Molecular transport calculations with Wannier functions

Mechanistic Insights into Electronic Current Flow through Quinone Devices

Molecular switches based on functionalized graphene nanoribbons (GNRs) are of great interest in the development of nanoelectronics. In experiment, it was found that a significant difference in the conductance of an anthraquinone derivative can be achieved by altering the pH value of the environment. Building on this, in this work we investigate the underlying mechanism behind this effect and propose a general design principle for a pH based GNR-based switch. The electronic structure of the investigated systems is calculated using density functional theory and the transport properties at the quasi-stationary limit are described using nonequilibrium Green's function and the Landauer formalism. This approach enables the examination of the local and the global transport through the system. The electrons are shown to flow along the edges of the GNRs. The central carbonyl groups allow for tunable transport through control of the oxidation state via the pH environment. Finally, we also test different types of GNRs (zigzag vs. armchair) to determine which platform provides the best transport switchability.

Edge Effect in Electronic and Transport Properties of 1D Fluorinated Graphene Materials

A systematic examination of the electronic and transport properties of 1D fluorine-saturated zigzag graphene nanoribbons (ZGNRs) is presented in this article. One publication (Withers et al., Nano Lett., 2011, 11, 3912-3916.) reported a controlled synthesis of fluorinated graphene via an electron beam, where the correlation between the conductivity of the resulting materials and the width of the fluorinated area is revealed. In order to understand the detailed transport mechanism, edge-fluorinated ZGNRs with different widths and fluorination degrees are investigated. Periodic density functional theory (DFT) is employed to determine their thermodynamic stabilities and electronic structures. The associated transport models of the selected structures are subsequently constructed. The combination of a non-equilibrium Green's function (NEGF) and a standard Landauer equation is applied to investigate the global transport properties, such as the total current-bias voltage dependence. By projecting the corresponding lesser Green's function on the atomic orbital basis and their spatial derivatives, the local current density maps of the selected systems are calculated. Our results suggest that specific fluorination patterns and fluorination degrees have significant impacts on conductivity. The conjugated π system is the dominate electron flux migration pathway, and the edge effect of the ZGNRs can be well observed in the local transport properties. In addition, with an asymmetric fluorination pattern, one can trigger spin-dependent transport properties, which shows its great potential for spintronics applications.

Local current analysis on defective zigzag graphene nanoribbons devices for biosensor material applications

In this contribution, we aim at investigating the mechanism of biosensing in graphene-based materials from first principles. Inspired by recent experiments, we construct an atomistic model composed of a pyrene molecule serving as a linker fragment, which is used in experiment to attach certain aptamers, and a defective zigzag graphene nanoribbons (ZGNRs). Density functional theory including dispersive interaction is employed to study the energetics of the linker absorption on the defective ZGNRs. Combining non-equilibrium Green's function and the Landauer formalism, the total current-bias voltage dependence through the device is evaluated. Modifying the distance between the linker molecule and the nanojunction plane reveals a quantitative change in the total current-bias voltage dependence, which correlates to the experimental measurements. In order to illuminate the geometric origin of these variation observed in the considered systems, the local currents through the device are investigated using the method originally introduced by Evers and co-workers. In our new implementation, the numerical efficiency is improved by applying sparse matrix storage and spectral filtering techniques, without compromising the resolution of the local currents. Local current density maps qualitatively demonstrate the local variation of the interference between the linker molecule and the nanojunction plane.

Local decomposition of hybridization functions: Chemical insight into correlated molecular adsorbates

Hybridization functions are an established tool for investigating the coupling between a correlated subsystem (often a single transition metal atom) and its uncorrelated environment (the substrate and any ligands present). The hybridization function can provide valuable insight into why and how strong correlation features such as the Kondo effect can be chemically controlled in certain molecular adsorbates. To deepen this insight, we introduce a local decomposition of the hybridization function, based on a truncated cluster approach, enabling us to study individual effects on this function coming from specific parts of the systems (e.g., the surface, ligands, or parts of larger ligands). It is shown that a truncated-cluster approach can reproduce the Co 3d and Mn 3d hybridization functions from periodic boundary conditions in Co(CO)₄/Cu(001) and MnPc/Ag(001) qualitatively well. By locally decomposing the hybridization functions, it is demonstrated at which energies the transition metal atoms are mainly hybridized with the substrate or with the ligand. For the Kondo-active 3d_x²-y² orbital in Co(CO)₄/Cu(001), the hybridization function at the Fermi energy is substrate-dominated, so we can assign its enhancement compared with ligand-free Co to an indirect effect of ligand-substrate interactions. In MnPc/Ag(001), the same is true for the Kondo-active orbital, but for two other orbitals, there are both direct and indirect effects of the ligand, together resulting in such strong screening that their potential Kondo activity is suppressed. A local decomposition of hybridization functions could also be useful in other areas, such as analyzing the electrode self-energies in molecular junctions.

