Basin-hopping Algorithm Research Articles

The chemical ordering and local pressure dependence for truncated octahedron PdAuRh nanoalloys

The optimal chemical ordering configurations of 38-atom trimetallic Pd n Au(32−n)Rh6 nanoalloys with truncated octahedron (TO) geometry were determined through Monte Carlo Basin-Hopping algorithm employing the Gupta potential, followed by local relaxations. Variations in mixing energy were assessed to compare relative stability, revealing the lowest excess energy at Pd16Au16Rh6 composition at the Gupta level. Furthermore, a comprehensive analysis of local atomic pressure was conducted, exploring the factors influencing these pressures.

Pd8 Cluster: Too Small to Melt? A BOMD Study.

The question of whether a solid-liquid phase transition occurs in small clusters poses a fundamental challenge. In this study, we attempt to elucidate this phenomenon through a thorough examination of the thermal behavior and structural stability of Pd8 clusters employing ab initio simulations. Initially, a systematic global search is carried out to identify the various isomers of the Pd8 cluster. This is accomplished by employing an ab initio basin-hopping algorithm and using the PBE/SDD scheme integrated in the Gaussian code. The resulting isomers are further refined through reoptimization using the deMon2k package. To ensure the structural firmness of the lowest-energy isomer, we calculated normal modes. The structural stability as a function of temperature is analyzed through the Born-Oppenheimer molecular dynamics (BOMD) approach. Multiple BOMD trajectories at distinct simulated temperatures are examined with data clustering analysis to determine cluster isomers. This analysis establishes a connection between the potential energy landscape and the simulated temperature. To address the question of cluster melting, canonical parallel-tempering BOMD runs are performed and analyzed with the multiple-histogram method. A broad maximum in the heat capacity curve indicates a melting transition between 500 and 600 K. To further examine this transition, the mean-squared displacement and the pair-distance distribution function are calculated. The results of these calculations confirm the existence of a solid-liquid phase transition, as indicated by the heat capacity curve.

Identifying optimal combinations of synchronous condensers for minimum grid strength compliance

This paper proposes a method for the automatic optimization of the size and location of synchronous condensers (SCs) to meet a minimum grid strength requirement that enables the high penetration of inverter-based resources (IBRs) in a weak network. The grid strength is quantified by the effective short-circuit ratio (ESCR), which is an heuristic index that accounts for the voltage interactions between IBRs. The basin hopping algorithm (BHA) is used in combination with the Nelder–Mead algorithm to minimize the total additional short-circuit contribution from the SCs, subject to a minimum ESCR constraint. It is shown that this optimization problem has several solutions with the minimum values of the objective function lying within a narrow range but different allocation of the SCs’ capacities to the candidate buses. Therefore, the BHA is iteratively applied to identify the area of the search space in which the optimum solutions are located, and additional criteria are proposed to rank the solutions based on cost and reliability attributes. The effectiveness of the proposed approach is shown using a modified 39-bus New England benchmark system in which conventional synchronous generators were replaced by IBRs, thus leading to weak network conditions.

Growth mechanism prediction for nanoparticles via structure matching polymerization.

Exploring structural and component evolution remains a challenging scientific problem for nanoscience. We propose a novel approach called principle of minimization of structure matching polymerization (SMP) change to rapidly explore the global minimum structure on the potential energy surface (PES). The new method can map low-dimensional stable structures to high-dimensional local minima, and this will make it possible for us to study the growth mechanisms of nanoparticles. Some new lowest-energy structures were found by SMP methods for sulfuric acid (SA)-dimethylamine (DMA) systems relative to previous studies. Additionally, we found that the growth process of boron clusters is mainly that the small-size boron clusters are continuously added to large-size boron clusters by structure matching for Bn (n = 2-36) systems, Bm + Bk → Bn, where m + k = n and 1 ≤ k ≤ 3. The SMP approach can greatly improve the search efficiency of other unbiased global optimization algorithms, such as basin-hopping (BH) and genetic algorithm (GA), with an enhancement of up to 19- and 7-fold relative to traditional BH and GA algorithms for searching the global minima of Bn (n = 14-22) systems. The SMP approach is general and flexible and can be applied to different kinds of problems, such as material structure design, crystal structure prediction, and new drug generation.

Hydrogen bond network structures of protonated 2,2,2-trifluoroethanol/ethanol mixed clusters probed by infrared spectroscopy combined with a deep-learning structure sampling approach: the origin of the linear type network preference in protonated fluoroalcohol clusters.

