Current‐voltage characteristics of molecular wires: Eigenvalue staircase, Coulomb blockade, and rectification

A Dynamically Weighted Constrained Complete Active Space Ansatz for Constructing Multiple Potential Energy Surfaces within the Anderson-Holstein Model

We derive and implement the necessary equations for solving a dynamically weighted, state-averaged constrained CASSCF(2,2) wave function describing a molecule on a metal surface, where we constrain the overlap between two active orbitals and the impurity atomic orbitals to be a finite number. We show that a partial constraint is far more robust than a full constraint. We further calculate the system-bath electronic couplings that arise because, near a metal, there is a continuum (rather than discrete) number of electronic states. This approach should be very useful for simulating heterogeneous electron transfer and electrochemical dynamics going forward.

Nonadiabatic Potential Energy Surfaces for a Molecule on a Surface as Found by Constrained Complete Active Space Theory

In order to study electron-transfer mediated chemical processes on a metal surface, one requires not one but two potential energy surfaces (one ground state and one excited state) as in Marcus theory. In this letter, we report that a novel, dynamically weighted, state-averaged constrained CASSCF(2,2) (DW-SA-cCASSCF(2,2)) can produce such surfaces for the Anderson impurity model. Both ground and excited state potentials are smooth, they incorporate states with a charge transfer character, and the accuracy of the ground state surface can be verified for some model problems by renormalization group theory. Future development of gradients and nonadiabatic derivative couplings should allow for the study of nonadiabatic dynamics for molecules near metal surfaces.

Application of Poly-L-Lysine for Tailoring Graphene Oxide Mediated Contact Formation between Lithium Titanium Oxide LTO Surfaces for Batteries

When producing stable electrodes, polymeric binders are highly functional materials that are effective in dispersing lithium-based oxides such as Li₄Ti₅O₁₂ (LTO) and carbon-based materials and establishing the conductivity of the multiphase composites. Nowadays, binders such as polyvinylidene fluoride (PVDF) are used, requiring dedicated recycling strategies due to their low biodegradability and use of toxic solvents to dissolve it. Better structuring of the carbon layers and a low amount of binder could reduce the number of inactive materials in the electrode. In this study, we use computational and experimental methods to explore the use of the poly amino acid poly-L-lysine (PLL) as a novel biodegradable binder that is placed directly between nanostructured LTO and reduced graphene oxide. Density functional theory (DFT) calculations allowed us to determine that the (111) surface is the most stable LTO surface exposed to lysine. We performed Kubo-Greenwood electrical conductivity (KGEC) calculations to determine the electrical conductivity values for the hybrid LTO-lysine-rGO system. We found that the presence of the lysine-based binder at the interface increased the conductivity of the interface by four-fold relative to LTO-rGO in a lysine monolayer configuration, while two-stack lysine molecules resulted in 0.3-fold (in the plane orientation) and 0.26-fold (out of plane orientation) increases. These outcomes suggest that monolayers of lysine would specifically favor the conductivity. Experimentally, the assembly of graphene oxide on poly-L-lysine-TiO₂ with sputter-deposited titania as a smooth and hydrophilic model substrate was investigated using a layer-by-layer (LBL) approach to realize the required composite morphology. Characterization techniques such as X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM), Kelvin probe force microscopy (KPFM), scanning electron microscopy (SEM) were used to characterize the formed layers. Our experimental results show that thin layers of rGO were assembled on the TiO₂ using PLL. Furthermore, the PLL adsorbates decrease the work function difference between the rGO- and the non-rGO-coated surface and increased the specific discharge capacity of the LTO-rGO composite material. Further experimental studies are necessary to determine the influence of the PLL for aspects such as the solid electrolyte interface, dendrite formation, and crack formation.

Enhanced current rectification in graphene nanoribbons: effects of geometries and orientations of nanopores

We discuss the possibility of getting rectification operation in graphene nanoribbon (GNR). For a system to be a rectifier, it must be physically asymmetric and we induce the asymmetry in GNR by introducing nanopores. The rectification properties are discussed for differently structured nanopores. We find that shape and orientation of the nanopores are critical and sensitive to the degree of current rectification. As the choice of Fermi energy is crucial for obtaining significant current rectification, explicit dependence of Fermi energy on the degree of current rectification is also studied for a particular shape of the nanopore. Finally, the role of nanopore size and different spatial distributions of the electrostatic potential profile across the GNR are explored. The stability of the nanopores is also discussed with a possible solution. Given the simplicity of the proposed method and promising results, the present proposition may lead to a new route of getting current rectification in different kinds of materials where nanopores can be formed selectively.