Smart local orbitals for efficient calculations within density functional theory and beyond

Localized basis sets in the projector augmented wave formalism allow for computationally efficient calculations within density functional theory (DFT). However, achieving high numerical accuracy requires an extensive basis set, which also poses a fundamental problem for the interpretation of the results. We present a way to obtain a reduced basis set of atomic orbitals through the subdiagonalization of each atomic block of the Hamiltonian. The resulting local orbitals (LOs) inherit the information of the local crystal field. In the LO basis, it becomes apparent that the Hamiltonian is nearly block-diagonal, and we demonstrate that it is possible to keep only a subset of relevant LOs that provide an accurate description of the physics around the Fermi level. This reduces to some extent the redundancy of the original basis set, and at the same time, it allows one to perform post-processing of DFT calculations, ranging from the interpretation of electron transport to extracting effective tight-binding Hamiltonians, very efficiently and without sacrificing the accuracy of the results.

Cyanographone and isocyanographone - Two asymmetrically functionalized graphene pseudohalides and their potential use in chemical sensing

Graphene pseudohalides are natural candidates for use in molecular sensing due to their greater chemical activity as compared to both graphene halides and pristine graphene. Though their study is still in its infancy, being hindered until recently by the unavailability of both selective and efficient procedures for their synthesis, they promise to considerably widen the application potential of chemically modified graphenes. Herein, we employ van der Waals density functional theory to study the structural and electronic properties of two selected graphene pseudohalides, namely, cyanographone and isocyanographone and investigate the potential use of the latter as a chemical sensor via electron transport calculations.

Distinctive electronic transport in pyridine-based devices with narrow graphene nanoribbon electrodes

Two kinds of pyridine-based molecular devices with the same narrow ZGNR electrodes show different and distinctive non-equilibrium electron transport properties.

The Mesoscopic Electrochemistry of Molecular Junctions

Within the context of an electron dynamic (time-dependent) perspective and a voltage driving force acting to redistribute electrons between metallic and addressable molecular states, we define here the associated electron admittance and conductance. We specifically present a mesoscopic approach to resolving the electron transfer rate associated with the electrochemistry of a redox active film tethered to metallic leads and immersed in electrolyte. The methodology is centred on aligning the lifetime of the process of electron exchange with associated resistance and capacitance quantities. Notably, however, these are no longer those empirically known as charge transfer resistance and pseudo-capacitance, but are those derived instead from a consideration of the quantum states contained in molecular films and their accessibility through a scattering region existing between them and the metallic probe. The averaged lifetime (τr) associated with the redox site occupancy is specifically dependent on scattering associated with the quantum channels linking them to the underlying metallic continuum and associated with both a quantum resistance (Rq) and an electrochemical (redox) capacitance (Cr). These are related to electron transfer rate through k = 1/τr = (RqCr)(-1). The proposed mesoscopic approach is consistent with Marcus's (electron transfer rate) theory and experimental measurements obtained by capacitance spectroscopy.

Distinctive electron transport on pyridine-linked molecular junctions with narrow monolayer graphene nanoribbon electrodes compared with metal electrodes and graphene electrodes

The electrodes in the molecular devices are essential for creating functional organic electronic devices.

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.

Incorporating single molecules into electrical circuits. The role of the chemical anchoring group

Constructing electronic circuits containing singly wired molecules is at the frontier of electrical device miniaturisation. Understanding the behaviour of different anchoring groups is key to this goal because of their significant role in determining the properties of the junction.

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.

Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, density functional formulation and nature of steady-state forces

The standard formulation of tunneling transport rests on an open-boundary modeling. There, conserving approximations to nonequilibrium Green function or quantum statistical mechanics provide consistent but computational costly approaches; alternatively, the use of density-dependent ballistic-transport calculations (e.g., Lang 1995 Phys. Rev. B 52 5335), here denoted 'DBT', provides computationally efficient (approximate) atomistic characterizations of the electron behavior but has until now lacked a formal justification. This paper presents an exact, variational nonequilibrium thermodynamic theory for fully interacting tunneling and provides a rigorous foundation for frozen-nuclei DBT calculations as a lowest-order approximation to an exact nonequilibrium thermodynamic density functional evaluation. The theory starts from the complete electron nonequilibrium quantum statistical mechanics and I identify the operator for the nonequilibrium Gibbs free energy which, generally, must be treated as an implicit solution of the fully interacting many-body dynamics. I demonstrate a minimal property of a functional for the nonequilibrium thermodynamic grand potential which thus uniquely identifies the solution as the exact nonequilibrium density matrix. I also show that the uniqueness-of-density proof from a closely related Lippmann-Schwinger collision density functional theory (Hyldgaard 2008 Phys. Rev. B 78 165109) makes it possible to express the variational nonequilibrium thermodynamic description as a single-particle formulation based on universal electron-density functionals; the full nonequilibrium single-particle formulation improves the DBT method, for example, by a more refined account of Gibbs free energy effects. I illustrate a formal evaluation of the zero-temperature thermodynamic grand potential value which I find is closely related to the variation in the scattering phase shifts and hence to Friedel density oscillations. This paper also discusses the difference between the here-presented exact thermodynamic forces and the often-used electrostatic forces. Finally the paper documents an inherent adiabatic nature of the thermodynamic forces and observes that these are suited for a nonequilibrium implementation of the Born-Oppenheimer approximation.

Robust conductance of dumbbell molecular junctions with fullerene anchoring groups

The conductance of a molecular wire connected to metallic electrodes is known to be sensitive to the atomic structure of the molecule-metal contact. This contact is to a large extent determined by the anchoring group linking the molecular wire to the metal. It has been found experimentally that a dumbbell construction with C(60) molecules acting as anchors yields more well-defined conductances as compared to the widely used thiol anchoring groups. Here, we use density functional theory to investigate the electronic properties of this dumbbell construction. The conductance is found to be stable against variations in the detailed bonding geometry and in good agreement with the experimental value of G=3×10(-4) G(0). Electron tunneling across the molecular bridge occurs via the lowest unoccupied orbitals of C(60) which are pinned close to the Fermi energy due to partial charge transfer. Our findings support the original motivation to achieve conductance values more stable towards changes in the structure of the molecule-metal contact leading to larger reproducibility in experiments.

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.

Calculation of transmission probability by solving an eigenvalue problem

The electron transmission probability in nanodevices is calculated by solving an eigenvalue problem. The eigenvalues are the transmission probabilities and the number of nonzero eigenvalues is equal to the number of open quantum transmission eigenchannels. The number of open eigenchannels is typically a few dozen at most, thus the computational cost amounts to the calculation of a few outer eigenvalues of a complex Hermitian matrix (the transmission matrix). The method is implemented on a real space grid basis providing an alternative to localized atomic orbital based quantum transport calculations. Numerical examples are presented to illustrate the efficiency of the method.

Conductance of sidewall-functionalized carbon nanotubes: universal dependence on adsorption sites

We use density functional theory to study the effect of molecular adsorbates on the conductance of metallic carbon nanotubes (CNT). The five molecules considered (NO2, NH2, H, COOH, OH) lead to very similar scattering of the electrons. The adsorption of a single molecule suppresses one of the two available transport channels at the Fermi level while the other is left undisturbed. If more molecules are adsorbed on the same sublattice, the remaining open channel may or may not be blocked, depending on the relative position of the adsorbates. If the relative positions satisfy a simple geometric condition, this channel remains fully open independently of the number of adsorbed molecules.

Comparative study of anchoring groups for molecular electronics: structure and conductance of Au-S-Au and Au-NH(2)-Au junctions

The electrical properties of single-molecule junctions, consisting of an organic molecule coupled to metal electrodes, are sensitive to the detailed atomic structure of the molecule-metal contact. This, in turn, is determined by the anchoring group linking the molecule to the metal. With the aim of identifying and comparing the intrinsic properties of two commonly used anchoring groups, namely thiol and amine groups, we have calculated the atomic structure and conductance traces of different Au-S-Au and Au-NH(2)-Au nanojunctions using density functional theory (DFT). Whereas NH(2) shows a strong structural selectivity towards atop-gold configurations, S shows large variability in its bonding geometries. As a result, the conductance of the Au-NH(2)-Au junction is less sensitive to the structure of the gold contacts than the Au-S-Au junction. These findings support recent experiments which show that amine-bonded molecules exhibit more well-defined conductance properties than do thiol-bonded molecules.

