Stochastic modulation in molecular electronic transport junctions: molecular dynamics coupled with charge transport calculations

Toward Density-Functional Theory-Based Structure-Conductance Relationships in Single Molecule Junctions

A method is presented that allows for the calculation using density functional theory (DFT) of the tunneling conductance of single molecule junctions for thousands of junction structures. With a single scaling parameter, conductance is evaluated from clusters consisting of the molecule bonded to one Au atom at each end. Junction geometries are obtained without any constraints from ab initio molecular dynamics simulations at room temperature. This method accurately reproduces standard DFT-based conductance values for several molecular and electrode structures while reducing the computational cost by a factor of ∼400×, allowing for the conductance of tens of thousands of geometries to be computed. When applied to a pair of conjugated molecules, these large data sets quantify the effect on conductance of molecular structure or quantum chemical properties. This methodology enables reliable DFT-based conductance calculations at a negligible computational cost and opens the way to quantitative structure-conductance relationships.

Development of Classical Force Fields for Interfaces between Single Molecules and Au

Interfaces between metals and organic materials play an essential role in molecular surface science, photovoltaics, or molecular electronics. Modeling the evolution of interface geometry over sufficiently long timescales requires an accurate parameterization of the relevant metal-molecule interactions. Here, we describe a method for calculating interface parameters from reference density functional theory calculations of small metal-molecule complexes. We apply this method to develop a parameter set for a series of metal-molecule-metal junctions. We study the dynamics of short oligophenyls with amine, methyl-sulfide, or direct Au-C links, which are bonded to Au(111) via small adatom structures. Nanosecond classical molecular dynamics simulations using the generated parameter set reveal insight into molecular degrees of freedom not accessible from ab initio molecular dynamics simulations.

Photoconductivity enhancement and charge transport properties in ruthenium-containing block copolymer/carbon nanotube hybrids

Functional polymer/carbon nanotube (CNT) hybrid materials can serve as a good model for light harvesting systems based on CNTs. This paper presents the synthesis of block copolymer/CNT hybrids and the characterization of their photocurrent responses by both experimental and computational approaches. A series of functional diblock copolymers was synthesized by reversible addition-fragmentation chain transfer polymerizations for the dispersion and functionalization of CNTs. The block copolymers contain photosensitizing ruthenium complexes and modified pyrene-based anchoring units. The photocurrent responses of the polymer/CNT hybrids were measured by photoconductive atomic force microscopy (PCAFM), from which the experimental data were analyzed by vigorous statistical models. The difference in photocurrent response among different hybrids was correlated to the conformations of the hybrids, which were elucidated by molecular dynamics simulations, and the electronic properties of polymers. The photoresponse of the block copolymer/CNT hybrids can be enhanced by introducing an electron-accepting block between the photosensitizing block and the CNT. We have demonstrated that the application of a rigorous statistical methodology can unravel the charge transport properties of these hybrid materials and provide general guidelines for the design of molecular light harvesting systems.

Estimation of π-π Electronic Couplings from Current Measurements

The π-π interactions between organic molecules are among the most important parameters for optimizing the transport and optical properties of organic transistors, light-emitting diodes, and (bio-) molecular devices. Despite substantial theoretical progress, direct experimental measurement of the π-π electronic coupling energy parameter t has remained an old challenge due to molecular structural variability and the large number of parameters that affect the charge transport. Here, we propose a study of π-π interactions from electrochemical and current measurements on a large array of ferrocene-thiolated gold nanocrystals. We confirm the theoretical prediction that t can be assessed from a statistical analysis of current histograms. The extracted value of t ≈35 meV is in the expected range based on our density functional theory analysis. Furthermore, the t distribution is not necessarily Gaussian and could be used as an ultrasensitive technique to assess intermolecular distance fluctuation at the subangström level. The present work establishes a direct bridge between quantum chemistry, electrochemistry, organic electronics, and mesoscopic physics, all of which were used to discuss results and perspectives in a quantitative manner.