Efficient current rectification in driven acenes

We examine the current–voltage (I–V) characteristics of different polyacenes, such as anthracene, tetracene, pentacene, etc., under the influence of an arbitrarily polarized light.

In the quest for a stable triplet state in small polyaromatic hydrocarbons: an in silico tool for rational design and prediction

Combining the roles of spin frustration and geometry of odd and even numbered rings in polyaromatic hydrocarbons (PAHs), we design small molecules that show exceedingly small singlet-triplet gaps and stable triplet ground states. Furthermore, a computationally efficient protocol with a model spin Hamiltonian is shown to be capable of qualitative agreement with respect to high level multireference calculations and therefore, can be used for fast molecular discovery and screening.

Quo vadis, unimolecular electronics?

This paper reviews the present status of unimolecular electronics (UME). The field started in the 1970s with a hope that some day organic molecules (∼2 nm in size), when used as electronic components, would challenge Si-based inorganic electronics in ultimate-high-density integrated circuits. The technological push to ever smaller inorganic device sizes (Moore's "law") was driven by a profit motive and by vast investments. UME, the underfunded pauper, may have lost that "race to the bottom", but some excellent science is left to be done.

Molecular rectifiers based on five-coordinate iron(iii)-containing surfactants

The state-of-the-art of metallorganic-based molecular rectification is reviewed with an emphasis on asymmetric five-coordinate Fe^III-containing surfactants in electrode|LB film|electrode assemblies.

Electronic structure and charge transport properties of atomic carbon wires

Atomic carbon wires represent the ultimate one-atom-thick one-dimensional structure.

Electrical transport properties of an isolated CdS microrope composed of twisted nanowires

CdS is one of the important II-VI group semiconductors. In this paper, the electrical transport behavior of an individual CdS microrope composed of twisted nanowires is studied. It is found that the current-voltage (I-V) characteristics show two distinct power law regions from 360 down to 60 K. Space-charge-limited current (SCLC) theory is used to explain these temperature- and electric-field-dependent I-V curves. The I-V data can be well fitted by this theory above 100 K, and the corresponding carrier mobility, trap energy, and trap concentration are also obtained. However, the I-V data exhibit some features of the Coulomb blockade effect below 80 K.

Molecular design of electron transport with orbital rule: toward conductance-decay free molecular junctions

In this study, we report our viewpoint of single molecular conductance in terms of frontier orbitals.

An orbital rule for electron transport in molecules

The transfer of electrons in molecules and solids is an essential process both in biological systems and in electronic devices. Devices that take advantage of the unique electronic properties of a single molecule have attracted much attention, and applications of these devices include molecular wire, molecular memory, and molecular diodes. The so-called Landauer formula with Green's function techniques provides a basis for theoretical calculations of coherent electron transport in metal-molecule-metal junctions. We have developed a chemical way of thinking about electron transport in molecules in terms of frontier orbital theory. The phase and amplitude of the HOMO and LUMO of π-conjugated molecules determine the essential properties of their electron transport. By considering a close relationship between Green's function and the molecular orbital, we derived an orbital rule that would help our chemical understanding of the phenomenon. First, the sign of the product of the orbital coefficients at sites r and s in the HOMO should be different from the sign of the product of the orbital coefficients at sites r and s in the LUMO. Second, sites r and s in which the amplitude of the HOMO and LUMO is large should be connected. The derived rule allows us to predict essential electron transport properties, which significantly depend on the route of connection between a molecule and electrodes. Qualitative analyses of the site-dependent electron transport in naphthalene (as shown in the graphics) demonstrate that connections 1-4, 1-5, 2-3, and 2-6 are symmetry-allowed for electron transmission, while connections 1-8 and 2-7 are symmetry-forbidden. On the basis of orbital interaction analysis, we have extended this rule to metal-molecule-metal junctions of dithiol derivatives in which two gold electrodes have direct contacts with a molecule through two Au-S bonds. Recently we confirmed these theoretical predictions experimentally by using nanofabricated mechanically controllable break junctions to measure the single-molecule conductance of naphthalene dithiol derivatives. The measurement of the symmetry-allowed 1,4-naphthalene dithiol shows a single-molecule conductance that exceeds that of the symmetry-forbidden 2,7-naphthalene dithiol by 2 orders of magnitude. Because the HOMO and LUMO levels and the HOMO-LUMO gaps are similar in the derivatives, the difference in the measured molecular conductances arises from the difference in the phase relationship of the frontier orbitals. Thus, the phase, amplitude, and spatial distribution of the frontier orbitals provide a way to rationally control electron transport properties within and between molecules.

