of these corrections to resonance energies to the atomistic structure of the tip. Benzenediamine DFT-based transmission spectra can be well approximated by a Lorentzian model involving only the highest occupied molecular orbital (HOMO). We show how benzenediamine calculated conductance values in quantitative agreement with previous experiments can be achieved from the combination of DFT-based spectra and corrections to the DFT-based HOMO energy and an accessible Lorentzian model.

Dielectric embedding GW for weakly coupled molecule-metal interfaces

Molecule-metal interfaces have a broad range of applications in nanoscale materials science. Accurate characterization of their electronic structures from first-principles is key in understanding material and device properties. The GW approach within many-body perturbation theory is the state-of-the-art and can in principle yield accurate quasiparticle energy levels and interfacial level alignments that are in quantitative agreement with experiments. However, the interfaces are large heterogeneous systems that are currently challenging for first-principles GW calculations. In this work, we develop a GW-based dielectric embedding approach for molecule-metal interfaces, significantly reducing the computational cost of direct GW without sacrificing the accuracy. To be specific, we perform explicit GW calculations only in the simulation cell of the molecular adsorbate, in which the dielectric effect of the metallic substrate is embedded. This is made possible via a real-space truncation of the substrate polarizability and the use of the interface plasma frequency in the adsorbate GW calculation. Here, we focus on the level alignment at weakly coupled molecule-metal interfaces, i.e., the energy difference between a molecular frontier orbital resonance and the substrate Fermi level. We demonstrate our method and assess a few GW-based approximations using two well-studied systems, benzene adsorbed on the Al (111) and on the graphite (0001) surfaces.

Accelerating GW-Based Energy Level Alignment Calculations for Molecule-Metal Interfaces Using a Substrate Screening Approach

The physics of electronic energy level alignment at interfaces formed between molecules and metals can in general be accurately captured by the ab initio GW approach. However, the computational cost of such GW calculations for typical interfaces is significant, given their large system size and chemical complexity. In the past, approximate self-energy corrections, such as those constructed from image-charge models together with gas-phase molecular level corrections, have been used to compute level alignment with good accuracy. However, these approaches often neglect dynamical effects of the polarizability and require the definition of an image plane. In this work, we propose a new approximation to enable more efficient GW-quality calculations of interfaces, where we greatly simplify the calculation of the noninteracting polarizability, a primary bottleneck for large heterogeneous systems. This is achieved by first computing the noninteracting polarizability of each individual component of the interface, e.g., the molecule and the metal, without the use of large supercells, and then using folding and spatial truncation techniques to efficiently combine these quantities. Overall this approach significantly reduces the computational cost for conventional GW calculations of level alignment without sacrificing the accuracy. Moreover, this approach captures both dynamical and nonlocal polarization effects without the need to invoke a classical image-charge expression or to define an image plane. We demonstrate our approach by considering a model system of benzene at relatively low coverage on the aluminum (111) surface. Although developed for such interfaces, the method can be readily extended to other heterogeneous interfaces.

Surface Adsorption from the Exchange-Hole Dipole Moment Dispersion Model

The accurate calculation of intermolecular interaction energies with density functional theory requires methods that include a treatment of long-range, nonlocal dispersion correlation. In this work, we explore the ability of the exchange-hole dipole moment (XDM) dispersion correction to model molecular surface adsorption. Adsorption energies are calculated for six small aromatic molecules (benzene, furan, pyridine, thiophene, thiophenol, and benzenediamine) and the four DNA nucleobases (adenine, thymine, guanine, and cytosine) on the (111) surfaces of the three coinage metals (copper, silver, and gold). For benzene, where the experimental reference data is most precise, the mean absolute error in the computed absorption energies is 0.04 eV. For the other aromatic molecules, the computed binding energies are found to be within 0.09 eV of the available reference data, on average, which is well below the expected experimental uncertainties for temperature-programmed desorption measurements. Unlike other dispersion-corrected functionals, adequate performance does not require changes to the canonical XDM implementation, and the good performance of XDM is explained in terms of the behavior of the exchange hole. Additionally, the base functional employed (B86bPBE) is also optimal for molecular studies, making B86bPBE-XDM an excellent candidate for studying chemistry on material surfaces. Finally, the noncovalent interaction (NCI) plot technique is shown to detect adsorption effects in real space on the order of tenths of an eV.

