Basin-hopping Research Articles

Growth of rare gases on coronene

We study the growth of rare gases (Rg) Ne, Ar and Kr on coronene (Cor) molecules, Cor-(Rg)\(_N\). The study is taken up to sizes N=60, and we show the global energy minima for those clusters. Improved Lennard-Jones and atom-bond potentials are used to represent the Rg-Rg and Rg-Cor interactions, respectively. The Basin-Hopping (BH) global optimization technique is employed to locate the putative global energy minimum structures. Results are presented for Cor-(Ne), Cor-(Ar) and Cor-(Kr) systems. Both classical Cor-(Ar)\(_N\) and Cor-(Kr)\(_N\) clusters present the same “magic numbers” for N=3, 6, 10, 14, 19 and 38. This last number marks the first layer of solvation. For Cor-(Ne)\(_N\) clusters, we consider quantum effects adding the zero-point energy (ZPE) into the classical potential energy minima (BH-ZPE). This semiclassical approximation is compared with quantum diffusion Monte Carlo (DMC) calculations up to N=20, obtaining a good agreement and showing that this approximation works reasonably well. In this BH-ZPE approach, high stability configurations for Cor-(Ne)\(_N\) clusters are obtained at N=6, 14, 42, 51 and 57. However, we have not found any evidence of a first solvation layer using either the semiclassical BH-ZPE or the classical BH one.

A Preliminary Impulsive Trajectory Design for (99942) Apophis Rendezvous Mission

In this study, a preliminary trajectory design is conducted for a conceptual spacecraft mission to a near-Earth asteroid (NEA) (99942) Apophis, which is expected to pass by Earth merely 32,000 km from the Earth’s surface in 2029. This close approach event will provide us with a unique opportunity to study changes induced in asteroids during close approaches to massive bodies, as well as the general properties of NEAs. The conceptual mission is set to arrive at and rendezvous with Apophis in 2028 for an advanced study of the asteroid, and some near-optimal (in terms of fuel consumption) trajectories under this mission architecture are to be investigated using a global optimization algorithm called monotonic basin hopping. It is shown that trajectories with a single swing-by from Venus or Earth, or even simpler ones without gravity assist, are the most feasible. In addition, launch opportunities in 2029 yield another possible strategy of leaving Earth around the 2029 close approach event and simply following the asteroid thereafter, which may be an alternative fuel-efficient option that can be adopted if advanced studies of Apophis are not required.

Application of Optimization Algorithms in Clusters.

The structural characterization of clusters or nanoparticles is essential to rationalize their size and composition-dependent properties. As experiments alone could not provide complete picture of cluster structures, so independent theoretical investigations are needed to find out a detail description of the geometric arrangement and corresponding properties of the clusters. The potential energy surfaces (PES) are explored to find several minima with an ultimate goal of locating the global minima (GM) for the clusters. Optimization algorithms, such as genetic algorithm (GA), basin hopping method and its variants, self-consistent basin-to-deformed-basin mapping, heuristic algorithm combined with the surface and interior operators (HA-SIO), fast annealing evolutionary algorithm (FAEA), random tunneling algorithm (RTA), and dynamic lattice searching (DLS) have been developed to solve the geometrical isomers in pure elemental clusters. Various model or empirical potentials (EPs) as Lennard–Jones (LJ), Born–Mayer, Gupta, Sutton–Chen, and Murrell–Mottram potentials are used to describe the bonding in different type of clusters. Due to existence of a large number of homotops in nanoalloys, genetic algorithm, basin-hopping algorithm, modified adaptive immune optimization algorithm (AIOA), evolutionary algorithm (EA), kick method and Knowledge Led Master Code (KLMC) are also used. In this review the optimization algorithms, computational techniques and accuracy of results obtained by using these mechanisms for different types of clusters will be discussed.

Analysis of the Ordering Effects in Anthraquinone Thin Films and Its Potential Application for Sodium Ion Batteries.

The ordering effects in anthraquinone (AQ) stacking forced by thin-film application and its influence on dimer solubility and current collector adhesion are investigated. The structural characteristics of AQ and its chemical environment are found to have a substantial influence on its electrochemical performance. Computational investigation for different charged states of AQ on a carbon substrate obtained via basin hopping global minimization provides important insights into the physicochemical thin-film properties. The results reveal the ideal stacking configurations of the individual AQ-carrier systems and show ordering effects in a periodic supercell environment. The latter reveals the transition from intermolecular hydrogen bonding toward the formation of salt bridges between the reduced AQ units and a stabilizing effect upon the dimerlike rearrangement, while the strong surface–molecular interactions in the thin-film geometries are found to be crucial for the formed dimers to remain electronically active. Both characteristics, the improved current collector adhesion and the stabilization due to dimerization, are mutual benefits of thin-film electrodes over powder-based systems. This hypothesis has been further investigated for its potential application in sodium ion batteries. Our results show that AQ thin-film electrodes exhibit significantly better specific capacities (233 vs 87 mAh g–1 in the first cycle), Coulombic efficiencies, and long-term cycling performance (80 vs 4 mAh g–1 after 100 cycles) over the AQ powder electrodes. By augmenting the experimental findings via computational investigations, we are able to suggest design strategies that may foster the performance of industrially desirable powder-based electrode materials.

