1
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Schwerdtfeger P, Wales DJ. 100 Years of the Lennard-Jones Potential. J Chem Theory Comput 2024; 20:3379-3405. [PMID: 38669689 DOI: 10.1021/acs.jctc.4c00135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/28/2024]
Abstract
It is now 100 years since Lennard-Jones published his first paper introducing the now famous potential that bears his name. It is therefore timely to reflect on the many achievements, as well as the limitations, of this potential in the theory of atomic and molecular interactions, where applications range from descriptions of intermolecular forces to molecules, clusters, and condensed matter.
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Affiliation(s)
- Peter Schwerdtfeger
- Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Private Bag 102904, Auckland 0745, New Zealand
| | - David J Wales
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
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2
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Woods EJ, Wales DJ. Analysis and interpretation of first passage time distributions featuring rare events. Phys Chem Chem Phys 2024; 26:1640-1657. [PMID: 38059562 DOI: 10.1039/d3cp04199a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/08/2023]
Abstract
In this contribution we consider theory and associated computational tools to treat the kinetics associated with competing pathways on multifunnel energy landscapes. Multifunnel landscapes are associated with molecular switches and multifunctional materials, and are expected to exhibit multiple relaxation time scales and associated thermodynamic signatures in the heat capacity. Our focus here is on the first passage time distribution, which is encoded in a kinetic transition network containing all the locally stable states and the pathways between them. This network can be renormalised to reduce the dimensionality, while exactly conserving the mean first passage time and approximately conserving the full distribution. The structure of the reduced network can be visualised using disconnectivity graphs. We show how features in the first passage time distribution can be associated with specific kinetic traps, and how the appearance of competing relaxation time scales depends on the starting conditions. The theory is tested for two model landscapes and applied to an atomic cluster and a disordered peptide. Our most important contribution is probably the reconstruction of the full distribution for long time scales, where numerical problems prevent direct calculations. Here we combine accurate treatment of the mean first passage time with the reliable part of the distribution corresponding to faster time scales. Hence we now have a fundamental understanding of both thermodynamic and kinetic signatures of multifunnel landscapes.
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Affiliation(s)
- Esmae J Woods
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge CB3 0HE, UK
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK.
| | - David J Wales
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK.
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3
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Roth M, Toker Y, Major DT. Monte Carlo-Simulated Annealing and Machine Learning-Based Funneled Approach for Finding the Global Minimum Structure of Molecular Clusters. ACS OMEGA 2024; 9:1298-1309. [PMID: 38222530 PMCID: PMC10785639 DOI: 10.1021/acsomega.3c07600] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/01/2023] [Revised: 11/09/2023] [Accepted: 11/15/2023] [Indexed: 01/16/2024]
Abstract
Understanding the physical underpinnings and geometry of molecular clusters is of great importance in many fields, ranging from studying the beginning of the universe to the formation of atmospheric particles. To this end, several approaches have been suggested, yet identifying the most stable cluster geometry (i.e., global potential energy minimum) remains a challenge, especially for highly symmetric clusters. Here, we suggest a new funneled Monte Carlo-based simulated annealing (SA) approach, which includes two key steps: generation of symmetrical clusters and classification of the clusters according to their geometry using machine learning (MCSA-ML). We demonstrate the merits of the MCSA-ML method in comparison to other approaches on several Lennard-Jones (LJ) clusters and four molecular clusters-Ser8(Cl-)2, H+(H2O)6, Ag+(CO2)8, and Bet4Cl-. For the latter of these clusters, the correct structure is unknown, and hence, we compare the experimental and simulated fragmentation patterns, and the fragmentation of the proposed global minimum matches experiments closely. Additionally, based on the fragmentation of the predicted betaine cluster, we were able to identify hitherto unknown neutral fragmentation channels. In comparison to results obtained with other methods, we demonstrated a superior ability of MCSA-ML to predict clusters with high symmetry and similar abilities to predict clusters with asymmetrical structures.
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Affiliation(s)
- Michal Roth
- Department
of Physics, Bar-Ilan University, Ramat-Gan 5290002, Israel
- Institute
of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 5290002, Israel
| | - Yoni Toker
- Department
of Physics, Bar-Ilan University, Ramat-Gan 5290002, Israel
- Institute
of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 5290002, Israel
| | - Dan T. Major
- Institute
of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 5290002, Israel
- Department
of Chemistry, Bar-Ilan University, Ramat-Gan 5290002, Israel
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4
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Liu YR, Jiang Y. Growth mechanism prediction for nanoparticles via structure matching polymerization. Phys Chem Chem Phys 2024; 26:1267-1273. [PMID: 38105690 DOI: 10.1039/d3cp04702d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2023]
Abstract
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.
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Affiliation(s)
- Yi-Rong Liu
- Public Experimental Teaching Center, Panzhihua University, Panzhihua, Sichuan 61700, China.
| | - Yan Jiang
- School of Vanadium and Titanium, Panzhihua University, Panzhihua, Sichuan 61700, China
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5
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Smith NB, Jowett T, Yu D, Pahl E, Garden AL. Comparison of Taboo Search Methods for Atomic Cluster Global Optimization with a Basin-Hopping Algorithm. J Chem Inf Model 2023; 63:5784-5793. [PMID: 37665618 DOI: 10.1021/acs.jcim.3c00526] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/05/2023]
Abstract
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.
