Targeted free energy perturbation

A generalization of the free energy perturbation identity is derived, and a computational strategy based on this result is presented. A simple example illustrates the efficiency gains that can be achieved with this method.Comment: 8 pages + 1 color figur

Dynamics of Lennard-Jones clusters: A characterization of the activation-relaxation technique

The potential energy surface (PES) of Lennard-Jones clusters is investigated using the activation-relaxation technique (ART). This method defines events in the configurational energy landscape as a two-step process: (a) a configuration is first activated from a local minimum to a nearby saddle-point and (b) is then relaxed to a new minimum. Although ART has been applied with success to a wide range of materials such as a-Si, a-SiO2 and binary Lennard-Jones glasses, questions remain regarding the biases of the technique. We address some of these questions in a detailed study of ART-generated events in Lennard-Jones (LJ) clusters, a system for which much is already known. In particular, we study the distribution of saddle-points, the pathways between configurations, and the reversibility of paths. We find that ART can identify all trajectories with a first-order saddle point leaving a given minimum, is fully reversible, and samples events following the Boltzmann weight at the saddle point.Comment: 8 pages, 7 figures in postscrip

Diffusion of gold nanoclusters on graphite

We present a detailed molecular-dynamics study of the diffusion and coalescence of large (249-atom) gold clusters on graphite surfaces. The diffusivity of monoclusters is found to be comparable to that for single adatoms. Likewise, and even more important, cluster dimers are also found to diffuse at a rate which is comparable to that for adatoms and monoclusters. As a consequence, large islands formed by cluster aggregation are also expected to be mobile. Using kinetic Monte Carlo simulations, and assuming a proper scaling law for the dependence on size of the diffusivity of large clusters, we find that islands consisting of as many as 100 monoclusters should exhibit significant mobility. This result has profound implications for the morphology of cluster-assembled materials

Fourier Acceleration of Langevin Molecular Dynamics

Fourier acceleration has been successfully applied to the simulation of lattice field theories for more than a decade. In this paper, we extend the method to the dynamics of discrete particles moving in continuum. Although our method is based on a mapping of the particles' dynamics to a regular grid so that discrete Fourier transforms may be taken, it should be emphasized that the introduction of the grid is a purely algorithmic device and that no smoothing, coarse-graining or mean-field approximations are made. The method thus can be applied to the equations of motion of molecular dynamics (MD), or its Langevin or Brownian variants. For example, in Langevin MD simulations our acceleration technique permits a straightforward spectral decomposition of forces so that the long-wavelength modes are integrated with a longer time step, thereby reducing the time required to reach equilibrium or to decorrelate the system in equilibrium. Speedup factors of up to 30 are observed relative to pure (unaccelerated) Langevin MD. As with acceleration of critical lattice models, even further gains relative to the unaccelerated method are expected for larger systems. Preliminary results for Fourier-accelerated molecular dynamics are presented in order to illustrate the basic concepts. Possible extensions of the method and further lines of research are discussed.Comment: 11 pages, two illustrations included using graphic

Vibrational properties of amorphous silicon from tight-binding O(N) calculation

We present an O(N) algorithm to study the vibrational properties of amorphous silicon within the framework of tight-binding approach. The dynamical matrix elements have been evaluated numerically in the harmonic approximation exploiting the short-range nature of the density matrix to calculate the vibrational density of states which is then compared with the same obtained from a standard O($N^4$) algorithm. For the purpose of illustration, an 1000-atom model is studied to calculate the localization properties of the vibrational eigenstates using the participation numbers calculation.Comment: 5 pages including 5 ps figures; added a figure and a few references; accepted in Phys. Rev.

Lattice Dynamics and the High Pressure Equation of State of Au

Elastic constants and zone-boundary phonon frequencies of gold are calculated by total energy electronic structure methods to twofold compression. A generalized force constant model is used to interpolate throughout the Brillouin zone and evaluate moments of the phonon distribution. The moments are used to calculate the volume dependence of the Gruneisen parameter in the fcc solid. Using these results with ultrasonic and shock data, we formulate the complete free energy for solid Au. This free energy is given as a set of closed form expressions, which are valid to compressions of at least V/V_0 = 0.65 and temperatures up to melting. Beyond this density, the Hugoniot enters the solid-liquid mixed phase region. Effects of shock melting on the Hugoniot are discussed within an approximate model. We compare with proposed standards for the equation of state to pressures of ~200 GPa. Our result for the room temperature isotherm is in very good agreement with an earlier standard of Heinz and Jeanloz.Comment: 13 pages, 8 figures. Accepted by Phys. Rev.

Electromigration-Induced Flow of Islands and Voids on the Cu(001) Surface

Electromigration-induced flow of islands and voids on the Cu(001) surface is studied at the atomic scale. The basic drift mechanisms are identified using a complete set of energy barriers for adatom hopping on the Cu(001) surface, combined with kinetic Monte Carlo simulations. The energy barriers are calculated by the embedded atom method, and parameterized using a simple model. The dependence of the flow on the temperature, the size of the clusters, and the strength of the applied field is obtained. For both islands and voids it is found that edge diffusion is the dominant mass-transport mechanism. The rate limiting steps are identified. For both islands and voids they involve detachment of atoms from corners into the adjacent edge. The energy barriers for these moves are found to be in good agreement with the activation energy for island/void drift obtained from Arrhenius analysis of the simulation results. The relevance of the results to other FCC(001) metal surfaces and their experimental implications are discussed.Comment: 9 pages, 13 ps figure

Block bond-order potential as a convergent moments-based method

The theory of a novel bond-order potential, which is based on the block Lanczos algorithm, is presented within an orthogonal tight-binding representation. The block scheme handles automatically the very different character of sigma and pi bonds by introducing block elements, which produces rapid convergence of the energies and forces within insulators, semiconductors, metals, and molecules. The method gives the first convergent results for vacancies in semiconductors using a moments-based method with a low number of moments. Our use of the Lanczos basis simplifies the calculations of the band energy and forces, which allows the application of the method to the molecular dynamics simulations of large systems. As an illustration of this convergent O(N) method we apply the block bond-order potential to the large scale simulation of the deformation of a carbon nanotube.Comment: revtex, 43 pages, 11 figures, submitted to Phys. Rev.

Ab initio atomistic thermodynamics and statistical mechanics of surface properties and functions

Previous and present "academic" research aiming at atomic scale understanding is mainly concerned with the study of individual molecular processes possibly underlying materials science applications. Appealing properties of an individual process are then frequently discussed in terms of their direct importance for the envisioned material function, or reciprocally, the function of materials is somehow believed to be understandable by essentially one prominent elementary process only. What is often overlooked in this approach is that in macroscopic systems of technological relevance typically a large number of distinct atomic scale processes take place. Which of them are decisive for observable system properties and functions is then not only determined by the detailed individual properties of each process alone, but in many, if not most cases also the interplay of all processes, i.e. how they act together, plays a crucial role. For a "predictive materials science modeling with microscopic understanding", a description that treats the statistical interplay of a large number of microscopically well-described elementary processes must therefore be applied. Modern electronic structure theory methods such as DFT have become a standard tool for the accurate description of individual molecular processes. Here, we discuss the present status of emerging methodologies which attempt to achieve a (hopefully seamless) match of DFT with concepts from statistical mechanics or thermodynamics, in order to also address the interplay of the various molecular processes. The new quality of, and the novel insights that can be gained by, such techniques is illustrated by how they allow the description of crystal surfaces in contact with realistic gas-phase environments.Comment: 24 pages including 17 figures, related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm