1
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Cerasoli FT, Donadio D. Effective optimization of atomic decoration in giant and superstructurally ordered crystals with machine learning. J Chem Phys 2024; 161:044101. [PMID: 39037130 DOI: 10.1063/5.0213132] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2024] [Accepted: 07/05/2024] [Indexed: 07/23/2024] Open
Abstract
Crystals with complicated geometry are often observed with mixed chemical occupancy among Wyckoff sites, presenting a unique challenge for accurate atomic modeling. Similar systems possessing exact occupancy on all the sites can exhibit superstructural ordering, dramatically inflating the unit cell size. In this work, a crystal graph convolutional neural network (CGCNN) is used to predict optimal atomic decorations on fixed crystalline geometries. This is achieved with a site permutation search (SPS) optimization algorithm based on Monte Carlo moves combined with simulated annealing and basin-hopping techniques. Our approach relies on the evidence that, for a given chemical composition, a CGCNN estimates the correct energetic ordering of different atomic decorations, as predicted by electronic structure calculations. This provides a suitable energy landscape that can be optimized according to site occupation, allowing the prediction of chemical decoration in crystals exhibiting mixed or disordered occupancy, or superstructural ordering. Verification of the procedure is carried out on several known compounds, including the superstructurally ordered clathrate compound Rb8Ga27Sb16 and vacancy-ordered perovskite Cs2SnI6, neither of which was previously seen during the neural network training. In addition, the critical temperature of an order-disorder phase transition in solid solution CuZn is probed with our SPS routines by sampling site configuration trajectories in the canonical ensemble. This strategy provides an accurate method for determining favorable decoration in complex crystals and analyzing site occupation at unprecedented speed and scale.
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Affiliation(s)
- Frank T Cerasoli
- Department of Chemistry, University of California, Davis, California 95616, USA
| | - Davide Donadio
- Department of Chemistry, University of California, Davis, California 95616, USA
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2
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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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3
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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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4
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Keith AD, Sawyer EB, Choy DCY, Xie Y, Biggs GS, Klein OJ, Brear PD, Wales DJ, Barker PD. Combining experiment and energy landscapes to explore anaerobic heme breakdown in multifunctional hemoproteins. Phys Chem Chem Phys 2024; 26:695-712. [PMID: 38053511 DOI: 10.1039/d3cp03897a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
To survive, many pathogens extract heme from their host organism and break down the porphyrin scaffold to sequester the Fe2+ ion via a heme oxygenase. Recent studies have revealed that certain pathogens can anaerobically degrade heme. Our own research has shown that one such pathway proceeds via NADH-dependent heme degradation, which has been identified in a family of hemoproteins from a range of bacteria. HemS, from Yersinia enterocolitica, is the main focus of this work, along with HmuS (Yersinia pestis), ChuS (Escherichia coli) and ShuS (Shigella dysenteriae). We combine experiments, Energy Landscape Theory, and a bioinformatic investigation to place these homologues within a wider phylogenetic context. A subset of these hemoproteins are known to bind certain DNA promoter regions, suggesting not only that they can catalytically degrade heme, but that they are also involved in transcriptional modulation responding to heme flux. Many of the bacterial species responsible for these hemoproteins (including those that produce HemS, ChuS and ShuS) are known to specifically target oxygen-depleted regions of the gastrointestinal tract. A deeper understanding of anaerobic heme breakdown processes exploited by these pathogens could therefore prove useful in the development of future strategies for disease prevention.
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Affiliation(s)
- Alasdair D Keith
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK.
| | - Elizabeth B Sawyer
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK.
| | - Desmond C Y Choy
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK.
| | - Yuhang Xie
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK.
| | - George S Biggs
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK.
| | - Oskar James Klein
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK.
| | - Paul D Brear
- Department of Biochemistry, University of Cambridge, Sanger Building, Cambridge CB2 1GA, UK
| | - David J Wales
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK.
| | - Paul D Barker
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, UK.
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5
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Nicy, Collepardo-Guevara R, Joseph JA, Wales DJ. Energy landscapes and heat capacity signatures for peptides correlate with phase separation propensity. QRB DISCOVERY 2023; 4:e7. [PMID: 37771761 PMCID: PMC10523320 DOI: 10.1017/qrd.2023.5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Revised: 07/09/2023] [Accepted: 07/17/2023] [Indexed: 09/30/2023] Open
Abstract
Phase separation plays an important role in the formation of membraneless compartments within the cell and intrinsically disordered proteins with low-complexity sequences can drive this compartmentalisation. Various intermolecular forces, such as aromatic-aromatic and cation-aromatic interactions, promote phase separation. However, little is known about how the ability of proteins to phase separate under physiological conditions is encoded in their energy landscapes and this is the focus of the present investigation. Our results provide a first glimpse into how the energy landscapes of minimal peptides that contain - and cation- interactions differ from the peptides that lack amino acids with such interactions. The peaks in the heat capacity () as a function of temperature report on alternative low-lying conformations that differ significantly in terms of their enthalpic and entropic contributions. The analysis and subsequent quantification of frustration of the energy landscape suggest that the interactions that promote phase separation lead to features (peaks or inflection points) at low temperatures in . More features may occur for peptides containing residues with better phase separation propensity and the energy landscape is more frustrated for such peptides. Overall, this work links the features in the underlying single-molecule potential energy landscapes to their collective phase separation behaviour and identifies quantities ( and frustration metric) that can be utilised in soft material design.