A theoretical view of unimolecular rectification

The concept of single molecule rectifiers proposed in a theoretical work by Aviram and Ratner in 1974 was the starting point of the now vibrant field of molecular electronics. In the meantime, a built-in asymmetry in the conductance of molecular junctions has been reported at the experimental level. In this contribution, we present a theoretical comparison of three different types of unimolecular rectifiers: (i) systems where the donor and acceptor parts of the molecules are taken from charge-transfer salt components; (ii) zwitterionic systems and (iii) tour wires with nitro substituents. We conduct an analysis of the rectification mechanism in these three different types of asymmetric molecules on the basis of parameterized quantum chemical models as well as with a full non-equilibrium Green's function-density functional theory (NEGF-DFT) treatment of the current-voltage characteristics of the respective metal-molecule-metal junctions. We put a particular emphasis on the prediction of rectification ratios (RRs), which are crucial for the assessment of the technological usefulness of single molecule junctions as diodes. We also compare our results with values reported in the literature for other types of molecular rectification, where the essential asymmetry is not induced by the structure of the molecule alone but either by a difference in the electronic coupling of the molecule to the two electrodes or by attaching alkyl chains of different lengths to the central molecular moiety.

Anomalous conductance oscillations and half-metallicity in atomic Ag-O chains

Using spin density functional theory, we study the electronic and magnetic properties of atomically thin, suspended chains containing silver and oxygen atoms in an alternating sequence. Chains longer than 4 atoms develop a half-metallic ground state implying fully spin-polarized charge carriers. The conductances of the chains exhibit weak even-odd oscillations around an anomalously low value of 0.1G0 (G0=2e2/h) which coincide with the averaged experimental conductance in the long chain limit. The unusual conductance properties are explained in terms of a resonating-chain model, which takes the reflection probability and phase shift of a single bulk-chain interface as the only input. The model also explains the conductance oscillations for other metallic chains.

Quantum chemistry calculations for molecules coupled to reservoirs: formalism, implementation, and application to benzenedithiol

Modern quantum chemistry calculations are usually implemented for isolated systems-big molecules or atom clusters; total energy and particle number are fixed. However, in many situations, like quantum transport calculations or molecules in a electrochemical environment, the molecule can exchange particles (and energy) with a reservoir. Calculations for such cases require to switch from the canonical to a grand canonical description, where one fixes the chemical potential rather than particle number. To achieve this goal, the authors propose an implementation in standard quantum chemistry packages. An application to the nonlinear charge transport through 1,4-benzenedithiol will be presented. They explain the leading finite bias effect on the transmission as a consequence of a nonequilibrium Stark effect and discuss the relation to earlier work.

Evidence for a single hydrogen molecule connected by an atomic chain

Stable, single-molecule conducting-bridge configurations are typically identified from peak structures in a conductance histogram. In previous work on Pt with H2 at cryogenic temperatures it has been shown that a peak near 1G0 identifies a single-molecule Pt-H2-Pt bridge. The histogram shows an additional structure with lower conductance that has not been identified. Here, we show that it is likely due to a hydrogen decorated Pt chain in contact with the H2 molecular bridge.

Nonequilibrium GW approach to quantum transport in nano-scale contacts

Correlation effects within the GW approximation have been incorporated into the Keldysh nonequilibrium transport formalism. We show that GW describes the Kondo effect and the zero-temperature transport properties of the Anderson model fairly well. Combining the GW scheme with density functional theory and a Wannier function basis set, we illustrate the impact of correlations by computing the I-V characteristics of a hydrogen molecule between two Pt chains. Our results indicate that self-consistency is fundamental for the calculated currents, but that it tends to wash out satellite structures in the spectral function.

Quantum transport in molecules and nanotube devices

Quantum transport is usually cast as an "open" scattering problem, for which available computational methods have not achieved the accuracy of methods for conventional "closed" problems. Here we cast quantum transport as a closed problem and demonstrate fully converged currents for the prototype benzene-dithiolate system. We further report results for carbon-nanotube field-effect transistors, highlighting differences with Si-based devices, e.g., band mixing caused by the gate electric field. We also find that the source-drain current exhibits an intrinsic saturation as a function of the gate voltage.