CHEMICALLY SELF-ASSEMBLED NANOELECTRONIC COMPUTING NETWORKS

Recent advances in chemical self-assembly will soon make it possible to synthesize extremely powerful computing machinery from metallic clusters and organic molecules. These self-organized networks can function as Boolean logic circuits, associative memory, image processors, and combinatorial optimizers. Computational or signal processing activity is elicited from simple charge interactions between clusters which are resistively/capacitively linked by conjugated molecular wires or ribbons. The resulting circuits are massively parallel, fault-tolerant, ultrafast, ultradense and dissipate very little power.

Inter-porphyrin coupling: how strong should it be for molecular electronics applications?

Porphyrins and phthalocyanines have now been assembled in a multitude of different architectures, each of which may be identified with a different scenario of the coupling acting between the porphyrins. The synthetic flexibility of these compounds makes possible the design of particular molecules for specific applications in molecular electronics, both in naturally occurring and synthetic devices. Here, we form an overview of these features and focus on the coupling strength, considering what values are appropriate for different molecular electronics applications. In particular, we focus on model compounds that have been prepared as mimics of naturally occurring photosynthetic functional units, oligoporphyrins molecular wires, and stacked systems in which small changes in geometry can affect significant changes in the inter-porphyrin coupling and hence produce dramatic changes in device properties.

QUANTUM TRANSPORT AND CURRENT-TRIGGERED DYNAMICS IN MOLECULAR TUNNEL JUNCTIONS

The modelling of nanoelectronic systems has been the topic of ever increasing activity for nearly two decades. Yet, new questions, challenges and opportunities continue to emerge. In this article we review theoretical and numerical work on two new developments in the theory of molecular-scale electronics. First we review a density functional theory analysis within the Keldysh non-equilibrium Green function formalism to predict nonlinear charge transport properties of nanoelectronic devices. Next we review a recently developed quantum mechanical formalism of current-triggered nuclear dynamics. Finally we combine these theories to describe from first principles the inelastic current and the consequent molecular dynamics in molecular heterojunctions.

CHARGE TRANSPORT THROUGH THIOPHENE BITHIOL MOLECULE AS A MOLECULAR WIRE

The conductance properties of the thiophene bithiol molecular wire, a nano-wire connecting two metallic electrodes, were investigated using quantum-mechanical based methods such as Density Functional Theory, in conjunction with non-equilibrium Green's function formalism. Using the quantum mechanics methods, the Hamiltonians of the three main parts of system, i.e. the right lead, the device, the left lead and conductance properties of this molecular wire such as I-V curve, were calculated.

Molecular Scale Electronics

This paper reports on some of the recent advances in the development and testing of molecular-scale electronic devices, devices that may ultimately be the basis of a molecular-based computer. These advances include: the synthesis of molecules which will perform specific electronic functions, self-assembled monolayer formation of rigid-rod conjugated oligomers, novel methodologies for the design and testing of molecular electronic devices, and the observance of negative differential resistance (NDR) through a molecule.

Molecular Scale Electronics. Critical Nanolithography Issues of Synthesis and Addressing

As we rapidly approach the point at which solid-state electronic devices cease to be made any smaller, molecular scale electronics offers, perhaps, the best chance for a continued miniaturization of computational devices. We must, however, completely re-think our approach to lithography. Presented in this paper are our solution-phase and solid-support based syntheses of molecular wires of precise length and dimensions, and our methods of addressing these wires via molecular “alligator clips” to gold and platinum electrodes of macroscale dimensions.

Towards supramolecular engineering of functional nanomaterials: pre-programming multi-component 2D self-assembly at solid-liquid interfaces

Materials with a pre-programmed order at the supramolecular level can be engineered with a sub-nanometer precision making use of reversible non- covalent interactions. The intrinsic ability of supramolecular materials to recognize and exchange their constituents makes them constitutionally dynamic materials. The tailoring of the materials properties relies on the full control over the self-assembly behavior of molecular modules exposing recognition sites and incorporating functional units. In this review we focus on three classes of weak-interactions to form complex 2D architectures starting from properly designed molecular modules: van der Waals, metallo-ligand and hydrogen bonding. Scanning tunneling microscopy studies will provide evidence with a sub-nanometer resolution, on the formation of responsive multicomponent architectures with controlled geometries and properties. Such endeavor enriches the scientist capability of generating more and more complex smart materials featuring controlled functions and unprecedented properties.

