Electronic structure calculations have become an indispensable tool in many areas of materials science and quantum chemistry. Even though the Kohn-Sham formulation of the density-functional theory (DFT) simplifies the many-body problem significantly, one is still confronted with several numerical challenges. In this article we present the projector augmented-wave (PAW) method as implemented in the GPAW program package (https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representation of the electronic wavefunctions. Compared to more traditional plane wave or localized basis set approaches, real-space grids offer several advantages, most notably good computational scalability and systematic convergence properties. However, as a unique feature GPAW also facilitates a localized atomic-orbital basis set in addition to the grid. The efficient atomic basis set is complementary to the more accurate grid, and the possibility to seamlessly switch between the two representations provides great flexibility. While DFT allows one to study ground state properties, time-dependent density-functional theory (TDDFT) provides access to the excited states. We have implemented the two common formulations of TDDFT, namely the linear-response and the time propagation schemes. Electron transport calculations under finite-bias conditions can be performed with GPAW using non-equilibrium Green functions and the localized basis set. In addition to the basic features of the real-space PAW method, we also describe the implementation of selected exchange-correlation functionals, parallelization schemes, Delta SCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.

https://iopscience.iop.org/article/10.1088/0953-8984/22/25/253202/pdf

Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method

Creating functional electrical circuits using individual or ensemble molecules, often termed as “molecular-scale electronics”, not only meets the increasing technical demands of the miniaturization of traditional Si-based electronic devices, but also provides an ideal window of exploring the intrinsic properties of materials at the molecular level. This Review covers the major advances with the most general applicability and emphasizes new insights into the development of efficient platform methodologies for building reliable molecular electronic devices with desired functionalities through the combination of programmed bottom-up self-assembly and sophisticated top-down device fabrication. First, we summarize a number of different approaches of forming molecular-scale junctions and discuss various experimental techniques for examining these nanoscale circuits in details. We then give a full introduction of characterization techniques and theoretical simulations for molecular electronics. Third, we highlig...

Molecular-Scale Electronics: From Concept to Function

Transport of electrons in a single molecule junction is the simplest problem in the general subject area of molecular electronics. In the past few years, this area has been extended to probe beyond the simple tunnelling associated with large energy gaps between electrode Fermi level and molecular levels, to deal with smaller gaps, with near-resonance tunnelling and, particularly, with effects due to interaction of electronic and vibrational degrees of freedom. This overview is devoted to the theoretical and computational approaches that have been taken to understanding transport in molecular junctions when these vibronic interactions are involved. After a short experimental overview, and discussion of different test beds and measurements, we define a particular microscopic model Hamiltonian. That overall Hamiltonian can be used to discuss all of the phenomena dealt with subsequently. These include transition from coherent to incoherent transport as electron/vibration interaction increases in strength, inelastic electron tunnelling spectroscopy and its interpretation and measurement, affects of interelectronic repulsion treated at the Hubbard level, noise in molecular transport junctions, non-linear conductance phenomena, heating and heat conduction in molecular transport junctions and current-induced chemical reactions. In each of these areas, we use the same simple model Hamiltonian to analyse energetics and dynamics. While this overview does not attempt survey the literature exhaustively, it does provide appropriate references to the current literature (both experimental and theoretical). We also attempt to point out directions in which further research is required to answer cardinal questions concerning the behaviour and understanding of vibrational effects in molecular transport junctions. (Some figures in this article are in colour only in the electronic version)

/pdf/molecular-transport-junctions-vibrational-effects-4dr06nme1x.pdf

Molecular transport junctions: vibrational effects

Ab initio computational methods for electronic transport in nanoscaled systems are an invaluable tool for the design of quantum devices. We have developed a flexible and efficient algorithm for evaluating I-V characteristics of atomic junctions, which integrates the nonequilibrium Green’s function method with density functional theory. This is currently implemented in the package SMEAGOL. The heart of SMEAGOL is our scheme for constructing the surface Green’s functions describing the current-voltage probes. It consists of a direct summation of both open and closed scattering channels together with a regularization procedure of the Hamiltonian and provides great improvements over standard recursive methods. In particular it allows us to tackle material systems with complicated electronic structures, such as magnetic transition metals. Here we present a detailed description of SMEAGOL together with an extensive range of applications relevant for the two burgeoning fields of spin and molecular electronics.