Searching the Hearts of Graphene-like Molecules for Simplicity, Sensitivity, and Logic

If quantum interference patterns in the hearts of polycyclic aromatic hydrocarbons could be isolated and manipulated, then a significant step toward realizing the potential of single-molecule electronics would be achieved. Here we demonstrate experimentally and theoretically that a simple, parameter-free, analytic theory of interference patterns evaluated at the mid-point of the HOMO-LUMO gap (referred to as M-functions) correctly predicts conductance ratios of molecules with pyrene, naphthalene, anthracene, anthanthrene, or azulene hearts. M-functions provide new design strategies for identifying molecules with phase-coherent logic functions and enhancing the sensitivity of molecular-scale interferometers.

Towards a full ab initio theory of strong electronic correlations in nanoscale devices

In this paper I give a detailed account of an ab initio methodology for describing strong electronic correlations in nanoscale devices hosting transition metal atoms with open d- or f-shells. The method combines Kohn-Sham density functional theory for treating the weakly interacting electrons on a static mean-field level with non-perturbative many-body methods for the strongly interacting electrons in the open d- and f-shells. An effective description of the strongly interacting electrons in terms of a multi-orbital Anderson impurity model is obtained by projection onto the strongly correlated subspace properly taking into account the non-orthogonality of the atomic basis set. A special focus lies on the ab initio calculation of the effective screened interaction matrix U for the Anderson model. Solution of the effective Anderson model with the one-crossing approximation or other impurity solver techniques yields the dynamic correlations within the strongly correlated subspace giving rise e.g. to the Kondo effect. As an example the method is applied to the case of a Co adatom on the Cu(0 0 1) surface. The calculated low-bias tunnel spectra show Fano-Kondo lineshapes similar to those measured in experiments. The exact shape of the Fano-Kondo feature as well as its width depend quite strongly on the filling of the Co 3d-shell. Although this somewhat hampers accurate quantitative predictions regarding lineshapes and Kondo temperatures, the overall physical situation can be predicted quite reliably.

Can molecular projected density of states (PDOS) be systematically used in electronic conductance analysis?

Using benzenediamine and benzenedithiol molecular junctions as benchmarks, we investigate the widespread analysis of the quantum transport conductance in terms of the projected density of states (PDOS) onto molecular orbitals (MOs). We first consider two different methods for identifying the relevant MOs: (1) diagonalization of the Hamiltonian of the isolated molecule and (2) diagonalization of a submatrix of the junction Hamiltonian constructed by considering only basis elements localized on the molecule. We find that these two methods can lead to substantially different MOs and hence PDOS. Furthermore, within Method 1, the PDOS can differ depending on the isolated molecule chosen to represent the molecular junction (e.g., with or without dangling bonds); within Method 2, the PDOS depends on the chosen basis set. We show that these differences can be critical when the PDOS is used to provide a physical interpretation of the conductance (especially when its value is small, as it happens typically at zero bias). In this work, we propose a new approach in an attempt to reconcile the two traditional methods. Although some improvements were achieved, the main problems remain unsolved. Our results raise more general questions and doubts on a PDOS-based analysis of the conductance.

Integer versus Fractional Charge Transfer at Metal(/Insulator)/Organic Interfaces: Cu(/NaCl)/TCNE

Semilocal and hybrid density functional theory was used to study the charge transfer and the energy-level alignment at a representative interface between an extended metal substrate and an organic adsorbate layer. Upon suppressing electronic coupling between the adsorbate and the substrate by inserting thin, insulating layers of NaCl, the hybrid functional localizes charge. The laterally inhomogeneous charge distribution resulting from this spontaneous breaking of translational symmetry is reflected in observables such as the molecular geometry, the valence and core density of states, and the evolution of the work function with molecular coverage, which we discuss for different growth modes. We found that the amount of charge transfer is determined, to a significant extent, by the ratio of the lateral spacing of the molecules and their distance to the metal. Therefore, charge transfer does not only depend on the electronic structure of the individual components but, just as importantly, on the interface geometry.