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Affiliation(s)
- Nicholas B Smith
- Department of Chemistry, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand
- MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand
| | - Tim Jowett
- Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand
| | - Diana Yu
- MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand
- Department of Physics, University of Auckland, Auckland 1010, New Zealand
| | - Elke Pahl
- MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand
- Department of Physics, University of Auckland, Auckland 1010, New Zealand
| | - Anna L Garden
- Department of Chemistry, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand
- MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand
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6
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Kanayama K, Seko A, Toyoura K. Structure search method for atomic clusters based on the dividing rectangles algorithm. Phys Rev E 2023; 108:035303. [PMID: 37849110 DOI: 10.1103/physreve.108.035303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2023] [Accepted: 08/11/2023] [Indexed: 10/19/2023]
Abstract
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.
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Affiliation(s)
- Kansei Kanayama
- Department of Materials Science and Engineering, Kyoto University, Kyoto 606-8501, Japan
| | - Atsuto Seko
- Department of Materials Science and Engineering, Kyoto University, Kyoto 606-8501, Japan
| | - Kazuaki Toyoura
- Department of Materials Science and Engineering, Kyoto University, Kyoto 606-8501, Japan
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7
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Wang Y, Lv J, Gao P, Ma Y. Crystal Structure Prediction via Efficient Sampling of the Potential Energy Surface. Acc Chem Res 2022; 55:2068-2076. [DOI: 10.1021/acs.accounts.2c00243] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yanchao Wang
- State Key Laboratory of Superhard Materials & International Center of Computational Method and Software, College of Physics, Jilin University, Changchun 130012, China
| | - Jian Lv
- State Key Laboratory of Superhard Materials & International Center of Computational Method and Software, College of Physics, Jilin University, Changchun 130012, China
| | - Pengyue Gao
- State Key Laboratory of Superhard Materials & International Center of Computational Method and Software, College of Physics, Jilin University, Changchun 130012, China
| | - Yanming Ma
- State Key Laboratory of Superhard Materials & International Center of Computational Method and Software, College of Physics, Jilin University, Changchun 130012, China
- International Center of Future Science, Jilin University, Changchun 130012, China
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8
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Cox S, White AD. Symmetric Molecular Dynamics. J Chem Theory Comput 2022; 18:4077-4081. [PMID: 35699649 PMCID: PMC9281392 DOI: 10.1021/acs.jctc.2c00401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
We derive a formulation
of molecular dynamics that generates only
symmetric configurations. We implement it for all 2D planar and 3D
space groups. An atlas of 2D Lennard-Jones crystals under all planar
groups is created with symmetric molecular dynamics.
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Affiliation(s)
- Sam Cox
- Department of Chemical Engineering, University of Rochester, Rochester, New York 14627, United States
| | - Andrew D White
- Department of Chemical Engineering, University of Rochester, Rochester, New York 14627, United States
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9
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Bauer MN, Probert MIJ, Panosetti C. Systematic Comparison of Genetic Algorithm and Basin Hopping Approaches to the Global Optimization of Si(111) Surface Reconstructions. J Phys Chem A 2022; 126:3043-3056. [PMID: 35522778 PMCID: PMC9126620 DOI: 10.1021/acs.jpca.2c00647] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
Abstract
![]()
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.
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Affiliation(s)
- Maximilian N Bauer
- Department of Physics, University of York, York YO10 5DD, United Kingdom.,Technical University of Munich, Lichtenbergstraße 4, 85748 Garching, Germany
| | - Matt I J Probert
- Department of Physics, University of York, York YO10 5DD, United Kingdom
| | - Chiara Panosetti
- Technical University of Munich, Lichtenbergstraße 4, 85748 Garching, Germany.,Fritz Haber Institute of the Max Planck Society, Faradayweg 4, 14195 Berlin, Germany
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10
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Weal GR, McIntyre SM, Garden AL. Development of a Structural Comparison Method to Promote Exploration of the Potential Energy Surface in the Global Optimization of Nanoclusters. J Chem Inf Model 2021; 61:1732-1744. [PMID: 33844537 DOI: 10.1021/acs.jcim.0c01128] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
A structural comparison method (SCM) was created to quantify the structural diversity of nanoclusters and was implemented into a global optimization algorithm to evaluate structural diversity between generated clusters on the fly and promote exploration of the potential energy surface. The SCM evaluated topological differences between clusters using the common neighbor analysis and provided a numerical measure of similarity between the two clusters. The SCM was implemented into a genetic algorithm by integrating it into a new structure + energy fitness operator such that structural diversity of clusters in the population and their energies were used to assign fitness values to clusters. The efficiency of the genetic algorithm with this new fitness operator was benchmarked against several Lennard-Jones clusters (LJ38, LJ75, and LJ98) known to be difficult cases for global optimization algorithms. For LJ38 and LJ75, this new structure + energy fitness operator performed equally well or better than the energy fitness operator. However, the efficiency of locating the global minimum of LJ98 decreased using this new structure + energy fitness operator. Further analysis of the genetic algorithm with this fitness operator showed that the algorithm did indeed promote exploration of the PES of LJ98 as desired but hindered refinement of clusters, preventing it from locating the global minimum even if the energy funnel of the global minimum had been located.
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Affiliation(s)
- Geoffrey R Weal
- Department of Chemistry, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand.,The MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand
| | - Samantha M McIntyre
- Department of Chemistry, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand.,The MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand
| | - Anna L Garden
- Department of Chemistry, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand.,The MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand
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11
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Srivastava R. Application of Optimization Algorithms in Clusters. Front Chem 2021; 9:637286. [PMID: 33777900 PMCID: PMC7994592 DOI: 10.3389/fchem.2021.637286] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2020] [Accepted: 01/21/2021] [Indexed: 12/23/2022] Open
Abstract
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.