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.

Designing field-controllable graphene-dot-graphene single molecule switches: A quantum-theoretical proof-of-concept under realistic operating conditions

A theoretical proof of the concept that a particularly designed graphene-based moletronics device, constituted by two semi-infinite graphene subunits, acting as source and drain electrodes, and a central benzenoid ring rotator (a "quantum dot"), could act as a field-controllable molecular switch is outlined and analyzed with the density functional theory approach. Besides the ideal (0 K) case, we also consider the operation of such a device under realistic operating (i.e., finite-temperature) conditions. An in-depth insight into the physics behind device controllability by an external field was gained by thorough analyses of the torsional potential of the dot under various conditions (absence or presence of an external gating field with varying strength), computing the torsional correlation time and transition probabilities within the Bloembergen-Purcell-Pound formalism. Both classical and quantum mechanical tunneling contributions to the intramolecular rotation were considered in the model. The main idea that we put forward in the present study is that intramolecular rotors can be controlled by the gating field even in cases when these groups do not possess a permanent dipole moment (as in cases considered previously by us [I. Petreska et al., J. Chem. Phys. 134, 014708-1-014708-12 (2011)] and also by other groups [P. E. Kornilovitch et al., Phys. Rev. B 66, 245413-1-245413-7 (2002)]). Consequently, one can control the molecular switching properties by an external electrostatic field utilizing even nonpolar intramolecular rotors (i.e., in a more general case than those considered so far). Molecular admittance of the currently considered graphene-based molecular switch under various conditions is analyzed employing non-equilibrium Green's function formalism, as well as by analysis of frontier molecular orbitals' behavior.

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.

Using the Chebychev expansion in quantum transport calculations

Irradiation by laser pulses and a fluctuating surrounding liquid environment can, for example, lead to time-dependent effects in the transport through molecular junctions. From the theoretical point of view, time-dependent theories of quantum transport are still challenging. In one of these existing transport theories, the energy-dependent coupling between molecule and leads is decomposed into Lorentzian functions. This trick has successfully been combined with quantum master approaches, hierarchical formalisms, and non-equilibrium Green's functions. The drawback of this approach is, however, its serious limitation to certain forms of the molecule-lead coupling and to higher temperatures. Tian and Chen [J. Chem. Phys. 137, 204114 (2012)] recently employed a Chebychev expansion to circumvent some of these latter problems. Here, we report on a similar approach also based on the Chebychev expansion but leading to a different set of coupled differential equations using the fact that a derivative of a zeroth-order Bessel function can again be given in terms of Bessel functions. Test calculations show the excellent numerical accuracy and stability of the presented formalism. The time span for which this Chebychev expansion scheme is valid without any restrictions on the form of the spectral density or temperature can be determined a priori.

Interplay between quantum interference and conformational fluctuations in single-molecule break junctions

We theoretically explored the combined role of conformational fluctuations and quantum interference in determining the electrical conductance of single-molecule break junctions. In particular we computed the conductance of a family of methylsulfide-functionalized trans-α,ω-diphenyloligoene molecules, with terminal phenyl rings containing meta or para linkages, for which (at least in the absence of fluctuations) destructive interference in the former is expected to decrease their electrical conductance compared with the latter. We compared the predictions of density functional theory (DFT), in which fluctuational effects are absent, with results for the conformationally-averaged conductance obtained from an ensemble of conformations obtained from classical molecular dynamics. We found that junctions formed from these molecules exhibit distinct transport regimes during junction evolution and the signatures of quantum interference in these molecules survive the effect of conformational fluctuations. Furthermore, the agreement between theory and experiment is significantly improved by including conformational averaging.