Reliable energy level alignment at physisorbed molecule-metal interfaces from density functional theory

A key quantity for molecule-metal interfaces is the energy level alignment of molecular electronic states with the metallic Fermi level. We develop and apply an efficient theoretical method, based on density functional theory (DFT) that can yield quantitatively accurate energy level alignment information for physisorbed metal-molecule interfaces. The method builds on the "DFT+Σ" approach, grounded in many-body perturbation theory, which introduces an approximate electron self-energy that corrects the level alignment obtained from conventional DFT for missing exchange and correlation effects associated with the gas-phase molecule and substrate polarization. Here, we extend the DFT+Σ approach in two important ways: first, we employ optimally tuned range-separated hybrid functionals to compute the gas-phase term, rather than rely on GW or total energy differences as in prior work; second, we use a nonclassical DFT-determined image-charge plane of the metallic surface to compute the substrate polarization term, rather than the classical DFT-derived image plane used previously. We validate this new approach by a detailed comparison with experimental and theoretical reference data for several prototypical molecule-metal interfaces, where excellent agreement with experiment is achieved: benzene on graphite (0001), and 1,4-benzenediamine, Cu-phthalocyanine, and 3,4,9,10-perylene-tetracarboxylic-dianhydride on Au(111). In particular, we show that the method correctly captures level alignment trends across chemical systems and that it retains its accuracy even for molecules for which conventional DFT suffers from severe self-interaction errors.

Length dependence of electron transport through molecular wires – a first principles perspective

The length dependence of coherent electron transport through molecular wires is discussed in the context of a survey of state-of-the-art first principles calculation methods.

Predictive DFT-based approaches to charge and spin transport in single-molecule junctions and two-dimensional materials: successes and challenges

CONSPECTUS: The emerging field of flexible electronics based on organics and two-dimensional (2D) materials relies on a fundamental understanding of charge and spin transport at the molecular and nanoscale. It is desirable to make predictions and shine light on unexplained experimental phenomena independently of experimentally derived parameters. Indeed, density functional theory (DFT), the workhorse of first-principles approaches, has been used extensively to model charge/spin transport at the nanoscale. However, DFT is essentially a ground state theory that simply guarantees correct total energies given the correct charge density, while charge/spin transport is a nonequilibrium phenomenon involving the scattering of quasiparticles. In this Account, we critically assess the validity and applicability of DFT to predict charge/spin transport at the nanoscale. We also describe a DFT-based approach, DFT+Σ, which incorporates corrections to Kohn-Sham energy levels based on many-electron calculations. We focus on single-molecule junctions and then discuss how the important considerations for DFT descriptions of transport can differ in 2D materials. We conclude that when used appropriately, DFT and DFT-based approaches can play an important role in making predictions and gaining insight into transport in these materials. Specifically, we shall focus on the low-bias quasi-equilibrium regime, which is also experimentally most relevant for single-molecule junctions. The next question is how well can the scattering of DFT Kohn-Sham particles approximate the scattering of true quasiparticles in the junction? Quasiparticles are electrons (holes) that are surrounded by a constantly changing cloud of holes (electrons), but Kohn-Sham particles have no physical significance. However, Kohn-Sham particles can often be used as a qualitative approximation to quasiparticles. The errors in standard DFT descriptions of transport arise primarily from errors in the Kohn-Sham energy levels (self-energy errors). These errors are small in the strong-coupling regime where the molecular levels are significantly broadened at the Fermi level but are large in the coherent off-resonant tunneling regime where DFT overestimates conductance by orders of magnitude. The DFT+Σ approach uses a physically motivated, parameter free estimate of the self-energy corrections to correct the energy levels in DFT, giving conductance in quantitative agreement with experiment for a large but nonexhaustive class of single-molecule junctions. In 2D materials, the self-energy error is relatively small, and critical issues stem instead from the large length scales in experiments, which make it necessary to consider band-bending within the 2D material, as well as scattering due to electron-phonon interactions, spin-flip interactions, defects, etc.