While preferential hydrogen bond network structures of cold protonated alcohol clusters H+(ROH)n are generally switched from a linear type to a cyclic one at n = 4-5, those of protonated 2,2,2-trifluoroethanol (TFE) clusters maintain linear type structures at least in the size range of n = 3-7. To explore the origin of the strong linear type network preference of H+(TFE)n, infrared spectra of protonated mixed clusters H+(TFE)m(ethanol)n (m + n = 5) were measured. An efficient structure sampling technique using parallelized basin-hopping algorithms and deep-learning neural network potentials is developed to search for essential isomers of the mixed clusters. Vibrational simulations based on the harmonic superposition approximation were compared with the observed spectra to identify the major isomer component at each mixing ratio. It was found that the formation of the cyclic structure occurs only in n ≥ 3 of the mixed clusters, in which the proton solvating sites and the double acceptor site are occupied by ethanol. The crucial role of the stability of the double acceptor site in the cyclic structure formation is discussed.

Fast and effortless computation of profile likelihoods using CONNECT

Abstract The frequentist method of profile likelihoods has recently received renewed attention in the field of cosmology. This is because the results of inferences based on the latter may differ from those of Bayesian inferences, either because of prior choices or because of non-Gaussianity in the likelihood function. Consequently, both methods are required for a fully nuanced analysis. However, in the last decades, cosmological parameter estimation has largely been dominated by Bayesian statistics due to the numerical complexity of constructing profile likelihoods, arising mainly from the need for a large number of gradient-free optimisations of the likelihood function. In this paper, we show how to accommodate the computational requirements of profile likelihoods using the publicly available neural network framework connect together with a novel modification of the gradient-based basin-hopping optimisation algorithm. Apart from the reduced evaluation time of the likelihood due to the neural network, we also achieve an additional speed-up of 1–2 orders of magnitude compared to profile likelihoods computed with the gradient-free method of simulated annealing, with excellent agreement between the two. This allows for the production of typical triangle plots normally associated with Bayesian marginalisation within cosmology (and previously unachievable using likelihood maximisation because of the prohibitive computational cost). We have tested the setup on three cosmological models: the ΛCDM model, an extension with varying neutrino mass, and finally a decaying cold dark matter model. Given the default precision settings in connect, we achieve a high precision in χ2 with a difference to the results obtained by class of Δχ2 ≈ 0.2 (and, importantly, without any bias in inferred parameter values) — easily good enough for profile likelihood analyses.

Adaptive warehouse storage location assignment with considerations to order-picking efficiency and worker safety

ABSTRACT Smart warehouses require software-based decision-making tools to manage the receiving, storing, and picking of products. A major challenge in achieving efficient operations is deciding where to store products associated with incoming orders. The storage location assignment problem (SLAP) is more complex in large-size warehouses due to several functional objectives and numerous possible shelving solutions. This paper introduces an artificial intelligence algorithm that seeks to find an acceptable solution to SLAP with presented linear and nonlinear objective functions. The near-optimal technique exploits basin-hopping and simulated-annealing algorithms to find a solution when considering four functional objectives including worker safety, which has not been optimized using similar approaches. The algorithm is experimentally evaluated, and results demonstrate that reasonablely achieved solutions are comparable to those obtained by well-known existing solvers. Furthermore, the problem could be solved with non-linear objectives which is beyond the commercial solvers’ like SCIP capability.

Comparison of Taboo Search Methods for Atomic Cluster Global Optimization with a Basin-Hopping Algorithm.

The basin-hopping algorithm (BHA) allows for the efficient exploration of atomic cluster potential energy surfaces by random perturbations in configuration space, followed by energy minimizations. Here, the taboo search method is incorporated to prevent the search from revisiting recently visited regions of the search space. Two taboo search modes are implemented, one mode resets the search to random coordinates upon encountering the taboo region, while the other simply rejects any proposed move into the taboo region. These two modes are tested and compared on a variety of potential energy surfaces─several clusters where atomic interactions are described by the Lennard-Jones potential, and Au55 where a semi-empirical tight binding potential is used to describe atomic interactions. Some differences in performance between the two taboo search modes were noted for LJ38 and Au55, with the mode that rejects all hops into the taboo region performing better, offering a means to improve the efficiency of the BHA for multifunnel systems. However, both taboo search modes failed to significantly improve performance on multifunnel systems where more than two funnels were present in the system.