Charge transport in desolvated DNA

The conductivity of DNA in molecular junctions is often probed experimentally under dry conditions, but it is unclear how much of the solvent remains attached to the DNA and how this impacts its structure, electronic states, and conductivity. Classical MD simulations show that DNA is unstable if the solvent is removed completely, while a micro-hydrated system with few water molecules shows similar charge transport properties as fully solvated DNA does. This surprising effect is analyzed in detail by mapping the density functional theory-based electronic structure to a tight-binding Hamiltonian, allowing for an estimate of conductivity of various DNA sequences with snapshot-averaged Landauer's approach. The characteristics of DNA charge transport turn out to be determined by the nearest hydration shell(s), and the removal of bulk solvent has little effect on the transport.

Epitaxial transfer through end-group coordination modulates the odd-even effect in an alkanethiol monolayer assembly

Short spacer length and high end-group coordination lead to the top network acting as a template for the buried sulfur-gold interface of n-alkanethiols (SH-(CH2)n-OH or SH-(CH2)n-CH3) on gold {111}. Annealing and templating both drive toward a higher sampling of the spatially favorable bridge adsorption sites. The hydrogen-bonded network increases in strength by increasing the number of hydrogens participating per oxygen, from 1.75 to 1.98 for n = 14-30. Higher n leads to better packing (five times for hydroxyl-terminated and seven times for methyl-terminated for n = 14-30) and stability of monolayers, while lower n results in better epitaxial transfer (transfer coefficient ratio = 13.5 for {SH-(CH2)14-OH}/{SH-(CH2)30-CH3}) and actuation. Odd values of n for the hydroxyl-terminated n-alkanethiols lead to lattice spacing of an average of 0.04 ± 0.01 Å higher than even values. There is a structural transition in properties around spacer length n = 24-27. Characterization of monolayer assembly through correlation between adatom and network layers provides recursive design principles for actuation and sensing applications.

Structural Origins of Conductance Fluctuations in Gold-Thiolate Molecular Transport Junctions

We report detailed atomistic simulations combined with high-fidelity conductance calculations to probe the structural origins of conductance fluctuations in thermally evolving Au-benzene-1,4-dithiolate-Au junctions. We compare the behavior of structurally ideal junctions (where the electrodes are modeled as flat surfaces) to structurally realistic, experimentally representative junctions resulting from break-junction simulations. The enhanced mobility of metal atoms in structurally realistic junctions results in significant changes to the magnitude and origin of the conductance fluctuations. Fluctuations are larger by a factor of 2-3 in realistic junctions compared to ideal junctions. Moreover, in junctions with highly deformed electrodes, the conductance fluctuations arise primarily from changes in the Au geometry, in contrast to results for junctions with nondeformed electrodes, where the conductance fluctuations are dominated by changes in the molecule geometry. These results provide important guidance to experimentalists developing strategies to control molecular conductance, and also to theoreticians invoking simplified structural models of junctions to predict their behavior.

Conformation-dependent conductance through a molecular break junction

Ab initio molecular dynamics simulations have been performed of a gold-1,4-benzenedithiol (BDT)-gold nanojunction under mechanical stress. For three different pulling rates between 10 and 40 m s(-1), it is found that the nanowire always ruptures between the second and third Au atom from the thiol sulfur. Larger rupture forces and longer extensions are required at higher pulling rates and vice versa. The electrical conductance was calculated along a pulling trajectory using the DFT-NEGF method to study the effect of thermal and stress-induced structural changes on the electrical transport properties. While the mechanically induced stretching of the junction is seen to lower the time-averaged conductance, thermal conformational changes are capable of altering the conductance by one order of magnitude. No single geometric quantity could be identified as the main contributor to the conductance fluctuations. Small modulations, however, can be explained in terms of C=C double bond vibrations in the BDT molecule. The dependence of the conductance on different geometric variables has further been investigated systematically by performing constrained geometry optimizations along a number of angle and dihedral coordinates. The largest changes in the conductance are observed when the Au-S-C angle and the Au-S-C-C dihedral are simultaneously constrained.