Structure and photochemistry of a potential precursor of circumstellar dust: The optical spectrum of Si4C2+

Mixed silicon carbide clusters are important components of circumstellar shells and their optical properties are fundamental for modelling the chemistry involved in the evolution of dust particles. Herein, we report the ultraviolet photodissociation (UVPD) spectrum of mass-selected Si4C2+ cations obtained in the 208–330 nm range (3.8–6.0 eV) in a quadrupole/time-of-flight tandem mass spectrometer coupled to a laser desorption source operating with a SiC rod and a broadly tuneable optical parametric oscillator laser. The UVPD spectrum is observed in the two lowest-energy fragment channels, corresponding to dominant loss of atomic Si at low energy and the rather stable Si2C molecule at high energy. The UVPD spectrum is analyzed by quantum chemical calculations at two levels of density functional theory (CAM-B3LYP, M11) to determine the structures, energies, electronic spectra, and fragmentation energies of the lowest-energy isomers. To locate these isomers on the multidimensional potential energy surface, basin hopping is employed as global optimization approach. The UVPD spectrum is consistent with the optical absorption spectrum computed for the two lowest-energy isomers, one of which is reported for the first time.

Exploration and Optimization in Crystal Structure Prediction: Combining Basin Hopping with Quasi-Random Sampling.

We describe the implementation of a Monte Carlo basin hopping (BH) global optimization procedure for the prediction of molecular crystal structures. The BH method is combined with quasi-random (QR) structure generation in a hybrid method for crystal structure prediction, QR-BH, which combines the low-discrepancy sampling provided by QR sequences with BH efficiency at locating low energy structures. Through tests on a set of single-component molecular crystals and co-crystals, we demonstrate that QR-BH provides faster location of low energy structures than pure QR sampling, while maintaining the efficient location of higher energy structures that are important for identifying important polymorphs.

Global optimization of chemical cluster structures: Methods, applications, and challenges

AbstractChemical clusters are relevant to many applications in catalysis, separations, materials, and energy sciences. Experimentally, the structure of clusters is difficult to determine, but it is very important in understanding their chemistry and properties. Computational methods can be used to examine cluster structure, however finding the most stable structure is not simple, particularly as the cluster size increases. Global optimization techniques have long been used to tackle the problem of the most stable structure, but such approaches would have to look for a global minimum, while sampling local minima over the whole potential energy surface as well. In this review, the state‐of‐the‐art theory of global optimization theory is summarized. First, the definition, significance, relation to experiments, and a brief history of global optimization is presented. We then discuss, in more detail, three versatile global optimization methods: the basin hopping, the artificial bee colony algorithm, and the genetic algorithm. We close with some representative application examples of global optimization of clusters since 2016 and the challenges, open questions and opportunities in this field.

Enantiomeric Transitions in the Chiral Cluster Au15 Studied by a Reaction Coordinate Deduced from Molecular Dynamics Simulations

A recently developed modified basin hopping (MBH) optimization algorithm, combined with an energy function calculated by the semiempirical density functional tight-binding (DFTB) theory, was applied to determine the lowest-energy structures of Aun clusters with size n = 3-20. It was predicted from the DFTB/MBH optimization algorithm calculations that clusters Au10, Au15, and Au18 exhibit chiral properties; i.e., each of these three clusters possesses the same energy value and associated with it are two nonsuperposable mirror-image clusters. In the potential energy landscape, there thus exist multidimensional barriers separating the two enantiomers, and this lowest-energy double-well morphology is surrounded by potential-energy minima of higher energies. In this paper, we have chosen to study the chiral cluster Au15 by employing an isothermal Brownian-type molecular dynamics simulation to discern in greater detail its conformational transition from one enantiomer, say left, to its right counterpart. To facilitate our analysis of the simulation data, we transpose the multidimensional configurational space description to a lower dimensional collective variable (CV) space spanned by two geometry-relevant CVs. The thermally driven progression and mechanism of enantiomeric transitions between the left and right enantiomers will be our main focus, and the strategy is to dissect the time development of the CVs collected from different sets of independent simulation runs. From simulation data, we found that an understanding of the dynamics of enantiomeric transitions needs first to seek out the left and right enantiomers through a molecular modeling and visualizing program, then to ferret out and identify between the left and right enantiomers a symmetrical structure, and finally to define from the latter a reaction coordinate. We showed in this work that this single reaction coordinate is predictive in unraveling the left ⇌ right enantiomeric transition events, providing a specific inkling of the transition time span and its associated distribution which can be checked further for its reasonableness by the autocorrelation function and a vibrational analysis, all of which shed light on the mechanisms of transition.

