Mikkel Strange

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

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.

Breakdown of interference rules in azulene, a nonalternant hydrocarbon.

We have designed and synthesized five azulene derivatives containing gold-binding 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 nonalternant 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 demonstrate that the measured conductance trend for all molecules studied actually agrees with predictions based on the more complete GW calculations for model systems.

Density functional theory based screening of ternary alkali-transition metal borohydrides: A computational material design project

We present a computational screening study of ternary metal borohydrides for reversible hydrogen storage based on density functional theory. We investigate the stability and decomposition of alloys containing 1 alkali metal atom, Li, Na, or K (M(1)); and 1 alkali, alkaline earth or 3d/4d transition metal atom (M(2)) plus two to five (BH(4))(-) groups, i.e., M(1)M(2)(BH(4))(2-5), using a number of model structures with trigonal, tetrahedral, octahedral, and free coordination of the metal borohydride complexes. Of the over 700 investigated structures, about 20 were predicted to form potentially stable alloys with promising decomposition energies. The M(1)(Al/Mn/Fe)(BH(4))(4), (Li/Na)Zn(BH(4))(3), and (Na/K)(Ni/Co)(BH(4))(3) alloys are found to be the most promising, followed by selected M(1)(Nb/Rh)(BH(4))(4) alloys.

Benchmark density functional theory calculations for nanoscale conductance

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 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. All calculations have been converged with respect to the supercell size and the number of k|| points in the surface plane. 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 downshift 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.

Formation and properties of metal?oxygen atomic chains

Suspended chains consisting of single noble metal and oxygen atoms have been formed. We provide evidence that oxygen can react with and be incorporated into metallic one-dimensional atomic chains. Oxygen incorporation reinforces the linear bonds in the chain, which facilitates the creation of longer atomic chains. The mechanical and electrical properties of these diatomic chains have been investigated by determining local vibration modes of the chain and by measuring the dependence of the average chain-conductance on the length of the chain. Additionally, we have performed calculations that give insight into the physical mechanism of the oxygen-induced strengthening of the linear bonds and the conductance of the metal–oxygen chains.

Quantum interference in off-resonant transport through single molecules

We provide a simple set of rules for predicting interference effects in off-resonant transport through single molecule junctions. These effects fall into two classes, showing, respectively, an odd or an even number of nodes in the linear conductance within a given molecular charge state, and we demonstrate how to decide the interference class directly from the contacting geometry. For neutral alternant hydrocarbons, we employ the Coulson-Rushbrooke-McLachlan pairing theorem to show that the interference class is decided simply by tunneling on and off the molecule from same or different sublattices. More generally, we investigate a range of smaller molecules by means of exact diagonalization combined with a perturbative treatment of the molecule-lead tunnel coupling. While these results generally agree well with GW calculations, they are shown to be at odds with simpler mean-field treatments. For molecules with spin-degenerate ground states, we show that for most junctions interference causes no transmission nodes, but we argue that it may lead to a nonstandard gate dependence of the zero-bias Kondo resonance. (Less)

Close relation between quantum interference in molecular conductance and diradical existence

Significance It might seem that the existence of a dramatic diminution in molecular conductance across a hydrocarbon (quantum interference, QI) would be unrelated to the existence of an important class of organic molecules with two electrons in two orbitals, diradicals. However, if you add two carbons to a planar π-electron hydrocarbon, you get a diradical if and only if there is a QI feature in conductance when two electrodes are attached to the molecule at the same sites. When you remove the two carbons where the electrodes are attached, you also generate a diradical. The connection, first empirically observed, is proven. Two kinds of diradicals, with different ground state spin consequences, are also easily distinguished by the relationship. 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 CH2 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.

Energy level alignment and quantum conductance of functionalized metal-molecule junctions: density functional theory versus GW calculations.

We study the effect of functional groups (CH3*4, OCH3, CH3, Cl, CN, F*4) on the electronic transport properties of 1,4-benzenediamine molecular junctions using the non-equilibrium Green function method. Exchange and correlation effects are included at various levels of theory, namely density functional theory (DFT), energy level-corrected DFT (DFT+Σ), Hartree-Fock and the many-body GW approximation. All methods reproduce the expected trends for the energy of the frontier orbitals according to the electron donating or withdrawing character of the substituent group. However, only the GW method predicts the correct ordering of the conductance amongst the molecules. The absolute GW (DFT) conductance is within a factor of two (three) of the experimental values. Correcting the DFT orbital energies by a simple physically motivated scissors operator, Σ, can bring the DFT conductances close to experiments, but does not improve on the relative ordering. We ascribe this to a too strong pinning of the molecular energy levels to the metal Fermi level by DFT which suppresses the variation in orbital energy with functional group.

Towards quantitative accuracy in first-principles transport calculations: The GW method applied to alkane/gold junctions

Summary 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.

Electron transport in aPt−CO−Ptnanocontact: Density functional theory calculations

We have performed first-principles calculations for the mechanic and electric properties of pure Pt nanocontacts and a Pt contact with a single CO molecule adsorbed. For the pure Pt contacts we see a clear difference between point contacts and short chains in good agreement with experiments. We identify a tilted bridge configuration for the