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12
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Swinburne TD, Kannan D, Sharpe DJ, Wales DJ. Rare events and first passage time statistics from the energy landscape. J Chem Phys 2020; 153:134115. [PMID: 33032418 DOI: 10.1063/5.0016244] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
We analyze the probability distribution of rare first passage times corresponding to transitions between product and reactant states in a kinetic transition network. The mean first passage times and the corresponding rate constants are analyzed in detail for two model landscapes and the double funnel landscape corresponding to an atomic cluster. Evaluation schemes based on eigendecomposition and kinetic path sampling, which both allow access to the first passage time distribution, are benchmarked against mean first passage times calculated using graph transformation. Numerical precision issues severely limit the useful temperature range for eigendecomposition, but kinetic path sampling is capable of extending the first passage time analysis to lower temperatures, where the kinetics of interest constitute rare events. We then investigate the influence of free energy based state regrouping schemes for the underlying network. Alternative formulations of the effective transition rates for a given regrouping are compared in detail to determine their numerical stability and capability to reproduce the true kinetics, including recent coarse-graining approaches that preserve occupancy cross correlation functions. We find that appropriate regrouping of states under the simplest local equilibrium approximation can provide reduced transition networks with useful accuracy at somewhat lower temperatures. Finally, a method is provided to systematically interpolate between the local equilibrium approximation and exact intergroup dynamics. Spectral analysis is applied to each grouping of states, employing a moment-based mode selection criterion to produce a reduced state space, which does not require any spectral gap to exist, but reduces to gap-based coarse graining as a special case. Implementations of the developed methods are freely available online.
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Affiliation(s)
- Thomas D Swinburne
- Aix-Marseille Université, CNRS, CINaM UMR 7325, Campus de Luminy, 13288 Marseille, France
| | - Deepti Kannan
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Daniel J Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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13
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Olson MA, Bhatia S, Larson P, Militzer B. Prediction of chlorine and fluorine crystal structures at high pressure using symmetry driven structure search with geometric constraints. J Chem Phys 2020; 153:094111. [PMID: 32891084 DOI: 10.1063/5.0018402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The high-pressure properties of fluorine and chlorine are not yet well understood because both are highly reactive and volatile elements, which have made conducting diamond anvil cell and x-ray diffraction experiments a challenge. Here, we use ab initio methods to search for stable crystal structures of both elements at megabar pressures. We demonstrate how symmetry and geometric constraints can be combined to efficiently generate crystal structures that are composed of diatomic molecules. Our algorithm extends the symmetry driven structure search method [R. Domingos et al., Phys. Rev. B 98, 174107 (2018)] by adding constraints for the bond length and the number of atoms in a molecule while still maintaining generality. As a method of validation, we have tested our approach for dense hydrogen and reproduced the known molecular structures of Cmca-12 and Cmca-4. We apply our algorithm to study chlorine and fluorine in the pressure range of 10 GPa-4000 GPa while considering crystal structures with up to 40 atoms per unit cell. We predict chlorine to follow the same series of phase transformations as elemental iodine from Cmca to Immm to Fm3¯m, but at substantially higher pressures. We predict fluorine to transition from a C2/c to Cmca structure at 70 GPa, to a novel orthorhombic and metallic structure with P42/mmc symmetry at 2500 GPa, and finally to its cubic analog form with Pm3¯n symmetry at 3000 GPa.
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Affiliation(s)
- Mark A Olson
- Department of Mathematics, University of California, Berkeley, California 94720, USA
| | - Shefali Bhatia
- Department of Electrical Engineering and Computer Science, University of California, Berkeley, California 94720, USA
| | - Paul Larson
- Department of Mathematics, Miami University, Oxford, Ohio 45056, USA
| | - Burkhard Militzer
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
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14
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Hernández-Rojas J, Calvo F. The Structure of Adamantane Clusters: Atomistic vs. Coarse-Grained Predictions From Global Optimization. Front Chem 2019; 7:573. [PMID: 31475136 PMCID: PMC6707085 DOI: 10.3389/fchem.2019.00573] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2019] [Accepted: 07/29/2019] [Indexed: 11/24/2022] Open
Abstract
Candidate structures for the global minima of adamantane clusters, (C10H16)N, are presented. Based on a rigid model for individual molecules with atom-atom pairwise interactions that include Lennard-Jones and Coulomb contributions, low-energy structures were obtained up to N = 42 using the basin-hopping method. The results indicate that adamantane clusters initially grow accordingly with an icosahedral packing scheme, followed above N = 14 by a structural transition toward face-centered cubic structures. The special stabilities obtained at N = 13, 19, and 38 are consistent with these two structural families, and agree with recent mass spectrometry measurements on cationic adamantane clusters. Coarse-graining the intermolecular potential by averaging over all possible orientations only partially confirm the all-atom results, the magic numbers at 13 and 38 being preserved. However, the details near the structural transition are not captured well, because despite their high symmetry the adamantane molecules are still rather anisotropic.
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Affiliation(s)
- Javier Hernández-Rojas
- Departamento de Física e IUdEA, Universidad de La Laguna, San Cristóbal de La Laguna, Spain
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15
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Li X, Tang Y, Li S, Gui Y. Spectroscopic properties and activated mechanism of NO on isolated cationic tantalum clusters: A first-principles study. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2019; 216:335-341. [PMID: 30909090 DOI: 10.1016/j.saa.2019.03.052] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2018] [Revised: 02/18/2019] [Accepted: 03/17/2019] [Indexed: 06/09/2023]
Abstract
The adsorption and dissociation of NO on the cationic Ta15+ cluster were investigated using the density-functional theory (DFT) calculations, and the Ta-centered bicapped hexagonal antiprism (BHA) structure of cationic Ta15+ cluster can be identified as the global minimum, which reproduces well the infrared multiple photo dissociation (IR-MPD) spectrum. Our results show that the cationic BHATa15+ cluster provides the hollow region for NO to interact effectively, and possess larger adsorption strength on the region than other sites. The density of states, charge density differences and frontier molecular orbitals were analyzed to understand the electronic properties of the stable NO-adsorbed isomers. The characteristic IR peaks of the firstly two low-lying isomers are properly assigned, in which the strongest IR peak originates from the N - O stretching vibration. For the dissociation of NO on the BHATa15+ cluster, it is found that the reaction path II easily occurs rather than path I due to small reaction barrier, and the cluster may possess the great catalytic behavior to dissociate NO molecule. The present results will inevitably stimulate future theoretical and experimental studies for the design of novel Ta-based catalytic materials for the NO dissociation.
