Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

The surface science of titanium dioxide

Density functional theory calculations explain copper's unique ability to convert CO2 into hydrocarbons, which may open up (photo-)electrochemical routes to fuels.

How copper catalyzes the electroreduction of carbon dioxide into hydrocarbon fuels

Reversible work transition state theory: application to dissociative adsorption of hydrogen

Point defects and impurities strongly affect the physical properties of materials and have a decisive impact on their performance in applications. First-principles calculations have emerged as a powerful approach that complements experiments and can serve as a predictive tool in the identification and characterization of defects. The theoretical modeling of point defects in crystalline materials by means of electronic-structure calculations, with an emphasis on approaches based on density functional theory (DFT), is reviewed. A general thermodynamic formalism is laid down to investigate the physical properties of point defects independent of the materials class (semiconductors, insulators, and metals), indicating how the relevant thermodynamic quantities, such as formation energy, entropy, and excess volume, can be obtained from electronic structure calculations. Practical aspects such as the supercell approach and efficient strategies to extrapolate to the isolated-defect or dilute limit are discussed. Recent advances in tractable approximations to the exchange-correlation functional ($\mathrm{DFT}+U$, hybrid functionals) and approaches beyond DFT are highlighted. These advances have largely removed the long-standing uncertainty of defect formation energies in semiconductors and insulators due to the failure of standard DFT to reproduce band gaps. Two case studies illustrate how such calculations provide new insight into the physics and role of point defects in real materials.

First-principles calculations for point defects in solids

Molecular-dynamics (MD) simulations have been carried out on a two-component Lennard-Jones system, quenched into supercooled and amorphous states. Two different regimes of viscous behavior are found in the time window accessible in MD simulation studies (of the order of nanoseconds if units appropriate for argon are used). The results for the time dependence of the self-intermediate scattering function ${\mathit{F}}^{\mathit{s}}$(q,t) show two different slow relaxation processes, where the slowest (\ensuremath{\alpha} relaxation) can be represented by a stretched exponential, exp[-(t/${\mathrm{\ensuremath{\tau}}}_{\mathrm{rel}}$${)}^{\mathrm{\ensuremath{\beta}}}$]. In the frequency domain this gives rise to a quasielastic peak, and it is found that its area, the nonergodicity parameter ${\mathit{f}}^{\mathit{s}}$(q)==a, shows an anomalous decrease when increasing the temperature towards a critical value ${\mathit{T}}_{\mathit{c}}$. This happens in the supercooled-liquid regime, and it is one of the basic predictions of the recent mode-coupling theory for the liquid-glass transition problem. In the strongly supercooled-liquid regime the diffusion is of the hopping type, and it is found to be strongly cooperative in nature.

Molecular-dynamics study of a supercooled two-component Lennard-Jones system

We have revealed, and resolved, an apparent inability of density functional theory, within the local density and generalized gradient approximations, to describe vacancies in Al accurately and consistently. The shortcoming is due to electron correlation effects near electronic edges and we show how to correct for them. We find that the divacancy in Al is energetically unstable and we show that anharmonic atomic vibrations explain the non-Arrhenius temperature dependence of the vacancy concentration.

Vacancies in metals: from first-principles calculations to experimental data

We report generalized stacking fault (GSF) curves along the [121] and [110] directions for Pd and Al, calculated from first principles. The GSF curves are applied in the classic PN model to calculate Peierls barriers and stresses for the Shockley partials and the unsplit edge dislocations in Pd and Al. The obtained stresses using relaxed GSF curves agree well with experiments. The numerical results are also compared with a recently derived analytical expression for the Peierls stress. The GSF curves have been calculated with a pseudopotential implementation of density functional theory. The accuracy of the method have been tested by calculating values for various stacking fault energies of Al, Ni, Cu, Ag, and Pd which favorably compare with other theoretical and experimental values.

Peierls barriers and stresses for edge dislocations in Pd and Al calculated from first principles

In this work, the stability and mobility of protonic defects in acceptor doped BaZrO3 are investigated using density functional theory in conjunction with kinetic modeling. The interaction between the mobile protons and Zr-site substituted trivalent dopants—Ga, Sc, In, Y, and Gd—is assessed by extensive mapping of migration pathways. In all cases, the interaction is attractive, which results in a stabilization, and hence a reduction of the mobility, of the proton. However, its strength and range vary substantially and are found to be strongly correlated to the ionic radius of the dopant. Further, it is shown that the observed correlation is related to a variation in strength of hydrogen bonds formed between protons and next nearest lattice oxygen ions in different environments. Finally, migration barriers and attempt frequencies obtained from first principles are used as input to a jump-diffusion model. The proton self-diffusion coefficient is evaluated for the different substituted phases, and the experimental trend in activation energies is reproduced.

Effect of acceptor dopants on the proton mobility in BaZrO3: A density functional investigation

With the purpose to understand the fundamental difference between two industrially important classes of hard materials, WC-Co cemented carbides and TiC-Co cermets, we do a comparative study of Co/WC and Co/TiC interface adhesion. Using first-principles density-functional plane-wave pseudopotential calculations, we analyze the energetics and electronic structure of the Co/WC interface, and compare with previously reported results for Co/TiC. Values for the work of separation and the interface energy are provided for a set of model Co(001)/WC(001) interfaces with fcc Co and cubic WC, which is a relevant case in sintering of Ti(W)C-Co cermets. The known fact of better wetting for Co on WC than on TiC is confirmed and explained in terms of the electronic structure. Both Co/WC and Co/TiC are characterized by strong covalent Co-C interface bonds. The stronger adhesion in the Co/WC case originates from a larger contribution of the Co-W metal-metal bonding rather than from the Co-C bonds.

Göran Wahnström

Papers

Molecular-dynamics study of a supercooled two-component Lennard-Jones system

Vacancies in metals: from first-principles calculations to experimental data

Peierls barriers and stresses for edge dislocations in Pd and Al calculated from first principles

Effect of acceptor dopants on the proton mobility in BaZrO3: A density functional investigation

First-principles simulations of metal-ceramic interface adhesion: Co/WC versus Co/TiC