Basin hopping with occasional jumping

Structure search method for atomic clusters based on the dividing rectangles algorithm

The Dividing Rectangles (DIRECT) algorithm is a deterministic optimization method to explore optimal solutions by repeatedly dividing a given hyperrectangle search space into subhyperrectangles. Herein, we propose a structure search method for atomic clusters based on the DIRECT algorithm in combination with a gradient-based local optimizer to enable an efficient structure search in high-dimensional search spaces. We use the Z-matrix representation for defining the hyperrectangle search space, in which the bond lengths, bond angles, and dihedral angles specify a cluster structure. To evaluate its performance, we applied the proposed method to the Lennard-Jones clusters and two kinds of real atomic clusters with many metastable structures, i.e., phosphorus and sulfur clusters, and compared the results with those of conventional methods. The proposed method exhibits a higher efficiency than random search and a comparable efficiency to basin hopping.

Systematic Comparison of Genetic Algorithm and Basin Hopping Approaches to the Global Optimization of Si(111) Surface Reconstructions

We present a systematic study of two widely used material structure prediction methods, the Genetic Algorithm and Basin Hopping approaches to global optimization, in a search for the 3 × 3, 5 × 5, and 7 × 7 reconstructions of the Si(111) surface. The Si(111) 7 × 7 reconstruction is the largest and most complex surface reconstruction known, and finding it is a very exacting test for global optimization methods. In this paper, we introduce a modification to previous Genetic Algorithm work on structure search for periodic systems, to allow the efficient search for surface reconstructions, and present a rigorous study of the effect of the different parameters of the algorithm. We also perform a detailed comparison with the recently improved Basin Hopping algorithm using Delocalized Internal Coordinates. Both algorithms succeeded in either resolving the 3 × 3, 5 × 5, and 7 × 7 DAS surface reconstructions or getting “sufficiently close”, i.e., identifying structures that only differ for the positions of a few atoms as well as thermally accessible structures within k_BT/unit area of the global minimum, with T = 300 K. Overall, the Genetic Algorithm is more robust with respect to parameter choice and in success rate, while the Basin Hopping method occasionally exhibits some advantages in speed of convergence. In line with previous studies, the results confirm that robustness, success, and speed of convergence of either approach are strongly influenced by how much the trial moves tend to preserve favorable bonding patterns once these appear.

Analysis of Spatial and Temporal Variability in Libya-4 with Landsat 8 and Sentinel-2 Data for Optimized Ground Target Location

Pseudo-Invariant Calibration Sites (PICS) have been widely used by the remote sensing community in recent decades for post-launch absolute calibration, cross-calibration, and the monitoring of radiometric stability. The Committee on Earth Observation Satellites (CEOS) has established several official PICS for these purposes. Of these, Libya-4 is the most commonly used, due to its high uniformity and stability. The site was chosen as a large-area site for medium resolution sensors, and with high-resolution sensors now common, smaller sites are being identified. This work has identified an improved area of interest (AOI) within Libya-4 by using combined Landsat 8 and Sentinel 2 data. The Optimized Ground Target (OGT) was determined by calculating the coefficient of variation along with the use of a quasi-Newton optimization algorithm combined with the Basin–Hopping global optimization technique to constrain a search area small enough to perform a final brute-force refinement. The Coefficient of Variation CV of the proposed OGT is significantly lower than that in the original CEOS area, with differences between the CV of both zones in the order of 1% in the visible near-infrared (VNIR) bands. This new AOI has the potential to improve the cross-calibration between high-resolution sensors using the PICS methodology through an OGT with more homogeneous and stable characteristics.

Sphere Encapsulated Monte Carlo: Obtaining Minimum Energy Configurations of Large Aromatic Systems

We introduce a simple global optimization approach that is able to find minimum energy configurations of clusters containing aromatic molecules. The translational and rotational perturbations required in Monte Carlo-based methods often lead to unrealistic configurations within which two or more molecular rings intersect, causing many of the computational steps to be rejected and the optimization process to be inefficient. Here we develop a modification of the basin-hopping global optimization procedure tailored to tackle problems with intersecting molecular rings. Termed the Sphere Encapsulated Monte Carlo (SEMC) method, this method introduces sphere-based rearrangement and minimization steps at each iteration, and its performance is shown through the exploration of potential energy landscapes of polycyclic aromatic hydrocarbon (PAH) clusters, systems of interest in combustion and astrophysics research. The SEMC method provides clusters that are accurate to 5% mean difference of the minimum energy at a 10-fold speed up compared to previous work using advanced molecular dynamics simulations. Importantly, the SEMC method captures key structural characteristics and molecular size partitioning trends as measured by the molecular radial distances and coordination numbers. The advantages of the SEMC method are further highlighted in its application to previously unstudied heterogeneous PAH clusters.

Modeling and simulation of protein-surface interactions: achievements and challenges

Understanding protein-inorganic surface interactions is central to the rational design of new tools in biomaterial sciences, nanobiotechnology and nanomedicine. Although a significant amount of experimental research on protein adsorption onto solid substrates has been reported, many aspects of the recognition and interaction mechanisms of biomolecules and inorganic surfaces are still unclear. Theoretical modeling and simulations provide complementary approaches for experimental studies, and they have been applied for exploring protein-surface binding mechanisms, the determinants of binding specificity towards different surfaces, as well as the thermodynamics and kinetics of adsorption. Although the general computational approaches employed to study the dynamics of proteins and materials are similar, the models and force-fields (FFs) used for describing the physical properties and interactions of material surfaces and biological molecules differ. In particular, FF and water models designed for use in biomolecular simulations are often not directly transferable to surface simulations and vice versa. The adsorption events span a wide range of time- and length-scales that vary from nanoseconds to days, and from nanometers to micrometers, respectively, rendering the use of multi-scale approaches unavoidable. Further, changes in the atomic structure of material surfaces that can lead to surface reconstruction, and in the structure of proteins that can result in complete denaturation of the adsorbed molecules, can create many intermediate structural and energetic states that complicate sampling. In this review, we address the challenges posed to theoretical and computational methods in achieving accurate descriptions of the physical, chemical and mechanical properties of protein-surface systems. In this context, we discuss the applicability of different modeling and simulation techniques ranging from quantum mechanics through all-atom molecular mechanics to coarse-grained approaches. We examine uses of different sampling methods, as well as free energy calculations. Furthermore, we review computational studies of protein-surface interactions and discuss the successes and limitations of current approaches.

The CO oxidation mechanism on the W(111) surface and the W helical nanowire investigated by the density functional theory calculation

Two CO oxidation reactions (CO + O2 → CO2 + O and CO + O → CO2) were considered in the Eley-Rideal (ER) reaction mechanism. These oxidation processes on the W(111) surface and the W helical nanowire were investigated by the density functional theory (DFT) calculation. The stable adsorption sites of O2 and O as well as their adsorption energies were obtained first. In order to understand the catalytic properties of the W helical nanowire, the Fukui function and local density of state (LDOS) profiles were determined. The nudged elastic band (NEB) method was applied to locate transition states and minimum energy pathways (MEPs) of CO oxidation processes on the W helical nanowire and on the W(111) surface. In this study, we have demonstrated that the catalytic ability of the W helical nanowire is superior to that of the W(111) surface for CO oxidation.

Rapid sampling of local minima in protein energy surface and effective reduction through a multi-objective filter

BACKGROUND

Many problems in protein modeling require obtaining a discrete representation of the protein conformational space as an ensemble of conformations. In ab-initio structure prediction, in particular, where the goal is to predict the native structure of a protein chain given its amino-acid sequence, the ensemble needs to satisfy energetic constraints. Given the thermodynamic hypothesis, an effective ensemble contains low-energy conformations which are similar to the native structure. The high-dimensionality of the conformational space and the ruggedness of the underlying energy surface currently make it very difficult to obtain such an ensemble. Recent studies have proposed that Basin Hopping is a promising probabilistic search framework to obtain a discrete representation of the protein energy surface in terms of local minima. Basin Hopping performs a series of structural perturbations followed by energy minimizations with the goal of hopping between nearby energy minima. This approach has been shown to be effective in obtaining conformations near the native structure for small systems. Recent work by us has extended this framework to larger systems through employment of the molecular fragment replacement technique, resulting in rapid sampling of large ensembles.

METHODS

This paper investigates the algorithmic components in Basin Hopping to both understand and control their effect on the sampling of near-native minima. Realizing that such an ensemble is reduced before further refinement in full ab-initio protocols, we take an additional step and analyze the quality of the ensemble retained by ensemble reduction techniques. We propose a novel multi-objective technique based on the Pareto front to filter the ensemble of sampled local minima.

RESULTS AND CONCLUSIONS

We show that controlling the magnitude of the perturbation allows directly controlling the distance between consecutively-sampled local minima and, in turn, steering the exploration towards conformations near the native structure. For the minimization step, we show that the addition of Metropolis Monte Carlo-based minimization is no more effective than a simple greedy search. Finally, we show that the size of the ensemble of sampled local minima can be effectively and efficiently reduced by a multi-objective filter to obtain a simpler representation of the probed energy surface.

Basin Hopping as a General and Versatile Optimization Framework for the Characterization of Biological Macromolecules

Since its introduction, the basin hopping (BH) framework has proven useful for hard nonlinear optimization problems with multiple variables and modalities. Applications span a wide range, from packing problems in geometry to characterization of molecular states in statistical physics. BH is seeing a reemergence in computational structural biology due to its ability to obtain a coarse-grained representation of the protein energy surface in terms of local minima. In this paper, we show that the BH framework is general and versatile, allowing to address problems related to the characterization of protein structure, assembly, and motion due to its fundamental ability to sample minima in a high-dimensional variable space. We show how specific implementations of the main components in BH yield algorithmic realizations that attain state-of-the-art results in the context of ab initio protein structure prediction and rigid protein-protein docking. We also show that BH can map intermediate minima related with motions connecting diverse stable functionally relevant states in a protein molecule, thus serving as a first step towards the characterization of transition trajectories connecting these states.

Searching for low-energy structures of nanoparticles: a comparison of different methods and algorithms

Nanoparticles can have unusual, low symmetry or non-crystalline shapes. Since structure determines nanoparticle physical and chemical properties, many efforts have been devoted to predict what are the most stable structural motifs depending on cluster size and composition. The global optimization of the 3N-dimensional potential energy surface of a nanocluster is nevertheless a very difficult computational problem. Here we depict the scenery of the global optimization strategies applied to the study of nanoclusters, focusing on genetic and Basin-hopping approaches. Moreover, several strategies to improve Basin-hopping efficiency are discussed and compared through the optimization of test-systems with different size and composition.