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Affiliation(s)
- Xiaojun Li
- School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, Shaanxi, China.
| | - Yongqiang Tang
- School of Chemical Engineering, Xi'an University, Xi'an, China
| | - Shuna Li
- School of Chemical Engineering, Xi'an University, Xi'an, China
| | - Yangyang Gui
- School of Chemical Engineering, Xi'an University, Xi'an, China
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16
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Röder K, Joseph JA, Husic BE, Wales DJ. Energy Landscapes for Proteins: From Single Funnels to Multifunctional Systems. ADVANCED THEORY AND SIMULATIONS 2019. [DOI: 10.1002/adts.201800175] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Konstantin Röder
- Department of ChemistryUniversity of CambridgeLensfield Road CB2 1EW Cambridge UK
| | - Jerelle A. Joseph
- Department of ChemistryUniversity of CambridgeLensfield Road CB2 1EW Cambridge UK
| | - Brooke E. Husic
- Department of ChemistryUniversity of CambridgeLensfield Road CB2 1EW Cambridge UK
| | - David J. Wales
- Department of ChemistryUniversity of CambridgeLensfield Road CB2 1EW Cambridge UK
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17
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Grajciar L, Heard CJ, Bondarenko AA, Polynski MV, Meeprasert J, Pidko EA, Nachtigall P. Towards operando computational modeling in heterogeneous catalysis. Chem Soc Rev 2018; 47:8307-8348. [PMID: 30204184 PMCID: PMC6240816 DOI: 10.1039/c8cs00398j] [Citation(s) in RCA: 114] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2018] [Indexed: 12/19/2022]
Abstract
An increased synergy between experimental and theoretical investigations in heterogeneous catalysis has become apparent during the last decade. Experimental work has extended from ultra-high vacuum and low temperature towards operando conditions. These developments have motivated the computational community to move from standard descriptive computational models, based on inspection of the potential energy surface at 0 K and low reactant concentrations (0 K/UHV model), to more realistic conditions. The transition from 0 K/UHV to operando models has been backed by significant developments in computer hardware and software over the past few decades. New methodological developments, designed to overcome part of the gap between 0 K/UHV and operando conditions, include (i) global optimization techniques, (ii) ab initio constrained thermodynamics, (iii) biased molecular dynamics, (iv) microkinetic models of reaction networks and (v) machine learning approaches. The importance of the transition is highlighted by discussing how the molecular level picture of catalytic sites and the associated reaction mechanisms changes when the chemical environment, pressure and temperature effects are correctly accounted for in molecular simulations. It is the purpose of this review to discuss each method on an equal footing, and to draw connections between methods, particularly where they may be applied in combination.
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Affiliation(s)
- Lukáš Grajciar
- Department of Physical and Macromolecular Chemistry
, Faculty of Science
, Charles University in Prague
,
128 43 Prague 2
, Czech Republic
.
;
;
| | - Christopher J. Heard
- Department of Physical and Macromolecular Chemistry
, Faculty of Science
, Charles University in Prague
,
128 43 Prague 2
, Czech Republic
.
;
;
| | - Anton A. Bondarenko
- TheoMAT group
, ITMO University
,
Lomonosova 9
, St. Petersburg
, 191002
, Russia
| | - Mikhail V. Polynski
- TheoMAT group
, ITMO University
,
Lomonosova 9
, St. Petersburg
, 191002
, Russia
| | - Jittima Meeprasert
- Inorganic Systems Engineering group
, Department of Chemical Engineering
, Faculty of Applied Sciences
, Delft University of Technology
,
Van der Maasweg 9
, 2629 HZ Delft
, The Netherlands
.
| | - Evgeny A. Pidko
- TheoMAT group
, ITMO University
,
Lomonosova 9
, St. Petersburg
, 191002
, Russia
- Inorganic Systems Engineering group
, Department of Chemical Engineering
, Faculty of Applied Sciences
, Delft University of Technology
,
Van der Maasweg 9
, 2629 HZ Delft
, The Netherlands
.
| | - Petr Nachtigall
- Department of Physical and Macromolecular Chemistry
, Faculty of Science
, Charles University in Prague
,
128 43 Prague 2
, Czech Republic
.