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Affiliation(s)
- Nicy
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, UK
| | - Rosana Collepardo-Guevara
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, UK
- Department of Physics, University of Cambridge, Cambridge, UK
- Department of Genetics, University of Cambridge, Cambridge, UK
| | - Jerelle A. Joseph
- Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ, USA
| | - David J. Wales
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, UK
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6
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Werkovits A, Jeindl A, Hörmann L, Cartus JJ, Hofmann OT. Toward Targeted Kinetic Trapping of Organic–Inorganic Interfaces: A Computational Case Study. ACS PHYSICAL CHEMISTRY AU 2022; 2:38-46. [PMID: 35098244 PMCID: PMC8796281 DOI: 10.1021/acsphyschemau.1c00015] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Revised: 09/21/2021] [Accepted: 09/23/2021] [Indexed: 11/29/2022]
Abstract
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Properties of inorganic–organic interfaces, such as their
interface dipole, strongly depend on the structural arrangements of
the organic molecules. A prime example is tetracyanoethylene (TCNE)
on Cu(111), which shows two different phases with significantly different
work functions. However, the thermodynamically preferred phase is
not always the one that is best suited for a given application. Rather,
it may be desirable to selectively grow a kinetically trapped structure.
In this work, we employ density functional theory and transition state
theory to discuss under which conditions such a kinetic trapping might
be possible for the model system of TCNE on Cu. Specifically, we want
to trap the molecules in the first layer in a flat-lying orientation.
This requires temperatures that are sufficiently low to suppress the
reorientation of the molecules, which is thermodynamically more favorable
for high dosages, but still high enough to enable ordered growth through
diffusion of molecules. On the basis of the temperature-dependent
diffusion and reorientation rates, we propose a temperature range
at which the reorientation can be successfully suppressed.
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Affiliation(s)
- Anna Werkovits
- Institute of Solid State Physics, TU Graz, NAWI Graz, Petersgasse 16/II, 8010 Graz, Austria
| | - Andreas Jeindl
- Institute of Solid State Physics, TU Graz, NAWI Graz, Petersgasse 16/II, 8010 Graz, Austria
| | - Lukas Hörmann
- Institute of Solid State Physics, TU Graz, NAWI Graz, Petersgasse 16/II, 8010 Graz, Austria
| | - Johannes J. Cartus
- Institute of Solid State Physics, TU Graz, NAWI Graz, Petersgasse 16/II, 8010 Graz, Austria
| | - Oliver T. Hofmann
- Institute of Solid State Physics, TU Graz, NAWI Graz, Petersgasse 16/II, 8010 Graz, Austria
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7
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Energy landscapes of perfect and defective solids: from structure prediction to ion conduction. Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02834-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
AbstractThe energy landscape concept is increasingly valuable in understanding and unifying the structural, thermodynamic and dynamic properties of inorganic solids. We present a range of examples which include (i) structure prediction of new bulk phases including carbon nitrides, phosphorus carbides, LiMgF3 and low-density, ultra-flexible polymorphs of B2O3, (ii) prediction of graphene and related forms of ZnO, ZnS and other compounds which crystallise in the bulk with the wurtzite structure, (iii) solid solutions, (iv) understanding grossly non-stoichiometric oxides including the superionic phases of δ-Bi2O3 and BIMEVOX and the consequences for the mechanisms of ion transport in these fast ion conductors. In general, examination of the energy landscapes of disordered materials highlights the importance of local structural environments, rather than sole consideration of the average structure.
