Basin-hopping Approach Research Articles

Global optimisation of hydroxylated silica clusters: A cascade Monte Carlo Basin Hopping approach

We report on a global optimisation study of hydroxylated silica nanoclusters (SiO2)M·(H2O)N with sizes M=6, 8, 10 12, and for each size with a variable number of dissociatively chemisorbed water molecules (N=1, 2, 3…). Due to the high structural complexity of these systems and the associated ruggedness of the underlying potential energy landscape, we employ a “cascade” global optimisation approach. Specifically, we use Monte Carlo Basin Hopping (MCBH) where for each step we employ two energy minimisations with: (i) a lightly parameterised but computationally efficient interatomic potential (IP) which does not distinguish between H-bonded conformational isomers, and then (ii) a more sophisticated IP which accounts for polarisation and H-bonding. Final energies from the MCBH search are then refined with optimisations using density functional theory. The reliability of our approach is first established via comparison with previously reported results for the (SiO2)8·(H2O)N case, and then applied to the M=6, 10 and 12 systems. For all systems studied our results follow the trend in hydroxylation energy versus N, whereby the energy gain with hydroxylation is found to level off at a point where the average tetrahedral distortion of the SiO4 centres is minimised. This optimal hydroxylation point is further found to follow an inverse power law with increasing cluster size (M) with an exponent close to −2/3, further confirming work in previous studies for other cluster sizes.

Coronene molecules in helium clusters: Quantum and classical studies of energies and configurations.

Coronene-doped helium clusters have been studied by means of classical and quantum mechanical (QM) methods using a recently developed He-C24H12 global potential based on the use of optimized atom-bond improved Lennard-Jones functions. Equilibrium energies and geometries at global and local minima for systems with up to 69 He atoms were calculated by means of an evolutive algorithm and a basin-hopping approach and compared with results from path integral Monte Carlo (PIMC) calculations at 2 K. A detailed analysis performed for the smallest sizes shows that the precise localization of the He atoms forming the first solvation layer over the molecular substrate is affected by differences between relative potential minima. The comparison of the PIMC results with the predictions from the classical approaches and with diffusion Monte Carlo results allows to examine the importance of both the QM and thermal effects.

Protein structure prediction: assembly of secondary structure elements by basin-hopping.

The prediction of protein tertiary structure from primary structure remains a challenging task. One possible approach to this problem is the application of basin-hopping global optimization combined with an all-atom force field. In this work, the efficiency of basin-hopping is improved by introducing an approach that derives tertiary structures from the secondary structure assignments of individual residues. This approach is termed secondary-to-tertiary basin-hopping and benchmarked for three miniproteins: trpzip, trp-cage and ER-10. For each of the three miniproteins, the secondary-to-tertiary basin-hopping approach successfully and reliably predicts their three-dimensional structure. When it is applied to larger proteins, correctly folded structures are obtained. It can be concluded that the assembly of secondary structure elements using basin-hopping is a promising tool for de novo protein structure prediction.

Protein structure prediction using global optimization by basin-hopping with NMR shift restraints

Computational methods that utilize chemical shifts to produce protein structures at atomic resolution have recently been introduced. In the current work, we exploit chemical shifts by combining the basin-hopping approach to global optimization with chemical shift restraints using a penalty function. For three peptides, we demonstrate that this approach allows us to find near-native structures from fully extended structures within 10,000 basin-hopping steps. The effect of adding chemical shift restraints is that the α and β secondary structure elements form within 1000 basin-hopping steps, after which the orientation of the secondary structure elements, which produces the tertiary contacts, is driven by the underlying protein force field. We further show that our chemical shift-restraint BH approach also works for incomplete chemical shift assignments, where the information from only one chemical shift type is considered. For the proper implementation of chemical shift restraints in the basin-hopping approach, we determined the optimal weight of the chemical shift penalty energy with respect to the CHARMM force field in conjunction with the FACTS solvation model employed in this study. In order to speed up the local energy minimization procedure, we developed a function, which continuously decreases the width of the chemical shift penalty function as the minimization progresses. We conclude that the basin-hopping approach with chemical shift restraints is a promising method for protein structure prediction.

On the stability of “non-magic” endohedrally doped Si clusters: A first-principles sampling study of M${\rm Si}_{16}^+$Si16+ (M = Ti,V,Cr)

Density-functional theory is used to study the geometric and electronic structure of cationic Si(16)(+) clusters with a Ti, V, or Cr dopant atom. Through unbiased global geometry optimization based on the basin-hopping approach, we confirm that a Frank-Kasper polyhedron, with the metal atom at the center, represents the ground-state isomer for all three systems. The endohedral cage geometry is thus stabilized even though only VSi(16)(+) achieves electronic shell closure within the prevalent spherical potential model. Our analysis of the electronic structure traces this diminished role of shell closure for the stabilization back to the adaptive capability of the metal-Si bonding, which is more the result of a complex hybridization than the originally proposed mere formal charge transfer. The resulting flexibility of the metal-Si bond can also help to stabilize "non-magic" cage-dopant combinations, which suggests that a wider range of materials may eventually be cast into this useful geometry for cluster-assembled materials.