Incorporating design consistency into risk-based geometric design of horizontal curves: a reliability-based optimization framework

Reliability theory has recently been utilized to consider the uncertainty in highway geometric design and optimize highway cross-section design safety by reducing crash risk. However, despite the importance of design consistency among successive highway segments and its impact on safety, most previous studies optimized road segments individually. This approach could limit the applicability and transferability of the optimization frameworks in practice. Thus, a system reliability-based optimization framework is proposed in this study to design successive highway cross-section elements while achieving overall design consistency and safety. A sequential search procedure with the basin-hopping stochastic algorithm is adopted to optimize the successive horizontal curve segments. A case study of a 12 km segment with 94 horizontal curves in the Sea-to-Sky Highway, Canada, is considered. The results show that the proposed optimization framework provided higher consistency successive cross-section elements design while minimizing the number of expected crashes and providing consistent crash risk levels.

Role of bimetallic Au-Ir subnanometer clusters mediating O2 adsorption and dissociation on anatase TiO2 (101).

A comprehensive computational study on the oxygen molecule (O2) adsorption and activation on bimetallic Au-Ir subnanometer clusters supported on TiO2(101)- up to five atoms in size-is performed. A global optimization density functional theory-based basin-hopping algorithm is used to determine putative global minima configurations of both mono- and bimetallic clusters supported on the metal oxide surface for all sizes and compositions. Our results indicate a strong cluster-oxide interaction for monometallic Ir clusters with calculated adsorption energy (Eads) values ranging from -3.11 to -5.91eV. Similar values are calculated for bimetallic Au-Ir clusters (-3.21 up to -5.69eV). However, weaker Eads values are calculated for Au clusters (ranging from -0.66 to -2.07eV). As a general trend, we demonstrate that for supported Au-Ir clusters on TiO2(101), those Ir atoms preferentially occupy cluster-oxide interface positions while acting as anchor sites for the Au atoms. The overall geometric arrangements of the putative global minima configurations define O2 adsorption and dissociation, particularly involving the monometallic Au5 and Ir5 as well as the bimetallic Au2Ir3 and Au3Ir2 supported clusters. Spontaneous O2 dissociation is observed on both Ir5 and on the Ir-metallic part of Au3Ir2 and Au2Ir3 supported clusters. This is in sharp contrast with supported Au5, where a large activation energy is needed (1.90eV). Interestingly, for Au5, we observe that molecular O2 adsorption is favorable at the cluster/oxide interface, followed by a smaller dissociation barrier (0.71eV). From a single cluster catalysis point of view, our results have strong implications in the ongoing understanding of oxide supported bimetallic while providing a useful first insight into the continuous in silico design of novel subnanometer catalysts.

Theoretical study on the cluster–surface interaction: The case of subnanometer Pt–Re clusters supported on MgO(100)

Bimetallic clusters in gas phase display novel physicochemical properties that are different from those present in their pure metal analogs. When bimetallic clusters are deposited on a substrate, such properties may change depending on the type and strength of the metal–support interaction. Here, we report a theoretical study, based on density functional theory (DFT), for sub-nanometer clusters of Pt–Re on the pristine MgO(100) surface, using the Basin-Hopping DFT algorithm to find the global minima. Then, their structural, energetic, electronic, and vibrational properties are calculated, and a comparison between gas- and supported-phase behavior is performed. It is obtained that the MgO(100) surface has a more relevant effect on the structural and vibrational properties of the Pt–Re bimetallic clusters and pure Pt clusters. For example, the metal–metal bond lengths of the supported clusters increase with respect to those observed in gas phase, also giving rise to red shifts in the corresponding vibrational frequencies. On the other hand, the structural and vibrational properties of pure gas- and supported-phase Re clusters are quite similar. These results are consistent with the adsorption energy calculations indicating a strong interaction between Pt–Re clusters and pure Pt clusters with the MgO(100) surface. Moreover, the metal–support interaction leads to a charge transfer from the metal oxide to the metal clusters and to the hybridization of the d- and s-states of the metal atoms with the p-states of the oxygen atoms present in the substrate. This work contributes to the understanding of the role of the support in bimetallic Pt–Re clusters on metal oxides, which would be of potential interest in the design of novel nanocatalysts.

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 kBT/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.

The local atomic pressures in 79 atom Pd-Ag-Pt truncated octahedron structure

The best chemical ordering structures of 79-atom trimetallic PdnAg(60−n)Pt19 nanoalloys with truncated octahedron (TO) geometry were optimized and local relaxations were performed by using Monte Carlo Basin-Hopping algorithm within Gupta potential. The mixing energy variations were calculated to compare the relative stability. The lowest excess energy value was obtained at the compositions of Pd25Ag35Pt19 at Gupta level. In addition, a detailed investigation of local atomic pressure has been carried out. The factors affecting local atomic pressures were discussed.

Iterative peak-fitting of frequency-domain data via deep convolution neural networks

High-throughput material screening for the discovery and design of novel functional materials requires automatized analyses of theoretical and experimental data. Here we study the subject of human-free analyses of one-dimensional spectroscopic data, {\it e.g.} in the frequency domain, via employing deep convolution neural network. Specifically, we trained various deep convolution neural network and benchmarked their performance in decomposing one-dimensional noisy data into multiple nonorthogonal peaks in an iterative manner, after which a conventional basin-hopping algorithm was applied to further reduce residual fitting error. Among six different network architectures, a variant of "Squeeze-and-excitation" network (SENet) structure that we first propose in this study shows the best performance. Dependency of training performance with respect to the choice of the loss function is also discussed. We conclude by applying our modified SENet model to experimental photoemission spectra of graphene, MoS$_2$, and WS$_2$ and address its potential applications and limitations.

Impurity transport studies at the HSX stellarator using active and passive CVI spectroscopy

The transport of carbon impurities has been studied in the helically symmetric stellarator experiment (HSX) using active and passive charge exchange recombination spectroscopy (CHERS). For the analysis of the CHERS signals, the STRAHL impurity transport code has been re-written in the python programming language and optimized for the application in stellarators. In addition, neutral hydrogen densities both along the NBI line of sight as well as for the background plasma have been calculated using the FIDASIM code. By using the basinhopping algorithm to minimize the difference between experimental and predicted active and passive signals, significant levels of impurity diffusion are observed. Comparisons with neoclassical calculations from DKES/PENTA show that the inferred levels exceed the neoclassical transport by about a factor of four in the core and more than 100 times towards the plasma edge, thus indicating a high level of anomalous transport. This observation is in agreement with experimental heat diffusivites determined from a power balance analysis which exhibits strong anomalous transport as well.

Drude-Lorentz Model for Optical Properties of Photoexcited Transition Metals under Electron-Phonon Nonequilibrium

Evaluating the optical properties of matter under the action of ultrafast light is crucial in modeling laser–surface interaction and interpreting laser processing experiments. We report optimized coefficients for the Drude-Lorentz model describing the permittivity of several transition metals (Cr, W, Ti, Fe, Au, and Ni) under electron-phonon nonequilibrium, with electrons heated up to 30,000 K and the lattice staying cold at 300 K. A Basin-hopping algorithm is used to fit the Drude-Lorentz model to the nonequilibrium permittivity calculated using ab initio methods. The fitting coefficients are provided and can be easily inserted into any calculation requiring the optical response of the metals during ultrafast irradiation. Moreover, our results shed light on the electronic structure modifications and the relative contributions of intraband and interband optical transitions at high electron temperatures corresponding to the laser excitation fluence used for surface nanostructuring.

A neural network potential for searching the atomic structures of pure and mixed nanoparticles. Application to ZnMg nanoalloys with an eye on their anticorrosive properties

The accurate description of the potential energy landscape of moderate-sized nanoparticles is a formidable task, but of paramount importance if one aims to characterize, in a realistic way, their physical and chemical properties. We present here a Neural Network potential able to predict structures of pure and mixed nanoparticles with an error in energy and forces of the order of chemical accuracy as compared with the values provided by the theoretical method used in the training process, in our case the density functional theory. The neural network is integrated into a basin-hopping algorithm which dynamically feeds the training process. The main ingredients of the neural network algorithm as well as the protocol used for its implementation and training are detailed, with particular emphasis on those aspects that make it so efficient and transferable. As a first test, we have applied it to the determination of the global minimum structures of ZnMg nanoalloys with up to 52 atoms and stoichiometries corresponding to MgZn2 and Mg2Zn11, of special interest in the context of anticorrosive coatings. We present and discuss the structural properties, chemical order, stability and pertinent electronic indicators, and we extract some conclusions on fundamental aspects that may be at the roots of the good performance of ZnMg nanoalloys as protective coatings. Finally, we comment on the step forward that the presented machine learning approach constitutes, both in the fact that it allows to accurately explore the potential energy surface of systems that other methodologies can not, and that it opens new prospects for a variety of problems in Materials Science.