Control of single-molecule junction conductance of porphyrins via a transition-metal center

Using scanning tunneling microscope break-junction experiments and a new first-principles approach to conductance calculations, we report and explain low-bias charge transport behavior of four types of metal-porphyrin-gold molecular junctions. A nonequilibrium Green's function approach based on self-energy corrected density functional theory and optimally tuned range-separated hybrid functionals is developed and used to understand experimental trends quantitatively. Importantly, due to the localized d states of the porphyrin molecules, hybrid functionals are essential for explaining measurements; standard semilocal functionals yield qualitatively incorrect results. Comparing directly with experiments, we show that the conductance can change by nearly a factor of 2 when different metal cations are used, counter to trends expected from gas-phase ionization energies which are relatively unchanged with the metal center. Our work explains the sensitivity of the porphyrin conductance with the metal center via a detailed and quantitative portrait of the interface electronic structure and provides a new framework for understanding transport quantitatively in complex junctions involving molecules with localized d states of relevance to light harvesting and energy conversion.

Breaking the theoretical scaling limit for predicting quasiparticle energies: the stochastic GW approach

We develop a formalism to calculate the quasiparticle energy within the GW many-body perturbation correction to the density functional theory. The occupied and virtual orbitals of the Kohn-Sham Hamiltonian are replaced by stochastic orbitals used to evaluate the Green function G, the polarization potential W, and, thereby, the GW self-energy. The stochastic GW (sGW) formalism relies on novel theoretical concepts such as stochastic time-dependent Hartree propagation, stochastic matrix compression, and spatial or temporal stochastic decoupling techniques. Beyond the theoretical interest, the formalism enables linear scaling GW calculations breaking the theoretical scaling limit for GW as well as circumventing the need for energy cutoff approximations. We illustrate the method for silicon nanocrystals of varying sizes with N_{e}>3000 electrons.

Determination of energy level alignment and coupling strength in 4,4'-bipyridine single-molecule junctions

We measure conductance and thermopower of single Au-4,4'-bipyridine-Au junctions in distinct low and high conductance binding geometries accessed by modulating the electrode separation. We use these data to determine the electronic energy level alignment and coupling strength for these junctions, which are known to conduct through the lowest unoccupied molecular orbital (LUMO). Contrary to intuition, we find that, in the high-conductance junction, the LUMO resonance energy is further away from the Au Fermi energy than in the low-conductance junction. However, the LUMO of the high-conducting junction is better coupled to the electrode. These results are in good quantitative agreement with self-energy corrected zero-bias density functional theory calculations. Our calculations show further that measurements of conductance and thermopower in amine-terminated oligophenyl-Au junctions, where conduction occurs through the highest occupied molecular orbitals, cannot be used to extract electronic parameters as their transmission functions do not follow a simple Lorentzian form.

Competing thermodynamic and dynamic factors select molecular assemblies on a gold surface

Controlling the self-assembly of surface-adsorbed molecules into nanostructures requires understanding physical mechanisms that act across multiple length and time scales. By combining scanning tunneling microscopy with hierarchical ab initio and statistical mechanical modeling of 1,4-substituted benzenediamine (BDA) molecules adsorbed on a gold (111) surface, we demonstrate that apparently simple nanostructures are selected by a subtle competition of thermodynamics and dynamics. Of the collection of possible BDA nanostructures mechanically stabilized by hydrogen bonding, the interplay of intermolecular forces, surface modulation, and assembly dynamics select at low temperature a particular subset: low free energy oriented linear chains of monomers and high free energy branched chains.