Structural richness of ionic binary materials: An exploration of the energy landscape of magnesium oxide

We search for polymorphs of magnesium oxide (MgO) close in energy to the rocksalt global minimum by using variants of the basin hopping approach. Our exploration clearly demonstrates that the energy landscape of this nominally octahedrally coordinated, densely packed solid is much more complicated than suggested by previous work. Specifically, we find that MgO has a dense spectrum of as yet undiscovered low-energy polymorphs, many of which have a much lower density than the rocksalt structure (as also recently shown for tetrahedrally coordinated binary solids (e.g., ZnO) [Phys. Rev. Lett. 104, 175503 (2010)]). Unlike in the case of tetrahedrally coordinated materials, we further find low-energy crystal structures with four-, five-, or six-coordinated atoms. Strikingly, some of these structures also have pores that are arguably large enough for small molecular species to enter, while others are found to be quasi-amorphous. We also discuss the problem of searching for systems that are currently too large to study by basin hopping (or similar approaches) in a tractable fashion, and the implications of our findings for other solids.

Transmembrane Structures for Alzheimer’s Aβ1−42 Oligomers

We model oligomers of the Alzheimer's amyloid β-peptide Aβ(1-42) in an implicit membrane to obtain insight into the mechanism of amyloid toxicity. It has been suggested that Aβ oligomers are the toxic species, causing membrane disruption in neuronal cells due to pore formation. We use basin-hopping global optimization to identify the most stable structures for the Aβ(1-42) peptide monomer and small oligomers up to the octamer inserted into a lipid bilayer. To improve the efficacy of the basin-hopping approach, we introduce a basin-hopping parallel tempering scheme and an oligomer generation procedure. The most stable membrane-spanning structure for the monomer is identified as a β-sheet, which exhibits the typical strand-turn-strand motif observed in NMR experiments. We find ordered β-sheets for the dimer to the hexamer, whereas for the octamer, we observe that the ordered structures separate into distinct tetrameric units that are rotated or shifted with respect to each other. This effect leads to an increase in favorable peptide-peptide interactions, thereby stabilizing the membrane-inserted octamer. On the basis of these results, we suggest that Aβ pores may consist of tetrameric and hexameric β-sheet subunits. These Aβ pore models are consistent with the results of biophysical and biochemical experiments.

Solving the problem of packing equal and unequal circles in a circular container

In this paper we propose a Monotonic Basin Hopping approach and its population-based variant Population Basin Hopping to solve the problem of packing equal and unequal circles within a circular container with minimum radius. Extensive computational experiments have been performed both to analyze the problem at hand, and to choose in an appropriate way the parameter values for the proposed methods. Different improvements with respect to the best results reported in the literature have been detected.

Magic silver cluster on a MgO(100) terrace with defects

The structure and energetics of ${\mathrm{Ag}}_{N}$ clusters $(N=2--10)$ adsorbed on a double vacancy (DV) neutral defect of a MgO(100) terrace are investigated via a density-functional basin-hopping approach. It is found that ${\mathrm{Ag}}_{8}$ is a surface magic cluster from both electronic and structural points of view, i.e., it exhibits enhanced stability with respect to neighboring sizes and a large highest occupied molecular orbital--lowest unoccupied molecular orbital gap. The possibility of synthesizing monodisperse ${\mathrm{Ag}}_{8}∕\mathrm{DV}∕\mathrm{Mg}\mathrm{O}(100)$ clusters is discussed. The first ionization potential, the electron affinity, and the interaction energies with atomic and molecular oxygen are evaluated for the adsorbed Ag clusters, showing that ${\mathrm{Ag}}_{8}$ exhibits appreciable differences in its electronic and chemical properties with respect to neighboring sizes.

Structures of bimetallic clusters

We report an optimization algorithm for studying bimetallic nanoclusters. The algorithm combines two state-of-the-art methods, the genetic algorithm and the basin hopping approach, widely employed in the literature for predicting structures of pure metallic and nonmetallic clusters. To critically test the present algorithm and its use in determining the lowest-energy structures of bimetallic nanoclusters, we apply it to study the bimetallic clusters Cu(n)Au(38-n) (0< or =n< or =38). It is predicted that the Au atoms, being larger in size than the Cu atoms, prefer to occupy surface sites showing thus the segregating behavior. As the atom fraction of Cu increases, the bimetallic cluster Cu(n)Au(38-n), as a whole, first takes on an amorphous structure and is followed by dramatic changes in structure with the Cu atoms revealing hexagonal, then assuming pentagonal, and finally shifting to octahedral symmetry in the Cu-rich range.

Energy landscapes and properties of biomolecules

Thermodynamic and dynamic properties of biomolecules can be calculated using a coarse-grained approach based upon sampling stationary points of the underlying potential energy surface. The superposition approximation provides an overall partition function as a sum of contributions from the local minima, and hence functions such as internal energy, entropy, free energy and the heat capacity. To obtain rates we must also sample transition states that link the local minima, and the discrete path sampling method provides a systematic means to achieve this goal. A coarse-grained picture is also helpful in locating the global minimum using the basin-hopping approach. Here we can exploit a fictitious dynamics between the basins of attraction of local minima, since the objective is to find the lowest minimum, rather than to reproduce the thermodynamics or dynamics.