Impact of dimerization and stretching on the transport properties of molybdenum atomic wires

We study the electrical and transport properties of monatomic Mo wires with different structural characteristics. We consider first periodic wires with interatomic distances ranging between the dimerized wire to that formed by equidistant atoms. We find that the dimerized case has a gap in the electronic structure which makes it insulating, as opposed to the equidistant or near-equidistant cases which are metallic. We also simulate two conducting one-dimensional Mo electrodes separated by a scattering region which contains a number of dimers between 1 and 6. The I-V characteristics strongly depend on the number of dimers and vary from ohmic to tunneling, with the presence of different gaps. We also find that stretched chains are ferromagnetic.

Exchange and correlation in molecular wire conductance: nonlocality is the key

We study real-time electron dynamics in a molecular junction with a variety of approximations to the electronic structure, toward the ultimate aim of determining what ingredients are crucial for the accurate prediction of charge transport. We begin with real-time, all electron simulations using some common density functionals that differ in how they treat long-range Hartree-Fock exchange. We find that the inclusion or exclusion of nonlocal exchange is the dominant factor determining the transport behavior, with all semilocal contributions having a smaller effect. In order to study nonlocal correlation, we first map our junction onto a simple Pariser-Parr-Pople (PPP) model Hamiltonian. The PPP dynamics are shown to faithfully reproduce the all electron results, and we demonstrate that nonlocal correlation can be readily included in the model space using the generator coordinate method (GCM). Our PPP-GCM simulations suggest that nonlocal correlation has a significant impact on the I-V character that is not captured even qualitatively by any of the common semilocal approximations to exchange and correlation. The implications of our results for transport calculations are discussed.

Negative differential resistance in nanoscale transport in the Coulomb blockade regime

Motivated by recent experiments, we have studied the transport behavior of coupled quantum dot systems in the Coulomb blockade regime using the master (rate) equation approach. We explore how electron-electron interactions in a donor-acceptor system, resembling weakly coupled quantum dots with varying charging energy, can modify the system's response to an external bias, taking it from normal Coulomb blockade behavior to negative differential resistance (NDR) in the current-voltage characteristics.

Cotunneling model for current-induced events in molecular wires

Many phenomena in molecular transport junctions involve transitions between electronic states of the molecular wire, and, therefore, cannot be described adequately using the Landauer picture. We present a model for cotunneling processes in molecular wires. These are coherent second-order processes that can be observed at low temperatures. As an example, we consider the STM-induced dissociation of acetylene. The large voltage threshold for dissociation observed experimentally is naturally accounted for within the cotunneling model.

Inelastic electron tunnelling in saturated molecules with different functional groups: correlations and symmetry considerations from a computational study

The inelastic electron tunnelling (IET) spectra of a series of molecules with the commonest functional groups are evaluated computationally. It is found that ether, secondary amine and thioether groups do not leave any characteristic signatures on the IET spectrum (in comparison with simple alkanes) and they cannot be used as 'tracers' for the tunnelling path of the electron. In contrast, carbonyl and ester groups modify the appearance of the IET spectrum considerably. The series of computations was also used to validate, for the case of saturated molecules, the propensity rules for IET spectroscopy proposed in the literature. It is found that totally symmetric vibrations give the largest contribution to the spectrum and that there is no correlation between IET and infrared or Raman absorption intensities.

Metal-insulator transition in an aperiodic ladder network: an exact result

We prove that a tight-binding ladder network composed of atomic sites with on-site potentials distributed according to the quasiperiodic Aubry model can exhibit a metal-insulator transition at multiple values of the Fermi energy. For specific values of the first and second neighbor electron hopping, the result is obtained exactly. With a more general model, we numerically calculate the two-terminal conductance. The numerical results corroborate the analytical findings.