Multiple-time-scale motion in molecularly linked nanoparticle arrays

We explore the transport of electrons between electrodes that encase a two-dimensional array of metallic quantum dots linked by molecular bridges (such as α,ω alkaline dithiols). Because the molecules can move at finite temperatures, the entire transport structure comprising the quantum dots and the molecules is in dynamical motion while the charge is being transported. There are then several physical processes (physical excursions of molecules and quantum dots, electronic migration, ordinary vibrations), all of which influence electronic transport. Each can occur on a different time scale. It is therefore not appropriate to use standard approaches to this sort of electron transfer problem. Instead, we present a treatment in which three different theoretical approaches-kinetic Monte Carlo, classical molecular dynamics, and quantum transport-are all employed. In certain limits, some of the dynamical effects are unimportant. But in general, the transport seems to follow a sort of dynamic bond percolation picture, an approach originally introduced as formal models and later applied to polymer electrolytes. Different rate-determining steps occur in different limits. This approach offers a powerful scheme for dealing with multiple time scale transport problems, as will exist in many situations with several pathways through molecular arrays or even individual molecules that are dynamically disordered.

Configurational Behavior and Conductance of Alkanedithiol Molecular Wires from Accelerated Dynamics Simulations

An accelerated dynamics scheme is employed to sample the configurational space of a system consisting of an alkanedithiol molecule confined to the gap between a metal tip and a perfect metal surface. With this information and by means of nonequilibrium green functions techniques (NEGF), conductance calculations are performed. The present results show that even for this system, which is one of the most simple conceivable because of the perfectness of the surface, a complex behavior appears due to the occurrence of an unexpected tip-molecule-surface arrangement, where the insertion of one of the molecular ends into the tip-surface gap generates configurations with strongly enhanced conductance. Estimates are also made for the time required to generate the molecular junction, indicating that it should depend on the tip-surface distance, thus opening the way to new experiments in this direction.

Time-dependent view of sequential transport through molecules with rapidly fluctuating bridges

Molecules in junctions often fluctuate considerably, especially when subject to the influence of solvent molecules. These fluctuations in site energies and couplings can be sampled, for example, by using molecular dynamics simulations, and can lead to incoherent effects in charge transport. To this end, a popular snapshot-averaged Landauer approach is compared to a time-dependent Green's function scheme. Since sequential transport dominates in systems with rapidly varying bridges, schemes not taking the time order of conformations into account, such as the Landauer approach, are inappropriate.

Signatures of cooperative effects and transport mechanisms in conductance histograms

We present a computational investigation into the line shapes of peaks in conductance histograms, finding that they possess high information content. In particular, the histogram peak associated with conduction through a single molecule elucidates the electron transport mechanism and is generally well-described by beta distributions. A statistical analysis of the peak corresponding to conduction through two molecules reveals the presence of cooperative effects between the molecules and also provides insight into the underlying conduction channels. This work describes tools for extracting additional interpretations from experimental statistical data, helping us better understand electron transport processes.

Large-scale atomistic simulations of environmental effects on the formation and properties of molecular junctions

Using an updated simulation tool, we examine molecular junctions composed of benzene-1,4-dithiolate bonded between gold nanotips, focusing on the importance of environmental factors and interelectrode distance on the formation and structure of bridged molecules. We investigate the complex relationship between monolayer density and tip separation, finding that the formation of multimolecule junctions is favored at low monolayer density, while single-molecule junctions are favored at high density. We demonstrate that tip geometry and monolayer interactions, two factors that are often neglected in simulation, affect the bonding geometry and tilt angle of bridged molecules. We further show that the structures of bridged molecules at 298 and 77 K are similar.

Nucleic Acid Charge Transfer: Black, White and Gray

Theoretical studies of charge transport in deoxyribonucleic acid (DNA) and peptide nucleic acid (PNA) indicate that structure and dynamics modulate the charge transfer rates, and that different members of a structural ensemble support different charge transport mechanisms. Here, we review the influences of nucleobase geometry, electronic structure, solvent environment, and thermal conformational fluctuations on the charge transfer mechanism. We describe an emerging framework for understanding the diversity of charge transport mechanisms seen in nucleic acids.