Search for Global Minimum Structures of (n = 1-15) Using xTB-Based Basin-Hopping Algorithm.

A new program for searching global minimum structures of atomic clusters using basin-hopping algorithm based on the xTB method was developed here. The program can be performed with a much higher speed than its replacement directly based on DFT methods. Considering the structural varieties and complexities in finding their global minimum structures, phosphorus cluster cations were studied by the program. The global minimum structures of cationic (n = 1–15) clusters are determined through the unbiased structure searching method. In the last step, further DFT optimization was performed for the selected isomers. For (n = 1–4, 7), the found global minimum structures are in consistent with the ones previously reported; while for (n = 5, 6, 8–12), newly found isomers are more energy-favorable than those previously reported. And those for (n = 13–15) are reported here for the first time. Among them, the most stable isomers of (n = 4–6, 9) are characterized by their C3v, Cs, C2v and Cs symmetry, in turn. But those of (n = 7, 8, 10–12), no symmetry has been identified. The most stable isomers of and are characterized by single P-P bonds bridging units inside the clusters. Further analysis shows that the pnicogen bonds play an important role in the stabilization of these clusters. These results show that the new developed program is effective and robust in searching global minimum structures for atom clusters, and it also provides new insights into the role of pnicogen bonds in phosphorus clusters.

Investigation of structural and energetic behavior of 55-atom Pt–Ag–Au ternary nanoalloys

A systematic theoretical investigation of structural and energetic behaviors of 55-atom Pt–Ag–Au ternary nanoalloys has been performed in two different composition systems. We have performed Gupta and Density Functional Theory (DFT) approaches on chosen systems. The Basin-Hopping algorithm is used for structural optimizations of PtnAg[Formula: see text]Au[Formula: see text] ([Formula: see text]–13) and PtnAu[Formula: see text]Ag[Formula: see text] ([Formula: see text]–13) ternary nanoalloys with Gupta many-body potential to model interatomic interactions. Local optimization results show that while the tendency of Au atoms to be located varies according to the composition system, the tendency of Pt and Ag atoms to be located does not change in both. For all compositions of Pt–Ag–Au nanoalloys, the structures with the best chemical ordering were then reoptimized by DFT relaxations and the mixing energies of the Gupta and DFT levels were compared. Our mixing energy analysis showed that PtnAg[Formula: see text]Au[Formula: see text] ([Formula: see text]–13) nanoalloys are not energetically suitable for mixing at both Gupta and DFT level. Also, mixing energy variations of PtnAu[Formula: see text]Ag[Formula: see text] ([Formula: see text]–13) nanoalloys obtained at Gupta level does not agree with the one obtained at DFT level. In addition, it has been found that the minimization energy changes when an atom in the central site is exchanging by an atom in the second shell and surface.

Investigation of the chemical ordering for PdnPt(32−n)Rh6 nanoalloys in TO structure

Using basin-hopping algorithm within the quantum corrected Sutton-Chen (Q-SC) many-body potential, a systematic investigation has been performed for the best chemical ordering structures of 38-atom trimetallic PdnPt[Formula: see text]Rh6 nanoalloys with truncated octahedral (TO) geometry. The atomic mixing degrees of Pd, Pt and Rh atoms were investigated by using order parameter ([Formula: see text]). The results show that demixing is energetically favorable for the investigated structures, where the number of Rh atoms fixed at 6. The only compositions with the number of hetero bonds lower than the homo bonds are Pt[Formula: see text]Rh6, Pd1Pt[Formula: see text]Rh6, Pd[Formula: see text]Pt[Formula: see text]Rh6 and Pd[Formula: see text]Rh6 which make segregation energetically favorable. The surface segregation of Pd atoms is explained by the lower cohesive energy of Pd atoms than Pt and Rh. The segregation of Pd atoms to the surface is also associated with the smaller surface energies compared with Pt and Rh atoms. Due to the comparable cohesive energies of Rh and Pt atoms, a computation occurs for filling the octahedral core between two kinds.