Theory of Covalent Adsorbate Frontier Orbital Energies on Functionalized Light-Absorbing Semiconductor Surfaces

Functional hybrid interfaces between organic molecules and semiconductors are central to many emerging information and solar energy conversion technologies. Here we demonstrate a general, empirical parameter-free approach for computing and understanding frontier orbital energies - or redox levels - of a broad class of covalently bonded organic-semiconductor surfaces. We develop this framework in the context of specific density functional theory (DFT) and many-body perturbation theory calculations, within the GW approximation, of an exemplar interface, thiophene-functionalized silicon (111). Through detailed calculations taking into account structural and binding energetics of mixed-monolayers consisting of both covalently attached thiophene and hydrogen, chlorine, methyl, and other passivating groups, we quantify the impact of coverage, nonlocal polarization, and interface dipole effects on the alignment of the thiophene frontier orbital energies with the silicon band edges. For thiophene adsorbate frontier orbital energies, we observe significant corrections to standard DFT (∼1 eV), including large nonlocal electrostatic polarization effects (∼1.6 eV). Importantly, both results can be rationalized from knowledge of the electronic structure of the isolated thiophene molecule and silicon substrate systems. Silicon band edge energies are predicted to vary by more than 2.5 eV, while molecular orbital energies stay similar, with the different functional groups studied, suggesting the prospect of tuning energy alignment over a wide range for photoelectrochemistry and other applications.

Theoretical study on the rectifying performance of organoimido derivatives of hexamolybdates

We design a new type of molecular diode, based on the organoimido derivatives of hexamolybdates, by exploring the rectifying performances using density functional theory combined with the non-equilibrium Green's function. Asymmetric current-voltage characteristics were obtained for the models with an unexpected large rectification ratio. The rectifying behavior can be understood by the asymmetrical shift of the transmission peak observed under different polarities. It is interesting to find that the preferred electron-transport direction in our studied system is different from that of the organic D-bridge-A system. The results show that the studied organic-inorganic hybrid systems have an intrinsically robust rectifying ratio, which should be taken into consideration in the design of the molecular diodes.

Quantifying through-space charge transfer dynamics in π-coupled molecular systems

Understanding the role of intermolecular interaction on through-space charge transfer characteristics in π-stacked molecular systems is central to the rational design of electronic materials. However, a quantitative study of charge transfer in such systems is often difficult because of poor control over molecular morphology. Here we use the core-hole clock implementation of resonant photoemission spectroscopy to study the femtosecond charge-transfer dynamics in cyclophanes, which consist of two precisely stacked π-systems held together by aliphatic chains. We study two systems, [2,2]paracyclophane (22PCP) and [4,4]paracyclophane (44PCP), with inter-ring separations of 3.0 and 4.0 Å, respectively. We find that charge transfer across the π-coupled system of 44PCP is 20 times slower than in 22PCP. We attribute this difference to the decreased inter-ring electronic coupling in 44PCP. These measurements illustrate the use of core-hole clock spectroscopy as a general tool for quantifying through-space coupling in π-stacked systems.

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.

Quantitative current-voltage characteristics in molecular junctions from first principles

Using self-energy-corrected density functional theory (DFT) and a coherent scattering-state approach, we explain current-voltage (IV) measurements of four pyridine-Au and amine-Au linked molecular junctions with quantitative accuracy. Parameter-free many-electron self-energy corrections to DFT Kohn-Sham eigenvalues are demonstrated to lead to excellent agreement with experiments at finite bias, improving upon order-of-magnitude errors in currents obtained with standard DFT approaches. We further propose an approximate route for prediction of quantitative IV characteristics for both symmetric and asymmetric molecular junctions based on linear response theory and knowledge of the Stark shifts of junction resonance energies. Our work demonstrates that a quantitative, computationally inexpensive description of coherent transport in molecular junctions is readily achievable, enabling new understanding and control of charge transport properties of molecular-scale interfaces at large bias voltages.

A periodic charge-dipole electrostatic model: parametrization for silver slabs

We present an extension of the charge-dipole model for the description of periodic systems. This periodic charge-dipole electrostatic model (PCDEM) allows one to describe the linear response of periodic structures in terms of charge- and dipole-type gaussian basis functions. The long-range electrostatic interaction is efficiently described by means of the continuous fast multipole method. As a first application, the PCDEM method is applied to describe the polarizability of silver slabs. We find that for a correct description of the polarizability of the slabs both charges and dipoles are required. However a continuum set of parametrizations, i.e., different values of the width of charge- and dipole-type gaussians, leads to an equivalent and accurate description of the slabs polarizability but a completely unphysical description of induced charge-density inside the slab. We introduced the integral squared density measure which allows one to obtain a unique parametrization which accurately describes both the polarizability and the induced density profile inside the slab. Finally the limits of the electrostatic approximations are also pointed out.

