Structural relaxation made simple.
TL;DR: A simple local atomic structure optimization algorithm which is significantly faster than standard implementations of the conjugate gradient method and often competitive with more sophisticated quasi-Newton schemes typically used in ab initio calculations is introduced.
Abstract: We introduce a simple local atomic structure optimization algorithm which is significantly faster than standard implementations of the conjugate gradient method and often competitive with more sophisticated quasi-Newton schemes typically used in ab initio calculations. It is based on conventional molecular dynamics with additional velocity modifications and adaptive time steps. The surprising efficiency and especially the robustness and versatility of the method is illustrated using a variety of test cases from nanoscience, solid state physics, materials research, and biochemistry.
Citations
More filters
University of the Basque Country1, University of Barcelona2, Technical University of Denmark3, Malmö University4, University of Copenhagen5, SINTEF6, Aarhus University7, Brown University8, University of Wisconsin-Madison9, University of Warwick10, Carnegie Mellon University11, Purdue University12, Karlsruhe Institute of Technology13, ETH Zurich14, University of Freiburg15
TL;DR: The atomic simulation environment (ASE) provides modules for performing many standard simulation tasks such as structure optimization, molecular dynamics, handling of constraints and performing nudged elastic band calculations.
Abstract: The Atomic Simulation Environment (ASE) is a software package written in the Python programming language with the aim of setting up, steering, and analyzing atomistic simula- tions. In ASE, tasks are fully scripted in Python. The powerful syntax of Python combined with the NumPy array library make it possible to perform very complex simulation tasks. For example, a sequence of calculations may be performed with the use of a simple "for-loop" construction. Calculations of energy, forces, stresses and other quantities are performed through interfaces to many external electronic structure codes or force fields using a uniform interface. On top of this calculator interface, ASE provides modules for performing many standard simulation tasks such as structure optimization, molecular dynamics, handling of constraints and performing nudged elastic band calculations.
2,282 citations
TL;DR: Several of the fundamental algorithms used in LAMMPS are described along with the design strategies which have made it flexible for both users and developers, and some capabilities recently added to the code which were enabled by this flexibility are highlighted.
1,956 citations
TL;DR: The Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) as mentioned in this paper is a simulator for particle-based modeling of materials at length scales ranging from atomic to mesoscale to continuum.
1,517 citations
TL;DR: If a highly accurate MEP is desired, it is found to be more efficient to descend from the saddle to the minima than to use a chain-of-states method with many images.
Abstract: A comparison of chain-of-states based methods for finding minimum energy pathways (MEPs) is presented. In each method, a set of images along an initial pathway between two local minima is relaxed to find a MEP. We compare the nudged elastic band (NEB), doubly nudged elastic band, string, and simplified string methods, each with a set of commonly used optimizers. Our results show that the NEB and string methods are essentially equivalent and the most efficient methods for finding MEPs when coupled with a suitable optimizer. The most efficient optimizer was found to be a form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno method in which the approximate inverse Hessian is constructed globally for all images along the path. The use of a climbing-image allows for finding the saddle point while representing the MEP with as few images as possible. If a highly accurate MEP is desired, it is found to be more efficient to descend from the saddle to the minima than to use a chain-of-states method with many images. Our results are based on a pairwise Morse potential to model rearrangements of a heptamer island on Pt(111), and plane-wave based density functional theory to model a rollover diffusion mechanism of a Pd tetramer on MgO(100) and dissociative adsorption and diffusion of oxygen on Au(111).
1,409 citations
TL;DR: QuantumATK as discussed by the authors is an integrated set of atomic-scale modelling tools developed since 2003 by professional software engineers in collaboration with academic researchers, which enable electronic-structure calculations using density functional theory or tight-binding model Hamiltonians, and also offers bonded or reactive empirical force fields in many different parametrizations.