Global Elucidation of Self-Consistent Field Solution Space Using Basin Hopping.

Reliable global elucidation of (subsets of) self-consistent field solutions is required for continued development and application of computational approaches that utilize these solutions as reference wavefunctions. We report the derivation and implementation of a stochastic approach to perform global elucidation of self-consistent field solutions by exploiting the connection between global optimization and global elucidation problems. We discuss the design of the algorithm through combining basin-hopping search algorithms with a Lie algebraic approach to linearize self-consistent field solution space, while also allowing preservation of desired spin-symmetry properties of the wavefunction. The performance of the algorithm is demonstrated on minimal basis C2v H4 due to its use as a model system for global self-consistent field solution exploration algorithms. Subsequently, we show that the model is capable of successfully identifying low-lying self-consistent solutions of benzene and NO2 with polarized double-zeta and triple-zeta basis sets and examine the properties of these solutions.

Novel structural motifs: Chiral AgCu nanoalloys with chiral Cu core

Chiral icosahedra have been previously reported for the core-shell AgCu nanoalloys. The chirality in these structures is due to the rearrangement of the Ag shell with achiral Cu core. In the current work, new type of chiral core-shell AgCu nanoalloys have been identified through a combination of growth simulations and global optimization searches using the basin hopping (BH) algorithm. These new AgCu nanoalloys, in contrast, have inherently chiral cores and belong to three different point group symmetries: T, D3, and C5. The energetic stability of these new chiral nanoalloys have been compared with other structures having chiral or anti-Mackay Ag shells with achiral Cu cores. The stability has also been studied with respect to the varying chemical composition at a fixed size of the nanoalloy. Finally, the analysis of the core-shell energetics reveal significant differences among the different types of structural motifs.

Effects of Hydration on the Conformational Behavior of Flexible Molecules with Two Charge Centers.

The hydration behavior of alkyl-diammonium di-cations and alkyl-dicarboxylate di-anions, of varying alkyl chain length, was examined using basin-hopping (BH) global optimization techniques. For every di-ion investigated, a conformational transition from linear to folded is observed at a critical hydration number, n*, specific to each di-ion. A stepwise hydration study has been undertaken for alkyl-dicarboxylate di-anions in finite water clusters containing 1-12 water molecules, and low-energy structures have been examined for larger water clusters. An even number of carbons in the alkyl chain gives rise to more stable conformations in unhydrated, implicitly solvated, and explicitly solvated conditions. This work provides valuable information on how the hydration of ammonium and carboxylate ions influence larger biomolecules' conformations.

New Algorithms in RNA Structure Prediction Based on BHG

There are some NP-hard problems in the prediction of RNA structures. Prediction of RNA folding structure in RNA nucleotide sequence remains an unsolved challenge. We investigate the computing algorithm in RNA folding structural prediction based on extended structure and basin hopping graph, it is a computing mode of basin hopping graph in RNA folding structural prediction including pseudoknots. This study presents the predicting algorithm based on extended structure, it also proposes an improved computing algorithm based on barrier tree and basin hopping graph, which are the attractive approaches in RNA folding structural prediction. Many experiments have been implemented in Rfam14.1 database and PseudoBase database, the experimental results show that our two algorithms are efficient and accurate than the other existing algorithms.

Basin Hopping Genetic Algorithm for Global Optimization of PtCo Clusters.

