Grid-Based Projector Augmented Wave (GPAW) Implementation of Quantum Mechanics/Molecular Mechanics (QM/MM) Electrostatic Embedding and Application to a Solvated Diplatinum Complex.

A multiscale density functional theory-quantum mechanics/molecular mechanics (DFT-QM/MM) scheme is presented, based on an efficient electrostatic coupling between the electronic density obtained from a grid-based projector augmented wave (GPAW) implementation of density functional theory and a classical potential energy function. The scheme is implemented in a general fashion and can be used with various choices for the descriptions of the QM or MM regions. Tests on H2O clusters, ranging from dimer to decamer show that no systematic energy errors are introduced by the coupling that exceeds the differences in the QM and MM descriptions. Over 1 ns of liquid water, Born-Oppenheimer QM/MM molecular dynamics (MD) are sampled combining 10 parallel simulations, showing consistent liquid water structure over the QM/MM border. The method is applied in extensive parallel MD simulations of an aqueous solution of the diplatinum [Pt2(P2O5H2)4]4- complex (PtPOP), spanning a total time period of roughly half a nanosecond. An average Pt-Pt distance deviating only 0.01 Å from experimental results, and a ground-state Pt-Pt oscillation frequency deviating by <2% from experimental results were obtained. The simulations highlight a remarkable harmonicity of the Pt-Pt oscillation, while also showing clear signs of Pt-H hydrogen bonding and directional coordination of water molecules along the Pt-Pt axis of the complex.

Ab initio calculations of the electronic properties of polypyridine transition metal complexes and their adsorption on metal surfaces in the presence of solvent and counterions.

Os(II)/(III) and Co(II)/(III) polypyridine complexes in aqueous solution are robust molecular entities both in freely solute state and adsorbed on Au(111)- and Pt(111)-electrode surfaces. This class of robust coordination chemical compounds have recently been characterized by electrochemical scanning tunneling microscopy (in situ STM). The Os-complexes were found to display strong tunneling spectroscopic (STS) features at the level of resolution of the single molecule while STS features of the Co complexes, although clear, were much weaker. The data was framed by concise but phenomenological theory of interfacial electrochemical electron transfer extended to the electrochemical in situ STM configuration. With a view on first-principle insight into the in situ STM behavior of robust redox (as opposed to nonredox) molecules, we present in this report a density functional theory (DFT) study of the complexes in both free and adsorbate state, in either state exposed to both stoichiometric counterions and a large assembly of solvent water molecules. The oxidation states of the complexes were controlled, first by introducing chlorine counter atoms followed by spontaneous attraction of electrons from the complexes, also at first in electrostatically neutral form. Second, the solvent is found to provide strong dielectric screening of this charge transfer process and to be crucial for achieving the full chemically meaningful charge separated ionic oxidation states. The molecular charge and structure of the complexes in the presence of the solvent, are conserved upon adsorption, whereas the structural features of the different oxidation states are completely lost upon adsorption under vacuum conditions. Detailed microscopic insight such as offered by the present study will be important in molecular-based approaches to "smart" redox molecules enclosed in in situ STM or other nanoscale and single-molecules scale configurations in condensed matter environments.

Communications: Elementary oxygen electrode reactions in the aprotic Li-air battery.

We discuss the electrochemical reactions at the oxygen electrode of an aprotic Li-air battery. Using density functional theory to estimate the free energy of intermediates during the discharge and charge of the battery, we introduce a reaction free energy diagram and identify possible origins of the overpotential for both processes. We also address the question of electron conductivity through the Li(2)O(2) electrode and show that in the presence of Li vacancies Li(2)O(2) becomes a conductor.

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.

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.

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.

Bayesian error estimation in density-functional theory.

We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities such as binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude for different systems in good agreement with existing experience.

Partly occupied Wannier functions.

We introduce a scheme for constructing partly occupied, maximally localized Wannier functions (WFs) for both molecular and periodic systems. Compared to the traditional occupied WFs the partly occupied WFs possess improved symmetry and localization properties achieved through a bonding-antibonding closing procedure. We demonstrate the equivalence between bonding-antibonding closure and the minimization of the average spread of the WFs in the case of a benzene molecule and a linear chain of Pt atoms. The general applicability of the method is demonstrated through the calculation of WFs for a metallic system with an impurity: a Pt wire with a hydrogen molecular bridge.