Abstract: QuantumATK is an integrated set of atomic-scale modelling tools developed since 2003 by professional software engineers in collaboration with academic researchers. While different aspects and individual modules of the platform have been previously presented,a#13; the purpose of this paper is to give a general overview of the platform. The QuantumATK simulation engines enable electronic-structure calculations using density functional theory or tight-binding model Hamiltonians, and also offers bonded or reactive empirical force fields in many different parametrizations. Density functional theory is implemented using either a plane-wave basis or expansion of electronic states in a linear combination of atomic orbitals. The platform includes a long list of advanced modules, including Green's-function methods for electron transport simulations and surface calculations, first-principles electron-phonon and electron-photon couplings,a#13; simulation of atomic-scale heat transport, ion dynamics, spintronics, optical properties of materials, static polarization, and more.a#13; Seamless integration of the different simulation engines into a common platform allows for easy combination of different simulation methods into complex workflows. Besides giving a general overview and presenting a number of implementation detailsa#13; not previously published, we also present four different application examples. These are calculations of the phonon-limited mobility of Cu, Ag and Au, electron transport in a gated 2D device, multi-model simulation of lithium ion drift through a battery cathode in an external electric field, and electronic-structure calculations of the composition-dependent band gap of SiGe alloys.a#13;
658 citations
References
More filters
Book•
01 Nov 2008TL;DR: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization, responding to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.
Abstract: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.
17,420 citations
"Structural relaxation made simple." refers methods in this paper
...To demonstrate the performance of FIRE, we compare it to two relaxation methods: the Polak-Ribière version of CG with the popular Numerical Recipes implementation [2], and the limited memory version of BFGS (L-BFGS) [1, 10]....
[...]
TL;DR: The numerical tests indicate that the L-BFGS method is faster than the method of Buckley and LeNir, and is better able to use additional storage to accelerate convergence, and the convergence properties are studied to prove global convergence on uniformly convex problems.
Abstract: We study the numerical performance of a limited memory quasi-Newton method for large scale optimization, which we call the L-BFGS method. We compare its performance with that of the method developed by Buckley and LeNir (1985), which combines cycles of BFGS steps and conjugate direction steps. Our numerical tests indicate that the L-BFGS method is faster than the method of Buckley and LeNir, and is better able to use additional storage to accelerate convergence. We show that the L-BFGS method can be greatly accelerated by means of a simple scaling. We then compare the L-BFGS method with the partitioned quasi-Newton method of Griewank and Toint (1982a). The results show that, for some problems, the partitioned quasi-Newton method is clearly superior to the L-BFGS method. However we find that for other problems the L-BFGS method is very competitive due to its low iteration cost. We also study the convergence properties of the L-BFGS method, and prove global convergence on uniformly convex problems.
7,004 citations
TL;DR: An improved way of estimating the local tangent in the nudged elastic band method for finding minimum energy paths is presented, and examples given where a complementary method, the dimer method, is used to efficiently converge to the saddle point.
Abstract: An improved way of estimating the local tangent in the nudged elastic band method for finding minimum energy paths is presented. In systems where the force along the minimum energy path is large compared to the restoring force perpendicular to the path and when many images of the system are included in the elastic band, kinks can develop and prevent the band from converging to the minimum energy path. We show how the kinks arise and present an improved way of estimating the local tangent which solves the problem. The task of finding an accurate energy and configuration for the saddle point is also discussed and examples given where a complementary method, the dimer method, is used to efficiently converge to the saddle point. Both methods only require the first derivative of the energy and can, therefore, easily be applied in plane wave based density-functional theory calculations. Examples are given from studies of the exchange diffusion mechanism in a Si crystal, Al addimer formation on the Al(100) surfa...
6,825 citations
Book•
01 Jan 1996
TL;DR: In this article, the authors introduce the concept of Computational Quantum Mechanics (CQM) and present four challenges in molecular modelling: Free Energies, Solvation, Reactions and Solid-State Defects.
Abstract: Preface. Symbols and physical constants. 1. Useful Concepts in Molecular Modelling. 2. An Introduction to Computational Quantum Mechanics. 3. Advanced AB Initio Methods, Density Functional Theory and Solid-State Quantum Mechanics. 4. Force Field Models: Molecular Mechanics. 5. Energy Minimisation and Related Methods for Exploring the Energy Surface. 6. Computer Simulation Methods. 7. Molecular Dynamics Simulation Methods. 8. Monte Carlo Simulation Methods. 9. Conformational Analysis. 10. Protein Structure Prediction, Sequence Analysis and Protein Folding. 11. Four Challenges in Molecular Modelling: Free Energies, Solvation, Reactions and Solid-State Defects. 12. The Use of Molecular Modelling and Chemoinformatics to Discover and Design New Molecules.
2,457 citations
TL;DR: In this article, the ability of the embedded-atom method (EAM) and the tight-binding (TB) method to predict reliably energies and stability of nonequilibrium structures by taking Cu as a model material was evaluated.
Abstract: 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.
1,803 citations