There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

A modification of the nudged elastic band method for finding minimum energy paths is presented. One of the images is made to climb up along the elastic band to converge rigorously on the highest saddle point. Also, variable spring constants are used to increase the density of images near the top of the energy barrier to get an improved estimate of the reaction coordinate near the saddle point. Applications to CH4 dissociative adsorption on Ir~111! and H2 on Si~100! using plane wave based density functional theory are presented. © 2000 American Institute of Physics. @S0021-9606~00!71246-3#

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A climbing image nudged elastic band method for finding saddle points and minimum energy paths

Molecular simulation is an extremely useful, but computationally very expensive tool for studies of chemical and biomolecular systems Here, we present a new implementation of our molecular simulation toolkit GROMACS which now both achieves extremely high performance on single processors from algorithmic optimizations and hand-coded routines and simultaneously scales very well on parallel machines The code encompasses a minimal-communication domain decomposition algorithm, full dynamic load balancing, a state-of-the-art parallel constraint solver, and efficient virtual site algorithms that allow removal of hydrogen atom degrees of freedom to enable integration time steps up to 5 fs for atomistic simulations also in parallel To improve the scaling properties of the common particle mesh Ewald electrostatics algorithms, we have in addition used a Multiple-Program, Multiple-Data approach, with separate node domains responsible for direct and reciprocal space interactions Not only does this combination of a

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GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation

http://theory.cm.utexas.edu/henkelman/pubs/henkelman06_354.pdf

A fast and robust algorithm for Bader decomposition of charge density

We evaluate the ability of the embedded-atom method ~EAM! potentials and the tight-binding ~TB! method to predict reliably energies and stability of nonequilibrium structures by taking Cu as a model material. Two EAM potentials are used here. One is constructed in this work by using more fitting parameters than usual and including ab initio energies in the fitting database. The other potential was constructed previously using a traditional scheme. Excellent agreement is observed between ab initio, TB, and EAM results for the energies and stability of several nonequilibrium structures of Cu, as well as for energies along deformation paths between different structures. We conclude that not only TB calculations but also EAM potentials can be suitable for simulations in which correct energies and stability of different atomic configurations are essential, at least for Cu. The bcc, simple cubic, and diamond structures of Cu were identified as elastically unstable, while some other structures ~e.g., hcp and 9R! are metastable. As an application of this analysis, nonequilibrium structures of epitaxial Cu films on~001!-oriented fcc or bcc substrates are evaluated using a simple model and atomistic simulations with an EAM potential. In agreement with experimental data, the structure of the film can be either deformed fcc or deformed hcp. The bcc structure cannot be stabilized by epitaxial constraints.

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Structural stability and lattice defects in copper: Ab initio , tight-binding, and embedded-atom calculations

I derive a general method for accelerating the molecular-dynamics (MD) simulation of infrequent events in solids. A bias potential ( $\ensuremath{\Delta}{V}_{b}$) raises the energy in regions other than the transition states between potential basins. Transitions occur at an accelerated rate and the elapsed time becomes a statistical property of the system. $\ensuremath{\Delta}{V}_{b}$ can be constructed without knowing the location of the transition states and implementation requires only first derivatives. I examine the diffusion mechanisms of a 10-atom Ag cluster on the Ag(111) surface using a $220\ensuremath{\mu}\mathrm{s}$ hyper-MD simulation.

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Hyperdynamics: Accelerated Molecular Dynamics of Infrequent Events

Although grain boundaries can serve as effective sinks for radiation-induced defects such as interstitials and vacancies, the atomistic mechanisms leading to this enhanced tolerance are still not well understood With the use of three atomistic simulation methods, we investigated defect-grain boundary interaction mechanisms in copper from picosecond to microsecond time scales We found that grain boundaries have a surprising "loading-unloading" effect Upon irradiation, interstitials are loaded into the boundary, which then acts as a source, emitting interstitials to annihilate vacancies in the bulk This unexpected recombination mechanism has a much lower energy barrier than conventional vacancy diffusion and is efficient for annihilating immobile vacancies in the nearby bulk, resulting in self-healing of the radiation-induced damage

https://science.sciencemag.org/content/sci/327/5973/1631.full.pdf

Efficient annealing of radiation damage near grain boundaries via interstitial emission.

We present a method for accelerating dynamic simulations of activated processes in solids. By raising the temperature, but allowing only those events that should occur at the original temperature, the time scale of a simulation is extended by orders of magnitude compared to ordinary molecular dynamics, while preserving the correct dynamics at the original temperature. The main assumption behind the method is harmonic transition state theory. Importantly, the method does not require any prior knowledge about the transition mechanisms. As an example, the method is applied to a study of surface diffusion, where concerted processes play a key role. In the example, times of hours are achieved at a temperature of 150 K.

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Temperature-accelerated dynamics for simulation of infrequent events

▪ Abstract Obtaining a good atomistic description of diffusion dynamics in materials has been a daunting task owing to the time-scale limitations of the molecular dynamics method. We discuss promising new methods, derived from transition state theory, for accelerating molecular dynamics simulations of these infrequent-event processes. These methods, hyperdynamics, parallel replica dynamics, temperature-accelerated dynamics, and on-the-fly kinetic Monte Carlo, can reach simulation times several orders of magnitude longer than direct molecular dynamics while retaining full atomistic detail. Most applications so far have involved surface diffusion and growth, but it is clear that these methods can address a wide range of materials problems.

Arthur F. Voter

Papers

Structural stability and lattice defects in copper: Ab initio , tight-binding, and embedded-atom calculations

Hyperdynamics: Accelerated Molecular Dynamics of Infrequent Events

Efficient annealing of radiation damage near grain boundaries via interstitial emission.

Temperature-accelerated dynamics for simulation of infrequent events

Extending the Time Scale in Atomistic Simulation of Materials