Electronic structure of atomically precise graphene nanoribbons

Some of the most intriguing properties of graphene are predicted for specifically designed nanostructures such as nanoribbons. Functionalities far beyond those known from extended graphene systems include electronic band gap variations related to quantum confinement and edge effects, as well as localized spin-polarized edge states for specific edge geometries. The inability to produce graphene nanostructures with the needed precision, however, has so far hampered the verification of the predicted electronic properties. Here, we report on the electronic band gap and dispersion of the occupied electronic bands of atomically precise graphene nanoribbons fabricated via on-surface synthesis. Angle-resolved photoelectron spectroscopy and scanning tunneling spectroscopy data from armchair graphene nanoribbons of width N = 7 supported on Au(111) reveal a band gap of 2.3 eV, an effective mass of 0.21 m(0) at the top of the valence band, and an energy-dependent charge carrier velocity reaching 8.2 × 10(5) m/s in the linear part of the valence band. These results are in quantitative agreement with theoretical predictions that include image charge corrections accounting for screening by the metal substrate and confirm the importance of electron-electron interactions in graphene nanoribbons.

The role of van der Waals interaction in the tilted binding of amine molecules to the Au(111) surface

We present the results of ab initio electronic structure calculations for the adsorption characteristics of three amine molecules on Au(111), which show that the inclusion of van der Waals interactions between the isolated molecule and the surface leads in general to good agreement with experimental data on the binding energies. Each molecule, however, adsorbs with a small tilt angle (between -5 and 9°). For the specific case of 1,4-diaminobenzene (BDA) our calculations reproduce the larger tilt angle (close to 24°) measured by photoemission experiments, when intermolecular (van der Waals) interactions (for about 8% coverage) are included. These results point not only to the important contribution of van der Waals interactions to molecule-surface binding energy, but also that of intermolecular interactions, often considered secondary to that between the molecule and the surface, in determining the adsorption geometry and pattern formation.

Charge transport in molecular electronic junctions: compression of the molecular tunnel barrier in the strong coupling regime

Molecular junctions are essentially modified electrodes familiar to electrochemists where the electrolyte is replaced by a conducting "contact." It is generally hypothesized that changing molecular structure will alter system energy levels leading to a change in the transport barrier. Here, we show the conductance of seven different aromatic molecules covalently bonded to carbon implies a modest range (< 0.5 eV) in the observed transport barrier despite widely different free molecule HOMO energies (> 2 eV range). These results are explained by considering the effect of bonding the molecule to the substrate. Upon bonding, electronic inductive effects modulate the energy levels of the system resulting in compression of the tunneling barrier. Modification of the molecule with donating or withdrawing groups modulate the molecular orbital energies and the contact energy level resulting in a leveling effect that compresses the tunneling barrier into a range much smaller than expected. Whereas the value of the tunneling barrier can be varied by using a different class of molecules (alkanes), using only aromatic structures results in a similar equilibrium value for the tunnel barrier for different structures resulting from partial charge transfer between the molecular layer and the substrate. Thus, the system does not obey the Schottky-Mott limit, and the interaction between the molecular layer and the substrate acts to influence the energy level alignment. These results indicate that the entire system must be considered to determine the impact of a variety of electronic factors that act to determine the tunnel barrier.

Single molecule electronics and devices

The manufacture of integrated circuits with single-molecule building blocks is a goal of molecular electronics. While research in the past has been limited to bulk experiments on self-assembled monolayers, advances in technology have now enabled us to fabricate single-molecule junctions. This has led to significant progress in understanding electron transport in molecular systems at the single-molecule level and the concomitant emergence of new device concepts. Here, we review recent developments in this field. We summarize the methods currently used to form metal-molecule-metal structures and some single-molecule techniques essential for characterizing molecular junctions such as inelastic electron tunnelling spectroscopy. We then highlight several important achievements, including demonstration of single-molecule diodes, transistors, and switches that make use of electrical, photo, and mechanical stimulation to control the electron transport. We also discuss intriguing issues to be addressed further in the future such as heat and thermoelectric transport in an individual molecule.