In general, searching the lowest-energy structures is considerably more time-consuming for bimetallic clusters than for monometallic ones because of the presence of an increasing number of homotops and geometrical isomers. In this article, a basin hopping genetic algorithm (BHGA), in which the genetic algorithm is implanted into the basin hopping (BH) method, is proposed to search the lowest-energy structures of 13-, 38-, and 55-atom PtCo bimetallic clusters. The results reveal that the proposed BHGA, as compared with the standard BH method, can markedly improve the convergent speed for global optimization and the possibility for finding the global minima on the potential energy surface. Meanwhile, referencing the monometallic structures in initializations may further raise the searching efficiency. For all the optimized clusters, both the excess energy and the second difference of the energy are calculated to examine their relative stabilities at different atomic ratios. The bond order parameter, the similarity function, and the shape factor are also adopted to quantitatively characterize the cluster structures. The results indicate that the 13- and the 55-atom systems tend to be icosahedral despite different degrees of lattice distortions. In contrast, for the 38-atom system, Pt10Co28, Pt11Co27, Pt17Co21, Pt19Co19, Pt20Co18, and Pt30Co8 tend to be disordered, while Pt21Co17 presents a defected face-centered cubic (fcc) structure, and the remaining clusters are perfect fcc. The methodology and results of this work have referential significance to the exploration of other alloy clusters.

Global Optimization of Adsorbate Covered Supported Cluster Catalysts: The Case of Pt7H10CH3 on α‐Al2O3

AbstractDetermining structures of supported sub‐nanometer catalytic clusters is important for finding binding sites, active sites, and reaction mechanisms. In realistic conditions, the cluster may be covered with adsorbed reactants and intermediates, which strongly affect the structure of the cluster compared to the low coverage regime. The global optimization of supported adsorbate‐covered clusters is not possible with existing methods. We present a customized Basin Hopping (BH) approach, with a core (metal cluster)‐shell (adsorbates) separation scheme, and perform first applications to the search of low‐energy isomers of Pt7/α‐Al2O3 at high hydrogen coverage (10H). The presence of adsorbates significantly alters the low‐energy isomers compared to bare Pt7/α‐Al2O3. Molecular dynamics simulations additionally show the different time‐scales associated with the mobility of H and Pt atoms. The revised BH method with core‐shell separation presents key advantages for the structural exploration of adsorbate‐covered supported catalysts, relevant to realistic catalytic conditions.

Efficient Model Points Selection in Insurance by Parallel Global Optimization Using Multi CPU and Multi GPU

In the insurance sector, Asset Liability Management refers to the joint management of the assets and liabilities of a company. The liabilities mainly consist of the policies portfolios of the insurance company, which usually contain a large amount of policies. In the article, the authors mainly develop a highly efficient automatic generation of model points portfolios to represent much larger real policies portfolios. The obtained model points portfolio must retain the market risk properties of the initial portfolio. For this purpose, the authors propose a risk measure that incorporates the uncertain evolution of interest rates to the portfolios of life insurance policies, following Ferri (Optimal model points portfolio in life, 2019, arXiv:1808.00866). This problem can be formulated as a minimization problem that has to be solved using global numerical optimization algorithms. The cost functional measures an appropriate distance between the original and the model point portfolios. In order to solve this problem in a reasonable computing time, sequential implementations become prohibitive, so that the authors speed up the computations by developing a high performance computing framework that uses hybrid architectures, which consist of multi CPUs together with accelerators (multi GPUs). Thus, in graphic processor units (GPUs) the evaluation of the cost function is parallelized, which requires a Monte Carlo method. For the optimization problem, the authors compare a metaheuristic stochastic differential evolution algorithm with a multi path variant of hybrid global optimization Basin Hopping algorithms, which combines Simulated Annealing with gradient local searchers (Ferreiro et al. in Appl Math Comput 356:282–298, 2019a). Both global optimizers are parallelized in a multi CPU together with a multi GPU setting.

What Electronic Structure Method Can Be Used in the Global Optimization of Nanoclusters?

The problem of obtaining the spatial structure of nanoclusters is known to be very difficult due to the large number of local minima associated with their potential energy surfaces (isomers). In global optimization approaches, such as basin hopping and genetic algorithms, the problem is normally tackled by first using a low-level and affordable method to evaluate the energy. Afterward, the putative global minimum (and often a few others) is refined with calculations using higher level methods and larger basis sets. There is no guarantee, however, that the structure obtained at the lower level method will be the global minimum at the refined one. In this work, we have performed benchmark coupled cluster calculations at the complete basis set limit for a large number of different isomers of representative clusters of third row elements. Such calculations are then employed to check the hypothesis that lower level methods can be used in the global optimization with reliable results. For this, we have developed a methodology that allows us to compare a large number of minima obtained at different calculation levels. The results indicate that, if the global optimization is capable of reaching not only the global minimum but also a reduced number of low lying structures, most of the tested density functional theory (DFT) functionals are good choices, with emphasis on TPSSh. Besides giving a more solid ground to this commonly used approach, this work helps guiding such global optimizations. The use of the MP2 method and several scaled variants is also assessed, from where it is concluded that the scaled variants yield better results than standard MP2 or DFT approaches, except for one system where a large number of van der Waals structures exist.