;
;
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18
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Aguado A, Vega A, Lebon A, von Issendorff B. Are zinc clusters really amorphous? A detailed protocol for locating global minimum structures of clusters. NANOSCALE 2018; 10:19162-19181. [PMID: 30302480 DOI: 10.1039/c8nr05517c] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We report the results of a conjoint experimental/theoretical effort to assess the structures of free-standing zinc clusters with up to 73 atoms. Experiment provides photoemission spectra for ZnN- cluster anions, to be used as fingerprints in structural assessment, as well as mass spectra for both anion and cation clusters. Theory provides both a detailed description of a novel protocol to locate global minimum structures of clusters in an efficient and reliable way, and its specific application to neutral and charged zinc clusters. Our methodology is based on the well-known hybrid EP-DFT (empirical potential-density functional theory) approach, in which the approximate potential energy surface generated by an empirical Gupta potential is first sampled with unbiased basin hopping simulations, and then a selection of the isomers so identified is re-optimized at a first-principles DFT level. The novelty introduced in our paper is a simple but efficient new recipe to obtain the best possible EP parameters for a given cluster system, with which the first step of the EP-DFT method is to be performed. Our method is able to reproduce experimental measurements at an excellent level for most cluster sizes, implying its ability to locate the true global minimum structures; meanwhile, if exactly the same method is applied based on the existing Gupta potential (fitted to bulk properties), it leads to wrong predicted structures with energies between 1 and 2 eV above the correct ones. Opposite to what was claimed in the past, our work unequivocally demonstrates that Zn clusters are not amorphous, and they rather adopt high symmetry structures for most sizes. We show that Zn clusters have a number of exotic, unprecedented structural and electronic properties which are not expected for clusters of a metallic element, and describe them in detail.
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Affiliation(s)
- Andrés Aguado
- Departamento de Física Teórica, Atómica y Óptica, University of Valladolid, Valladolid 47071, Spain.
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19
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Li X, Li S, Wang Z, Yang X, Yan Z. A Frank-Kasper polyhedral structure of 17-atom vanadium clusters. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2018.08.024] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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20
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Elenewski JE, Velizhanin KA, Zwolak M. A spin-1 representation for dual-funnel energy landscapes. J Chem Phys 2018; 149:035101. [PMID: 30037251 PMCID: PMC7723752 DOI: 10.1063/1.5036677] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
The interconversion between the left- and right-handed helical folds of a polypeptide defines a dual-funneled free energy landscape. In this context, the funnel minima are connected through a continuum of unfolded conformations, evocative of the classical helix-coil transition. Physical intuition and recent conjectures suggest that this landscape can be mapped by assigning a left- or right-handed helical state to each residue. We explore this possibility using all-atom replica exchange molecular dynamics and an Ising-like model, demonstrating that the energy landscape architecture is at odds with a two-state picture. A three-state model-left, right, and unstructured-can account for most key intermediates during chiral interconversion. Competing folds and excited conformational states still impose limitations on the scope of this approach. However, the improvement is stark: Moving from a two-state to a three-state model decreases the fit error from 1.6 kBT to 0.3 kBT along the left-to-right interconversion pathway.
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Affiliation(s)
- Justin E. Elenewski
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
- Maryland Nanocenter, University of Maryland, College Park, MD 20742, USA
| | | | - Michael Zwolak
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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21
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Abstract
Recent advances in the potential energy landscapes approach are highlighted, including both theoretical and computational contributions. Treating the high dimensionality of molecular and condensed matter systems of contemporary interest is important for understanding how emergent properties are encoded in the landscape and for calculating these properties while faithfully representing barriers between different morphologies. The pathways characterized in full dimensionality, which are used to construct kinetic transition networks, may prove useful in guiding such calculations. The energy landscape perspective has also produced new procedures for structure prediction and analysis of thermodynamic properties. Basin-hopping global optimization, with alternative acceptance criteria and generalizations to multiple metric spaces, has been used to treat systems ranging from biomolecules to nanoalloy clusters and condensed matter. This review also illustrates how all this methodology, developed in the context of chemical physics, can be transferred to landscapes defined by cost functions associated with machine learning.
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Affiliation(s)
- David J Wales
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom;
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22
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Ballard AJ, Das R, Martiniani S, Mehta D, Sagun L, Stevenson JD, Wales DJ. Energy landscapes for machine learning. Phys Chem Chem Phys 2018; 19:12585-12603. [PMID: 28367548 DOI: 10.1039/c7cp01108c] [Citation(s) in RCA: 62] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the corresponding machine learning landscape. Methods to explore and visualise molecular potential energy landscapes can be applied to these machine learning landscapes to gain new insight into the solution space involved in training and the nature of the corresponding predictions. In particular, we can define quantities analogous to molecular structure, thermodynamics, and kinetics, and relate these emergent properties to the structure of the underlying landscape. This Perspective aims to describe these analogies with examples from recent applications, and suggest avenues for new interdisciplinary research.
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Affiliation(s)
- Andrew J Ballard
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK.
| | - Ritankar Das
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK.
| | - Stefano Martiniani
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK.
| | - Dhagash Mehta
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, IN, USA
| | - Levent Sagun
- Mathematics Department, Courant Institute, New York University, NY, USA
| | | | - David J Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK.
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23
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24
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Lazauskas T, Sokol AA, Woodley SM. An efficient genetic algorithm for structure prediction at the nanoscale. NANOSCALE 2017; 9:3850-3864. [PMID: 28252128 DOI: 10.1039/c6nr09072a] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
We have developed and implemented a new global optimization technique based on a Lamarckian genetic algorithm with the focus on structure diversity. The key process in the efficient search on a given complex energy landscape proves to be the removal of duplicates that is achieved using a topological analysis of candidate structures. The careful geometrical prescreening of newly formed structures and the introduction of new mutation move classes improve the rate of success further. The power of the developed technique, implemented in the Knowledge Led Master Code, or KLMC, is demonstrated by its ability to locate and explore a challenging double funnel landscape of a Lennard-Jones 38 atom system (LJ38). We apply the redeveloped KLMC to investigate three chemically different systems: ionic semiconductor (ZnO)1-32, metallic Ni13 and covalently bonded C60. All four systems have been systematically explored on the energy landscape defined using interatomic potentials. The new developments allowed us to successfully locate the double funnels of LJ38, find new local and global minima for ZnO clusters, extensively explore the Ni13 and C60 (the buckminsterfullerene, or buckyball) potential energy surfaces.
