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, ΔSCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.

The atomic simulation environment (ASE) is a software package written in the Python programming language with the aim of setting up, steering, and analyzing atomistic simulations. In ASE, tasks are fully scripted in Python. The powerful syntax of Python combined with the NumPy array library make it possible to perform very complex simulation tasks. For example, a sequence of calculations may be performed with the use of a simple 'for-loop' construction. Calculations of energy, forces, stresses and other quantities are performed through interfaces to many external electronic structure codes or force fields using a uniform interface. On top of this calculator interface, ASE provides modules for performing many standard simulation tasks such as structure optimization, molecular dynamics, handling of constraints and performing nudged elastic band calculations.

We introduce the Computational 2D Materials Database (C2DB), which organises a variety of structural, thermodynamic, elastic, electronic, magnetic, and optical properties of around 1500 two-dimensional materials distributed over more than 30 different crystal structures. Material properties are systematically calculated by density functional theory and many-body perturbation theory (G 0 W 0 and the Bethe-Salpeter Equation for ∼250 materials) following a semi-automated workflow for maximal consistency and transparency. The C2DB is fully open and can be browsed online at c2db.fysik.dtu.dk or downloaded in its entirety. In this paper, we describe the workflow behind the database, present an overview of the properties and materials currently available, and explore trends and correlations in the data. Moreover, we identify a large number of new potentially synthesisable 2D materials with interesting properties targeting applications within spintronics, (opto-)electronics, and plasmonics. The C2DB offers a comprehensive and easily accessible overview of the rapidly expanding family of 2D materials and forms an ideal platform for computational modeling and design of new 2D materials and van der Waals heterostructures.

The electronic conductance of a benzene molecule connected to gold electrodes via thiol, thiolate, or amino anchoring groups is calculated using nonequilibrium Green functions in combination with the fully self-consistent GW approximation for exchange and correlation. The calculated conductance of benzenedithiol and benzenediamine is one-fifth that predicted by standard density functional theory (DFT), in very good agreement with experiments. In contrast, the widely studied benzenedithiolate structure is found to have a significantly higher conductance due to the unsaturated sulfur bonds. These findings suggest that more complex gold-thiolate structures where the thiolate anchors are chemically passivated by Au adatoms are responsible for the measured conductance. Analysis of the energy level alignment obtained with DFT, Hartree-Fock, and GW reveals the importance of self-interaction corrections (exchange) on the molecule and dynamical screening at the metal-molecule interface. The main effect of the GW self-energy is to renormalize the level positions; however, its influence on the shape of molecular resonances also affects the conductance. Non-self-consistent G 0 W 0 calculations, starting from either DFT or Hartree-Fock, yield conductance values within 50% of the self-consistent GW results.

We have designed and synthesized five azulene derivatives containing goldbinding groups at different points of connectivity within the azulene core to probe the effects of quantum interference through single-molecule conductance measurements. We compare conducting paths through the 5-membered ring, 7-membered ring, and across the long axis of azulene. We find that changing the points of connectivity in the azulene impacts the optical properties (as determined from UV-Vis absorption spectra) and the conductivity. Importantly, we show here that simple models cannot be used to predict quantum interference characteristics of non-alternant hydrocarbons. As an exemplary case, we show that azulene derivatives that are predicted to exhibit destructive interference based on widely accepted atom-counting models show a significant conductance at low biases. Although simple models to predict the low-bias conductance do not hold with all azulene derivatives, we show that the measured conductance trend for all molecules studied actually agrees with predictions based on the more complete GW calculations for model systems.

No abstract

We present a set of benchmark calculations for the Kohn-Sham elastic transmission function of five representative single-molecule junctions. The transmission functions are calculated using two different density functional theory (DFT) methods, namely an ultrasoft pseudopotential plane wave code in combination with maximally localized Wannier functions, and the norm-conserving pseudopotential code Siesta which applies an atomic orbital basis set. For all systems we find that the Siesta transmission functions converge toward the plane-wave result as the Siesta basis is enlarged. Overall, we find that an atomic basis with double-zeta and polarization is sufficient (and in some cases even necessary) to ensure quantitative agreement with the plane-wave calculation. We observe a systematic down shift of the Siesta transmission functions relative to the plane-wave results. The effect diminishes as the atomic orbital basis is enlarged, however, the convergence can be rather slow.

An empirical observation of a relationship between a striking feature of electronic transmission through a π-system, destructive quantum interference (QI), on one hand, and the stability of diradicals on the other, leads to the proof of a general theorem that relates the two. Subject to a number of simplifying assumptions, in a π-electron system, QI occurs when electrodes are attached to those positions of an N-carbon atom N-electron closed-shell hydrocarbon where the matrix elements of the Green's function vanish. These zeros come in two types, which are called easy and hard. Suppose an N+2 atom, N+2 electron hydrocarbon is formed by substituting 2 CH 2 groups at two atoms, where the electrodes were. Then, if a QI feature is associated with electrode attachment to the two atoms of the original N atom system, the resulting augmented N+2 molecule will be a diradical. If there is no QI feature, i.e., transmission of current is normal if electrodes are attached to the two atoms, the resulting hydrocarbon will not be a diradical but will have a classical closed-shell electronic structure. Moreover, where a diradical exists, the easy zero is associated with a nondisjoint diradical, and the hard zero is associated with a disjoint one. A related theorem is proven for deletion of two sites from a hydrocarbon. molecular conductance | diradicals | quantum interference | determinants | nonbonding orbitals C onnections between concepts that at first sight seem unrelated are always intriguing, and hint at an underlying cause. We came across one such correspondence recently, between the existence of π-diradicals, on one hand, and quantum interference (QI) in the transmission of electrons across a π-system on the other.