Electrostatics-Assisted Building-Up Procedure for Capturing Energy Minima of Metal Clusters: Test Case of Agn Clusters.

Global geometry optimization of metal clusters is an important problem in nanophysics. The starting geometries of the clusters generated with empirical or other model potentials are generally optimized further by density functional theory (DFT)-based energy minimization. For this purpose, several algorithms such as simulated annealing, genetic algorithms, basin hopping, etc. are used. Our building-up procedure generates putative lower-energy structures of metal (M) clusters, Mn+1, Mn+2, etc., by anchoring one or more metal atoms in the vicinity of the minima of the molecular electrostatic potential (MESP) of Mn. Here, we report an application of this method to Agn clusters, for 5 ≤ n ≤ 20, followed up by DFT-based geometry optimization, generating several lower-energy structures than those reported in the literature. New low-energy isomers are obtained by applying the same procedure to the test case of mixed-metal clusters, NinAgm, for n + m = 4 and 5. In conclusion, our MESP-based building-up procedure offers a new general methodology for generating lower-energy geometries of metal clusters.

Augmenting Basin-Hopping With Techniques From Unsupervised Machine Learning: Applications in Spectroscopy and Ion Mobility.

Evolutionary algorithms such as the basin-hopping (BH) algorithm have proven to be useful for difficult non-linear optimization problems with multiple modalities and variables. Applications of these algorithms range from characterization of molecular states in statistical physics and molecular biology to geometric packing problems. A key feature of BH is the fact that one can generate a coarse-grained mapping of a potential energy surface (PES) in terms of local minima. These results can then be utilized to gain insights into molecular dynamics and thermodynamic properties. Here we describe how one can employ concepts from unsupervised machine learning to augment BH PES searches to more efficiently identify local minima and the transition states connecting them. Specifically, we introduce the concepts of similarity indices, hierarchical clustering, and multidimensional scaling to the BH methodology. These same machine learning techniques can be used as tools for interpreting and rationalizing experimental results from spectroscopic and ion mobility investigations (e.g., spectral assignment, dynamic collision cross sections). We exemplify this in two case studies: (1) assigning the infrared multiple photon dissociation spectrum of the protonated serine dimer and (2) determining the temperature-dependent collision cross-section of protonated alanine tripeptide.

Adaptive multi-population inflationary differential evolution

This paper proposes a multi-population adaptive version of inflationary differential evolution algorithm. Inflationary differential evolution algorithm (IDEA) combines basic differential evolution (DE) with some of the restart and local search mechanisms of Monotonic Basin Hopping (MBH). In the adaptive version presented in this paper, the DE parameters { CR} and F are automatically adapted together with the size of the local restart bubble and the number of local restarts of MBH. The proposed algorithm implements a simple but effective mechanism to avoid multiple detections of the same local minima. The novel mechanism allows the algorithm to decide whether to start or not a local search. The algorithm has been extensively tested over more than fifty test functions from the competitions of the Congress on Evolutionary Computation (CEC), CEC 2005, CEC 2011 and CEC 2014, and compared against all the algorithms participating in those competitions. For each test function, the paper reports best, worst, median, mean and standard deviation values of the best minimum found by the algorithm. Comparisons with other algorithms participating in the CEC competitions are presented in terms of relative ranking, Wilcoxon tests and success rates. For completeness, the paper presents also the single population adaptive IDEA, that can adapt only textit{CR} and F, and shows that this simpler version can outperform the multi-population one if the radius of the restart bubble and the number of restarts are properly chosen.

Modified Particle Swarm Optimization Algorithms for the Generation of Stable Structures of Carbon Clusters, Cn (n = 3-6, 10).

Particle Swarm Optimization (PSO), a population based technique for stochastic search in a multidimensional space, has so far been employed successfully for solving a variety of optimization problems including many multifaceted problems, where other popular methods like steepest descent, gradient descent, conjugate gradient, Newton method, etc. do not give satisfactory results. Herein, we propose a modified PSO algorithm for unbiased global minima search by integrating with density functional theory which turns out to be superior to the other evolutionary methods such as simulated annealing, basin hopping and genetic algorithm. The present PSO code combines evolutionary algorithm with a variational optimization technique through interfacing of PSO with the Gaussian software, where the latter is used for single point energy calculation in each iteration step of PSO. Pure carbon and carbon containing systems have been of great interest for several decades due to their important role in the evolution of life as well as wide applications in various research fields. Our study shows how arbitrary and randomly generated small Cn clusters (n = 3–6, 10) can be transformed into the corresponding global minimum structure. The detailed results signify that the proposed technique is quite promising in finding the best global solution for small population size clusters.