Conduction mechanism in a molecular hydrogen contact.

We present first principles calculations for the conductance of a hydrogen molecule bridging a pair of Pt electrodes. The transmission function has a wide plateau with T approximately 1 which extends across the Fermi level and indicates the existence of a single, robust conductance channel with nearly perfect transmission. Through a detailed Wannier function analysis we show that the H(2) bonding state is not involved in the transport and that the plateau forms due to strong hybridization between the H(2) antibonding state and states on the adjacent Pt atoms. The Wannier functions furthermore allow us to derive a resonant-level model for the system with all parameters determined from the fully self-consistent Kohn-Sham Hamiltonian.

Four-atom period in the conductance of monatomic Al wires.

We present first-principles calculations based on density functional theory for the conductance of monatomic Al wires between Al(111) electrodes. In contrast to the even-odd oscillations observed in other metallic wires, the conductance of the Al wires is found to oscillate with a period of four atoms as the length of the wire is varied. Although local charge neutrality can account for the observed period, it leads to an incorrect phase. We explain the conductance behavior using a resonant transport model based on the electronic structure of the infinite wire.

Combined electronic structure and evolutionary search approach to materials design.

We show that density functional theory calculations have reached an accuracy and speed making it possible to use them in conjunction with an evolutionary algorithm to search for materials with specific properties. The approach is illustrated by finding the most stable four component alloys out of the 192 016 possible fcc and bcc alloys that can be constructed out of 32 different metals. A number of well known and new "super alloys" are identified in this way.

Atomic-scale structure of dislocations revealed by scanning tunneling microscopy and molecular dynamics.

The intersection between dislocations and a Ag(111) surface has been studied using an interplay of scanning tunneling microscopy (STM) and molecular dynamics. Whereas the STM provides atomically resolved information about the surface structure and Burgers vectors of the dislocations, the simulations can be used to determine dislocation structure and orientation in the near-surface region. In a similar way, the subsurface structure of other extended defects can be studied. The simulations show dislocations to reorient the partials in the surface region leading to an increased splitting width at the surface, in agreement with the STM observations. Implications for surface-induced cross slip are discussed.

One-dimensional metallic edge states in MoS2.

By the use of density functional calculations it is shown that the edges of a two-dimensional slab of insulating MoS2 exhibit several metallic states. These edge states can be viewed as one-dimensional conducting wires, and we show that they can be observed directly using scanning tunneling microscopy for single-layer MoS2 nanoparticles grown on a support.

Adsorption-induced step formation.

Through an interplay between density functional calculations, Monte Carlo simulations and scanning tunneling microscopy experiments, we show that an intermediate coverage of CO on the Pt(110) surface gives rise to a new rough equilibrium structure with more than 50% step atoms. CO is shown to bind so strongly to low-coordinated Pt atoms that it can break Pt-Pt bonds and spontaneously form steps on the surface. It is argued that adsorption-induced step formation may be a general effect, in particular at high gas pressures and temperatures.

Calculation of quantum tunneling for a spatially extended defect: the dislocation kink in copper has a low effective mass.

Several experiments indicate that there are atomic tunneling defects in plastically deformed metals. How this is possible has not been clear, given the large mass of the metal atoms. Using a classical molecular-dynamics calculation, we determine the structures, energy barriers, effective masses, and quantum tunneling rates for dislocation kinks and jogs in copper screw dislocations. We find that jogs are unlikely to tunnel, but the kinks should have large quantum fluctuations. The kink motion involves hundreds of atoms each shifting a tiny amount, leading to a small effective mass and tunneling barrier.

Chain formation of metal atoms.

The possibility of formation of single-atomic chains by manipulation of nanocontacts is studied for a selection of metals (Ni, Pd, Pt, Cu, Ag, Au). Molecular dynamics simulations show that the tendency for chain formation is strongest for Au and Pt. Density functional theory calculations indicate that the metals which form chains exhibit pronounced many-atom interactions with strong bonding in low coordinated systems.