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Affiliation(s)
- Tomas Lazauskas
- University College London, Kathleen Lonsdale Materials Chemistry, Department of Chemistry, 20 Gordon Street, London WC1H 0AJ, UK.
| | - Alexey A Sokol
- University College London, Kathleen Lonsdale Materials Chemistry, Department of Chemistry, 20 Gordon Street, London WC1H 0AJ, UK.
| | - Scott M Woodley
- University College London, Kathleen Lonsdale Materials Chemistry, Department of Chemistry, 20 Gordon Street, London WC1H 0AJ, UK.
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25
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Zhao J, Shi R, Sai L, Huang X, Su Y. Comprehensive genetic algorithm forab initioglobal optimisation of clusters. MOLECULAR SIMULATION 2016. [DOI: 10.1080/08927022.2015.1121386] [Citation(s) in RCA: 52] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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26
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Ballard AJ, Stevenson JD, Das R, Wales DJ. Energy landscapes for a machine learning application to series data. J Chem Phys 2016; 144:124119. [DOI: 10.1063/1.4944672] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andrew J. Ballard
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Jacob D. Stevenson
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Ritankar Das
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J. Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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27
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Abstract
We introduce grand and semigrand canonical global optimization approaches using basin-hopping with an acceptance criterion based on the local contribution of each potential energy minimum to the (semi)grand potential. The method is tested using local harmonic vibrational densities of states for atomic clusters as a function of temperature and chemical potential. The predicted global minima switch from dissociated states to clusters for larger values of the chemical potential and lower temperatures, in agreement with the predictions of a model fitted to heat capacity data for selected clusters. Semigrand canonical optimization allows us to identify particularly stable compositions in multicomponent nanoalloys as a function of increasing temperature, whereas the grand canonical potential can produce a useful survey of favorable structures as a byproduct of the global optimization search.
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Affiliation(s)
- F Calvo
- Université Grenoble Alpes , LIPHY, F-38000 Grenoble, France.,CNRS , LIPHY, F-38000 Grenoble, France
| | - D Schebarchov
- University Chemical Laboratories , Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - D J Wales
- University Chemical Laboratories , Lensfield Road, Cambridge CB2 1EW, United Kingdom
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29
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Zhang J, Dolg M. Global optimization of clusters of rigid molecules using the artificial bee colony algorithm. Phys Chem Chem Phys 2016; 18:3003-10. [DOI: 10.1039/c5cp06313b] [Citation(s) in RCA: 195] [Impact Index Per Article: 24.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
The global optimization of molecular clusters is an important topic encountered in many fields of chemistry. Our free and black-box software ABCluster is a useful tool in solving this problem.
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Affiliation(s)
- Jun Zhang
- Theoretical Chemistry
- University of Cologne
- 50939 Cologne
- Germany
| | - Michael Dolg
- Theoretical Chemistry
- University of Cologne
- 50939 Cologne
- Germany
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30
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Three-Dimensional Assignment of the Structures of Atomic Clusters: an Example of Au8M (M=Si, Ge, Sn) Anion Clusters. Sci Rep 2015; 5:17738. [PMID: 26631620 PMCID: PMC4668548 DOI: 10.1038/srep17738] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2015] [Accepted: 10/30/2015] [Indexed: 11/29/2022] Open
Abstract
Identification of different isomer structures of atomic and molecular clusters has long been a challenging task in the field of cluster science. Here we present a three-dimensional (3D) assignment method, combining the energy (1D) and simulated (2D) spectra to assure the assignment of the global minimum structure. This method is more accurate and convenient than traditional methods, which only consider the total energy and first vertical detachment energies (VDEs) of anion clusters. There are two prerequisites when the 3D assignment method is ultilized. First, a reliable global minimum search algorithm is necessary to explore enough valleys on the potential energy surface. Second, trustworthy simulated spectra are necessary, that is to say, spectra that are in quantitative agreement. In this paper, we demonstrate the validity of the 3D assignment method using Au8M− (M = Si, Ge, Sn) systems. Results from this study indicate that the global minimum structures of Au8Ge− and Au8Sn− clusters are different from those described in previous studies.
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31
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Neogi SG, Chaudhury P. Structure, electronic properties and vibrational spectra of (MgF2)nclusters through a combination of genetic algorithm and DFT-based approach. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1059508] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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32
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Schebarchov D, Wales DJ. Quasi-combinatorial energy landscapes for nanoalloy structure optimisation. Phys Chem Chem Phys 2015; 17:28331-8. [PMID: 25970479 DOI: 10.1039/c5cp01198a] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We formulate nanoalloy structure prediction as a mixed-variable optimisation problem, where the homotops can be associated with an effective, quasi-combinatorial energy landscape in permutation space. We survey this effective landscape for a representative set of binary systems modelled by the Gupta potential. In segregating systems with small lattice mismatch, we find that homotops have a relatively straightforward landscape with few local optima - a scenario well-suited for local (combinatorial) optimisation techniques that scale quadratically with system size. Combining these techniques with multiple local-neighbourhood structures yields a search for multiminima, and we demonstrate that generalised basin-hopping with a metropolis acceptance criterion in the space of multiminima can then be effective for global optimisation of binary and ternary nanoalloys.
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Affiliation(s)
- D Schebarchov
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK.