STRANGE EFFECT OF DISORDER ON ELECTRON TRANSPORT THROUGH A THIN FILM

A novel feature of electron transport is explored through a thin film of varying impurity density with the distance from its surface. The film, attached to two metallic electrodes, is described by simple tight-binding model and its coupling to the electrodes is treated through Newns–Anderson chemisorption theory. It is observed that in the strong disorder regime the amplitude of the current passing through the film increases with the increase of the disorder strength, while it decreases in the weak disorder regime. This anomalous behavior is completely opposite to that of conventional disordered systems. Our results also predict that the electron transport is significantly influenced by the finite size of the thin film.

ELECTRON TRANSPORT THROUGH MULTILEVEL QUANTUM DOT

Quantum transport properties through some multilevel quantum dots sandwiched between two metallic contacts are investigated by the use of Green's function technique. Here, we do parametric calculations, based on the tight-binding model, to study the transport properties through such bridge systems. The electron transport properties are significantly influenced by (a) the number of quantized energy levels in the dots, (b) the dot-to-electrodes coupling strength, (c) the location of the equilibrium Fermi energy E F , and (d) the surface disorder. In the limit of weak-coupling, the conductance (g) shows sharp resonance peaks associated with the quantized energy levels in the dots, while, they get substantial broadening in the strong-coupling limit. The behavior of the electron transfer through these systems becomes much more clearly visible from our study of the current–voltage (I–V) characteristics. In this context, we also describe the noise power of current fluctuations (S) and determine the Fano factor (F) which provides an important information about the electron correlation among the charge carriers. Finally, we explore a novel transport phenomenon by studying the surface disorder effect in which the current amplitude increases with the increase of the surface disorder strength in the strong disorder regime, while, the amplitude decreases in the limit of weak disorder. Such an anomalous behavior is completely opposite to that of bulk disordered system where the current amplitude always decreases with the disorder strength. It is also observed that the current amplitude strongly depends on the system size which reveals the finite quantum size effect.

QUANTUM TRANSPORT THROUGH SINGLE PHENALENYL MOLECULE: EFFECT OF INTERFACE STRUCTURE

The electronic transport characteristics through a single phenalenyl molecule sandwiched between two metallic electrodes are investigated by using Green's function technique. A parametric approach, based on the tight-binding model, is used to study the transport characteristics through such molecular bridge system. The electronic transport properties are significantly influenced by (a) the molecule-to-electrodes interface structure and (b) the molecule-to-electrodes coupling strength.

The Green's Function Density Functional Tight-Binding (gDFTB) Method for Molecular Electronic Conduction

A review is presented of the nonequilibrium Green's function (NEGF) method "gDFTB" for evaluating elastic and inelastic conduction through single molecules employing the density functional tight-binding (DFTB) electronic structure method. This focuses on the possible advantages that DFTB implementations of NEGF have over conventional methods based on density functional theory, including not only the ability to treat large irregular metal-molecule junctions with high nonequilibrium thermal distributions but perhaps also the ability to treat dispersive forces, bond breakage, and open-shell systems and to avoid large band lineup errors. New results are presented indicating that DFTB provides a useful depiction of simple gold-thiol interactions. Symmetry is implemented in DFTB, and the advantages it brings in terms of large savings of computational resources with significant increase in numerical stability are described. The power of DFTB is then harnessed to allow the use of gDFTB as a real-time tool to discover the nature of the forces that control inelastic charge transport through molecules and the role of molecular symmetry in determining both elastic and inelastic transport. Future directions for the development of the method are discussed.

A theoretical study of molecular conduction. III. A nonequilibrium-Green’s-function-based Hartree-Fock approach

Many recent experimental and theoretical studies have paid attention to the conductivity of single molecule transport junctions, both because it is fundamentally important and because of its significance in the development of molecular-based electronics. In this paper, we discuss a nonequilibrium Green's function (NEGF)-based Hartree-Fock (HF) approach; the NEGF method can appropriately accommodate charge distributions in molecules connected to electrodes. In addition, we show that a NEGF-based density matrix can reduce to an ordinary HF density matrix for an isolated molecule if the molecule does not interact with electrodes. This feature of the NEGF-based density matrix also means that NEGF-based Mulliken charges can be reduced to ordinary Mulliken charges in those cases. Therefore, the NEGF-based HF approach can directly compare molecules that are connected to electrodes with isolated ones, and is useful in investigating complicated features of molecular conduction. We also calculated the transmission probability and conduction for benzenedithiol under finite electrode biases. The coupling between the electrodes and molecule causes electron transfer from the molecule to the electrodes, and the applied bias modifies this electron transfer. In addition, we found that the molecule responds capacitively to the applied bias, by shifting the molecular orbital energies.