Inelastic electron tunneling spectroscopy of gold-benzenedithiol-gold junctions: accurate determination of molecular conformation

The gold-benzenedithiol-gold junction is the classic prototype of molecular electronics. However, even with the similar experimental setup, it has been difficult to reproduce the measured results because of the lack of basic information about the molecular confirmation inside the junction. We have performed systematic first principles study on the inelastic electron tunneling spectroscopy of this classic junction. By comparing the calculated spectra with four different experimental results, the most possible conformations of the molecule under different experimental conditions have been successfully determined. The relationship between the contact configuration and the resulted spectra is revealed. It demonstrates again that one should always combine the theoretical and experimental inelastic electron tunneling spectra to determine the molecular conformation in a junction. Our simulations have also suggested that in terms of the reproducibility and stability, the electromigrated nanogap technique is much better than the mechanically controllable break junction technique.

Polarizabilities of adsorbed and assembled molecules: measuring the conductance through buried contacts

We have measured the polarizabilities of four families of molecules adsorbed to Au{111} surfaces, with structures ranging from fully saturated to fully conjugated, including single-molecule switches. Measured polarizabilities increase with increasing length and conjugation in the adsorbed molecules and are consistent with theoretical calculations. For single-molecule switches, the polarizability reflects the difference in substrate-molecule electronic coupling in the ON and OFF conductance states. Calculations suggest that the switch between the two conductance states is correlated with an oxidation state change in a nitro functional group in the switch molecules.

Progress with molecular electronic junctions: meeting experimental challenges in design and fabrication

Molecular electronics seeks to incorporate molecular components as functional elements in electronic devices. There are numerous strategies reported to date for the fabrication, design, and characterization of such devices, but a broadly accepted example showing structure-dependent conductance behavior has not yet emerged. This progress report focuses on experimental methods for making both single-molecule and ensemble molecular junctions, and highlights key results from these efforts. Based on some general objectives of the field, particular experiments are presented to show progress in several important areas, and also to define those areas that still need attention. Some of the variable behavior of ostensibly similar junctions reported in the literature is attributable to differences in the way the junctions are fabricated. These differences are due, in part, to the multitude of methods for supporting the molecular layer on the substrate, including methods that utilize physical adsorption and covalent bonds, and to the numerous strategies for making top contacts. After discussing recent experimental progress in molecular electronics, an assessment of the current state of the field is presented, along with a proposed road map that can be used to assess progress in the future.

The nature of transport variations in molecular heterojunction electronics

Transport fluctuations and variations in a series of metal-molecule-metal junctions were quantified through measurements of their thermopower. Thiol bound aromatic molecules of various lengths and degrees of freedom were chosen to understand the magnitude and origins of the variations. Junction thermopower was determined by measuring the voltage difference across molecules trapped between two gold contacts held at different temperatures. While any given measurement was remarkably stable, the breadth of distributions from repeated measurements implies variations in the offset of the highest occupied molecular orbital (HOMO) relative to the Fermi Energy of the contacts, similar in magnitude to the nominal offset itself. Statistical analysis of data shows that these variations are born at the junction formation, increase with molecular length, and are dominated by variations in contact geometry and orbital hybridization, as well as intermolecular interactions.

Electron transmission characteristics of Au/1,4-benzenedithiol/Au junctions

Electron transmission through individual 1,4-benzenedithiol molecules bridging between two gold electrodes (Au/BDT/Au junctions) has been studied by measuring the current-voltage (I-V) characteristics. Measurements were made at room temperature on three junction states of conductance 0.005G(0), 0.01G(0), and 0.1G(0), respectively, where G(0) is the quantum unit of conductance. All I-V curves are linear around zero bias and nonlinearly increase upward for biases above approximately 0.2 V. Absence of plateaus in the observed I-V characteristics up to +/- 1 V indicates that the electron transmission spectrum of Au/BDT/Au has no peaks within +/- 0.5 eV from the Fermi level.