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33
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Wales DJ. Perspective: Insight into reaction coordinates and dynamics from the potential energy landscape. J Chem Phys 2015; 142:130901. [DOI: 10.1063/1.4916307] [Citation(s) in RCA: 73] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Affiliation(s)
- D. J. Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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34
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35
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Guo Y, Bo M, Wang Y, Liu Y, Huang Y, Sun CQ. Atomistic bond relaxation, energy entrapment, and electron polarization of the RbN and CsN clusters (N ≤ 58). Phys Chem Chem Phys 2015; 17:30389-97. [DOI: 10.1039/c5cp05729a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A coordination environment resolves the electron binding-energy shift of Rb and Cs clusters.
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Affiliation(s)
- Yongling Guo
- Key Laboratory of Low-Dimensional Materials and Application Technologies (Ministry of Education)
- Hunan Provincial Key Laboratory of Thin Film Materials and Devices
- Faculty of Materials Science and Engineering
- Xiangtan University
- Hunan 411105
| | - Maolin Bo
- Key Laboratory of Low-Dimensional Materials and Application Technologies (Ministry of Education)
- Hunan Provincial Key Laboratory of Thin Film Materials and Devices
- Faculty of Materials Science and Engineering
- Xiangtan University
- Hunan 411105
| | - Yan Wang
- School of Information and Electronic Engineering
- Hunan University of Science and Technology
- Hunan 411201
- China
| | - Yonghui Liu
- Key Laboratory of Low-Dimensional Materials and Application Technologies (Ministry of Education)
- Hunan Provincial Key Laboratory of Thin Film Materials and Devices
- Faculty of Materials Science and Engineering
- Xiangtan University
- Hunan 411105
| | - Yongli Huang
- Key Laboratory of Low-Dimensional Materials and Application Technologies (Ministry of Education)
- Hunan Provincial Key Laboratory of Thin Film Materials and Devices
- Faculty of Materials Science and Engineering
- Xiangtan University
- Hunan 411105
| | - Chang Q. Sun
- NOVITAS
- School of Electrical and Electronic Engineering
- Nanyang Technological University
- Singapore 639798
- Singapore
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36
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Zhang J, Dolg M. ABCluster: the artificial bee colony algorithm for cluster global optimization. Phys Chem Chem Phys 2015; 17:24173-81. [DOI: 10.1039/c5cp04060d] [Citation(s) in RCA: 271] [Impact Index Per Article: 30.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Global optimization of cluster geometries is of fundamental importance in chemistry and an interesting problem in applied mathematics. We apply a swarm-intelligence based heuristic algorithm, i.e. the artificial bee colony algorithm to solve this problem for various kinds of clusters.
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Affiliation(s)
- Jun Zhang
- Theoretical Chemistry
- University of Cologne
- 50939 Cologne
- Germany
| | - Michael Dolg
- Theoretical Chemistry
- University of Cologne
- 50939 Cologne
- Germany
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37
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Ballard AJ, Wales DJ. Superposition-Enhanced Estimation of Optimal Temperature Spacings for Parallel Tempering Simulations. J Chem Theory Comput 2014; 10:5599-5605. [PMID: 25512744 PMCID: PMC4262936 DOI: 10.1021/ct500797a] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2014] [Indexed: 01/31/2023]
Abstract
Effective parallel tempering simulations rely crucially on a properly chosen sequence of temperatures. While it is desirable to achieve a uniform exchange acceptance rate across neighboring replicas, finding a set of temperatures that achieves this end is often a difficult task, in particular for systems undergoing phase transitions. Here we present a method for determination of optimal replica spacings, which is based upon knowledge of local minima in the potential energy landscape. Working within the harmonic superposition approximation, we derive an analytic expression for the parallel tempering acceptance rate as a function of the replica temperatures. For a particular system and a given database of minima, we show how this expression can be used to determine optimal temperatures that achieve a desired uniform acceptance rate. We test our strategy for two atomic clusters that exhibit broken ergodicity, demonstrating that our method achieves uniform acceptance as well as significant efficiency gains.
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Affiliation(s)
- Andrew J. Ballard
- University
Chemical Laboratories, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United
Kingdom
| | - David J. Wales
- University
Chemical Laboratories, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United
Kingdom
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38
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Chill ST, Stevenson J, Ruehle V, Shang C, Xiao P, Farrell JD, Wales DJ, Henkelman G. Benchmarks for Characterization of Minima, Transition States, and Pathways in Atomic, Molecular, and Condensed Matter Systems. J Chem Theory Comput 2014; 10:5476-82. [DOI: 10.1021/ct5008718] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Samuel T. Chill
- Department
of Chemistry and the Institute for Computational and Engineering Sciences, The University of Texas at Austin, Austin, Texas 78712-0165, United States
| | - Jacob Stevenson
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Victor Ruehle
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Cheng Shang
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Penghao Xiao
- Department
of Chemistry and the Institute for Computational and Engineering Sciences, The University of Texas at Austin, Austin, Texas 78712-0165, United States
| | - James D. Farrell
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J. Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Graeme Henkelman
- Department
of Chemistry and the Institute for Computational and Engineering Sciences, The University of Texas at Austin, Austin, Texas 78712-0165, United States
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39
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Barcaro G, Sementa L, Fortunelli A. A grouping approach to homotop global optimization in alloy nanoparticles. Phys Chem Chem Phys 2014; 16:24256-65. [DOI: 10.1039/c4cp03745f] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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40