Effect of the environment on the electrical conductance of the single benzene-1,4-diamine molecule junction

We investigated the effect of the environment on the electrical conductance of a single benzene-1,4-diamine (BDA) molecule bridging Au electrodes, using the scanning tunneling microscope (STM). The conductance of the single BDA molecule junction decreased upon a change in the environment from tetraglyme, to mesitylene, to water, and finally to N(2) gas, while the spread in the conductance value increased. The order of the conductance values of the single BDA molecule junction was explained by the strength of the interaction between the solvent molecules and the Au electrodes. The order of the spread in the conductance values was explained by the diversity in the coverage of the BDA molecule at metal electrodes and atomic and molecular motion of the single-molecule junction.

Towards quantitative accuracy in first-principles transport calculations: The GW method applied to alkane/gold junctions

The calculation of the electronic conductance of nanoscale junctions from first principles is a long-standing problem in the field of charge transport. Here we demonstrate excellent agreement with experiments for the transport properties of the gold/alkanediamine benchmark system when electron-electron interactions are described by the many-body GW approximation. The conductance follows an exponential length dependence: G(n) = G(c) exp(-βn). The main difference from standard density functional theory (DFT) calculations is a significant reduction of the contact conductance, G(c), due to an improved alignment of the molecular energy levels with the metal Fermi energy. The molecular orbitals involved in the tunneling process comprise states delocalized over the carbon backbone and states localized on the amine end groups. We find that dynamic screening effects renormalize the two types of states in qualitatively different ways when the molecule is inserted in the junction. Consequently, the GW transport results cannot be mimicked by DFT calculations employing a simple scissors operator.

Environmental control of single-molecule junction transport

The conductance of individual 1,4-benzenediamine (BDA)-Au molecular junctions is measured in different solvent environments using a scanning tunneling microscope based point-contact technique. Solvents are found to increase the conductance of these molecular junctions by as much as 50%. Using first principles calculations, we explain this increase by showing that a shift in the Au contact work function is induced by solvents binding to undercoordinated Au sites around the junction. Increasing the Au contact work function reduces the separation between the Au Fermi energy and the highest occupied molecular orbital of BDA in the junction, increasing the measured conductance. We demonstrate that the solvent-induced shift in conductance depends on the affinity of the solvent to Au binding sites and also on the induced dipole (relative to BDA) upon adsorption. Via this mechanism, molecular junction level alignment and transport properties can be statistically altered by solvent molecule binding to the contact surface.

Thermopower of amine-gold-linked aromatic molecular junctions from first principles

Using a self-energy corrected scattering-state approach based on density functional theory (DFT), we explain recent measurements of the thermopower or the Seebeck coefficient, S, for oligophenyldiamine-gold single-molecule junctions and show that they are consistent with separate measurements of their electrical conductance, G. Our calculations with self-energy corrections to the DFT electronic states in the junction predict low-bias S and G values in good quantitative agreement with experiments. We find S varies linearly with the number of phenyls N, with a gradient β(S) of 2.1 μV/K, in excellent agreement with experiment. In contrast, DFT calculations without self-energy corrections overestimate both S and β(S) (with a DFT value for β(S) three times too large). While β(S) is found to be a robust quantity independent of junction geometry, the computed values of S show significant sensitivity to the contact atomic structure-more so than the computed values of G. This observation is consistent with the experimentally measured spreads in S and G for amine-Au junctions. Taken together with previous computations of the electrical conductance (as reported in Quek, S. Y.; et al., Nano Lett. 2009, 9, 3949), our calculations of S conclusively demonstrate, for the first time, the consistency of two complementary yet distinct measurements of charge transport through single-molecule junctions and substantiate the need for an accurate treatment of junction electronic level alignment to describe off-resonant tunneling in these junctions.