/pdf/spin-and-molecular-electronics-in-atomically-generated-4pemerbpje.pdf

Spin and molecular electronics in atomically generated orbital landscapes

The field of single-molecule electronics harnesses expertise from engineering, physics and chemistry to realize circuit elements at the limit of miniaturization; it is a subfield of nanoelectronics in which the electronic components are single molecules. In this Review, we survey the field from a chemical perspective and discuss the structure–property relationships of the three components that form a single-molecule junction: the anchor, the electrode and the molecular bridge. The spatial orientation and electronic coupling between each component profoundly affect the conductance properties and functions of the single-molecule device. We describe the design principles of the anchor group, the influence of the electronic configuration of the electrode and the effect of manipulating the structure of the molecular backbone and of its substituent groups. We discuss single-molecule conductance switches as well as the phenomenon of quantum interference and then trace their fundamental roots back to chemical principles. Single-molecule electronic junctions comprise three components: anchors, electrodes and the molecular bridge. This Review surveys the relationship between the chemical structures and the electronic properties of each component, and extends the discussion to switching functions and the phenomenon of quantum interference.

Chemical principles of single-molecule electronics

Highly conductive molecular junctions were formed by direct binding of benzene molecules between two Pt electrodes. Measurements of conductance, isotopic shift in inelastic spectroscopy, and shot noise compared with calculations provide indications for a stable molecular junction where the benzene molecule is preserved intact and bonded to the Pt leads via carbon atoms. The junction has a conductance comparable to that for metallic atomic junctions (around 0:1–1G0), where the conductance and the number of transmission channels are controlled by the molecule’s orientation at different interelectrode distances.

/pdf/highly-conductive-molecular-junctions-based-on-direct-3l35ayjlra.pdf

Highly conductive molecular junctions based on direct binding of benzene to platinum electrodes.

A single atom or molecule with an almost transparent single conductance channel leading to a conductance near the conductance quantum 2e 2 =h�� 1G0� can be contacted to leads. Conduction electrons can pass through such junction ballistically for low bias voltages since the mean free path of the electrons is much larger than the size of the contact. However, the contact is not entirely ballistic in the sense that once the excess energy of the conduction electrons becomes equal to or larger than the energy of a local mode of the contact, the electrons can scatter inelastically by exciting a local mode. This results in the case of a perfectly transmitting single channel contact to a small decrease in the conductance, since the forward traveling electrons are backscattered due to the energy loss in the inelastic scattering process. Differential conductance (dI=dV) measurements have identified vibration modes of single molecules in an atomic contact [1]. This technique, also called point contact spectroscopy is analogous to inelastic electron tunneling spectroscopy (IETS) for single molecules [2,3], with the difference that the conductance in the latter case increases due to the opening of an additional conductance channel. In this Letter we present the observation of anomalous spikes, rather than steps, in dI=dV measurements on various single-molecule contacts. We present a model that involves two-level systems, which describes our data very well. It may be used as a new spectroscopic tool for identifying molecular vibration modes in single-molecule junctions.

/pdf/vibrationally-induced-two-level-systems-in-single-molecule-hjm2zbirae.pdf

Vibrationally induced two-level systems in single-molecule junctions.

Stable, single-molecule conducting-bridge configurations are typically identified from peak structures in a conductance histogram. In previous work on Pt with ${\mathrm{H}}_{2}$ at cryogenic temperatures it has been shown that a peak near $1{G}_{0}$ identifies a single-molecule $\mathrm{Pt}\mathrm{\text{\ensuremath{-}}}{\mathrm{H}}_{2}\mathrm{\text{\ensuremath{-}}}\mathrm{Pt}$ 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 ${\mathrm{H}}_{2}$ molecular bridge.

/pdf/evidence-for-a-single-hydrogen-molecule-connected-by-an-30otaourqx.pdf

Evidence for a single hydrogen molecule connected by an atomic chain.

Single-molecule junctions are found to show anomalous spikes in dI/dV spectra. The position in energy of the spikes is related to local vibration mode energies. A model of vibrationally induced two-level systems reproduces the data very well. This mechanism is expected to be quite general for single-molecule junctions. It acts as an intrinsic amplification mechanism for local vibration mode features and may be exploited as a new spectroscopic tool.

http://absimage.aps.org/image/MAR07/MWS_MAR07-2006-003856.pdf

Vibrationally induced two-level systems in single molecule junctions

We have measured the effect of bonding of a CO molecule on the conductance of Au, Cu, Pt and Ni atomic contacts at 4.2 K. When CO gas is admitted to the metal nanocontacts, a conductance feature appears in the conductance histogram near 0.5 of the quantum unit of conductance, for all metals. For Au, the intensity of this fractional conductance feature can be tuned with the bias voltage, and it disappears at high bias voltage (above ∼200 mV). The bonding of CO to Au appears to be weakest, and associated with the formation of monatomic Au wire.

The effect of bonding of a CO molecule on the conductance of atomic metal wires.

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