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Truong NX, Savoca M, Harding DJ, Fielicke A, Dopfer O. Vibrational spectra and structures of neutral Si6X clusters (X = Be, B, C, N, O). Phys Chem Chem Phys 2014; 16:22364-72. [DOI: 10.1039/c4cp03414g] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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41
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Hédin F, Plattner N, Doll JD, Meuwly M. Spatial Averaging: Sampling Enhancement for Exploring Configurational Space of Atomic Clusters and Biomolecules. J Chem Theory Comput 2014; 10:4284-96. [DOI: 10.1021/ct500529w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Affiliation(s)
- Florent Hédin
- Department
of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Nuria Plattner
- Department
of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, D-14195 Berlin, Germany
| | - J. D. Doll
- Department
of Chemistry, Brown University, Providence, Rhode Island 02912, United States
| | - Markus Meuwly
- Department
of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
- Department
of Chemistry, Brown University, Providence, Rhode Island 02912, United States
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42
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Wu X, Wu G. An adaptive immune optimization algorithm with dynamic lattice searching operation for fast optimization of atomic clusters. Chem Phys 2014. [DOI: 10.1016/j.chemphys.2014.06.002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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43
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44
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Gould AL, Heard CJ, Logsdail AJ, Catlow CRA. Segregation effects on the properties of (AuAg)147. Phys Chem Chem Phys 2014; 16:21049-61. [DOI: 10.1039/c4cp00753k] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
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45
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Liu YR, Wen H, Huang T, Lin XX, Gai YB, Hu CJ, Zhang WJ, Huang W. Structural Exploration of Water, Nitrate/Water, and Oxalate/Water Clusters with Basin-Hopping Method Using a Compressed Sampling Technique. J Phys Chem A 2014; 118:508-16. [DOI: 10.1021/jp4109128] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yi-Rong Liu
- Laboratory of Atmospheric Physico-Chemistry, Anhui Institute of Optics & Fine Mechanics, Chinese Academy of Sciences, 350 Shushan Lake Road, Hefei, Anhui 230031, China
| | - Hui Wen
- Laboratory of Atmospheric Physico-Chemistry, Anhui Institute of Optics & Fine Mechanics, Chinese Academy of Sciences, 350 Shushan Lake Road, Hefei, Anhui 230031, China
| | - Teng Huang
- Laboratory of Atmospheric Physico-Chemistry, Anhui Institute of Optics & Fine Mechanics, Chinese Academy of Sciences, 350 Shushan Lake Road, Hefei, Anhui 230031, China
| | - Xiao-Xiao Lin
- Laboratory of Atmospheric Physico-Chemistry, Anhui Institute of Optics & Fine Mechanics, Chinese Academy of Sciences, 350 Shushan Lake Road, Hefei, Anhui 230031, China
| | - Yan-Bo Gai
- Laboratory of Atmospheric Physico-Chemistry, Anhui Institute of Optics & Fine Mechanics, Chinese Academy of Sciences, 350 Shushan Lake Road, Hefei, Anhui 230031, China
| | - Chang-Jin Hu
- Laboratory of Atmospheric Physico-Chemistry, Anhui Institute of Optics & Fine Mechanics, Chinese Academy of Sciences, 350 Shushan Lake Road, Hefei, Anhui 230031, China
| | - Wei-Jun Zhang
- Laboratory of Atmospheric Physico-Chemistry, Anhui Institute of Optics & Fine Mechanics, Chinese Academy of Sciences, 350 Shushan Lake Road, Hefei, Anhui 230031, China
- School of Environmental Science & Optoelectronic Technology, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026, China
| | - Wei Huang
- Laboratory of Atmospheric Physico-Chemistry, Anhui Institute of Optics & Fine Mechanics, Chinese Academy of Sciences, 350 Shushan Lake Road, Hefei, Anhui 230031, China
- School of Environmental Science & Optoelectronic Technology, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui 230026, China
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46
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Performance of modified Lennard–Jones potential to seed ab initio calculations of small cadmium clusters. COMPUT THEOR CHEM 2013. [DOI: 10.1016/j.comptc.2013.07.041] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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47
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Rondina GG, Da Silva JLF. Revised Basin-Hopping Monte Carlo Algorithm for Structure Optimization of Clusters and Nanoparticles. J Chem Inf Model 2013; 53:2282-98. [DOI: 10.1021/ci400224z] [Citation(s) in RCA: 85] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Gustavo G. Rondina
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970, São
Carlos, SP, Brazil
| | - Juarez L. F. Da Silva
- Instituto de Química de São Carlos, Universidade de São Paulo, Caixa Postal 780, 13560-970, São
Carlos, SP, Brazil
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48
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Rogan J, Varas A, Valdivia JA, Kiwi M. A strategy to find minimal energy nanocluster structures. J Comput Chem 2013; 34:2548-56. [PMID: 24037778 DOI: 10.1002/jcc.23419] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2013] [Revised: 07/25/2013] [Accepted: 08/04/2013] [Indexed: 12/19/2022]
Abstract
An unbiased strategy to search for the global and local minimal energy structures of free standing nanoclusters is presented. Our objectives are twofold: to find a diverse set of low lying local minima, as well as the global minimum. To do so, we use massively the fast inertial relaxation engine algorithm as an efficient local minimizer. This procedure turns out to be quite efficient to reach the global minimum, and also most of the local minima. We test the method with the Lennard-Jones (LJ) potential, for which an abundant literature does exist, and obtain novel results, which include a new local minimum for LJ13 , 10 new local minima for LJ14 , and thousands of new local minima for 15≤N≤65. Insights on how to choose the initial configurations, analyzing the effectiveness of the method in reaching low-energy structures, including the global minimum, are developed as a function of the number of atoms of the cluster. Also, a novel characterization of the potential energy surface, analyzing properties of the local minima basins, is provided. The procedure constitutes a promising tool to generate a diverse set of cluster conformations, both two- and three-dimensional, that can be used as an input for refinement by means of ab initio methods.
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Affiliation(s)
- José Rogan
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile 7800024, and Centro para el Desarrollo de la Nanociencia y la Nanotecnología (CEDENNA), Avda., Ecuador 3493, Santiago, Chile, 9170124
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