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8
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Determination of stable structure of a cluster using convolutional neural network and particle swarm optimization. Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02726-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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9
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Syuhada I, Hauwali NUJ, Rosikhin A, Sustini E, Noor FA, Winata T. Bond order redefinition needed to reduce inherent noise in molecular dynamics simulations. Sci Rep 2021; 11:3674. [PMID: 33574347 PMCID: PMC7878785 DOI: 10.1038/s41598-020-80217-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Accepted: 12/17/2020] [Indexed: 01/30/2023] Open
Abstract
In this work, we present the bond order redefinition needed to reduce the inherent noise in order to enhance the accuracy of molecular dynamics simulations. We propose defining the bond order as a fraction of energy distribution. It happens due to the character of the material in nature, which tries to maintain its environment. To show the necessity, we developed a factory empirical interatomic potential (FEIP) for carbon that implements the redefinition with a short-range interaction approach. FEIP has been shown to enhance the accuracy of the calculation of lattice constants, cohesive energy, elastic properties, and phonons compared to experimental data, and can even be compared to other potentials with the long-range interaction approach. The enhancements due to FEIP can reduce the inherent noise, then provide a better prediction of the energy based on the behaviour of the atomic environment. FEIP can also transform simple two-body interactions into many-body interactions, which is useful for enhancing accuracy. Due to implementing the bond order redefinition, FEIP offers faster calculations than other complex interatomic potentials.
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Affiliation(s)
- Ibnu Syuhada
- Physics of Electronic Materials Research Division, Department of Physics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung, 40132, Indonesia.
| | - Nikodemus Umbu Janga Hauwali
- Physics of Electronic Materials Research Division, Department of Physics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung, 40132, Indonesia
| | - Ahmad Rosikhin
- Physics of Electronic Materials Research Division, Department of Physics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung, 40132, Indonesia
| | - Euis Sustini
- Physics of Electronic Materials Research Division, Department of Physics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung, 40132, Indonesia
| | - Fatimah Arofiati Noor
- Physics of Electronic Materials Research Division, Department of Physics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung, 40132, Indonesia.
| | - Toto Winata
- Physics of Electronic Materials Research Division, Department of Physics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung, 40132, Indonesia.
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10
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Rodríguez-Kessler PL, Rodríguez-Domínguez AR, Muñoz-Castro A. Systematic cluster growth: a structure search method for transition metal clusters. Phys Chem Chem Phys 2021; 23:4935-4943. [DOI: 10.1039/d0cp06179d] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The systematic cluster growth (SCG) method is a biased structure search strategy based on a seeding process for investigating the structural evolution and growth pattern of transition metal clusters.
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Affiliation(s)
- Peter L. Rodríguez-Kessler
- Grupo de Química Inorgánica y Materiales Moleculares
- Facultad de Ingeniería
- Universidad Autónoma de Chile
- Santiago
- Chile
| | | | - Alvaro Muñoz-Castro
- Grupo de Química Inorgánica y Materiales Moleculares
- Facultad de Ingeniería
- Universidad Autónoma de Chile
- Santiago
- Chile
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11
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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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12
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Ghosh K, Sharma R, Chaudhury P. Structure elucidation and construction of isomerisation pathways in small to moderate-sized (6-27) MgO nanoclusters: an adaptive mutation simulated annealing based analysis with quantum chemical calculations. Phys Chem Chem Phys 2020; 22:9616-9629. [PMID: 32324181 DOI: 10.1039/c9cp06947j] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Determination of global minimum structures and elucidation of reaction paths or minimum energy paths between low-lying minima are of great chemical importance. To that end, we have used our own Adaptive Mutation Simulated Annealing method to determine the global minimum and the minimum energy paths for various isomerisation reactions for small to moderate-sized (MgO)n (n = 6-27) clusters, using the Born-Mayer potential with suitable parameter values. The minimum energy structures obtained by us match well with previously reported data and are used as guess structures for further optimisation at the DFT level (using the B3LYP functional and DGDZVP basis set). Our optimised structures are found to match very well with the further DFT optimised structures, where the comparison is done by determining the root mean square deviation values as well as the radial distribution function profiles. A scheme is proposed to determine the minimum energy paths for isomerisation reactions for some cluster sizes where the transition state/s obtained by us, at very low computational cost, match well with those obtained from further optimisation using DFT calculations. We have shown the efficacy of our method in determining the reaction pathways, even for cases that involve multi-step reactions.
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Affiliation(s)
- Kuntal Ghosh
- Department of Chemistry, St. Xavier's College, 30 Mother Teresa Sarani, Kolkata - 700016, India.
| | - Rahul Sharma
- Department of Chemistry, St. Xavier's College, 30 Mother Teresa Sarani, Kolkata - 700016, India.
| | - Pinaki Chaudhury
- Department of Chemistry, University of Calcutta, Kolkata - 700009, India.
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13
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Becker S, Zhang Y, Lee AA. Geometry of Energy Landscapes and the Optimizability of Deep Neural Networks. PHYSICAL REVIEW LETTERS 2020; 124:108301. [PMID: 32216422 DOI: 10.1103/physrevlett.124.108301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2018] [Revised: 11/13/2019] [Accepted: 02/06/2020] [Indexed: 06/10/2023]
Abstract
Deep neural networks are workhorse models in machine learning with multiple layers of nonlinear functions composed in series. Their loss function is highly nonconvex, yet empirically even gradient descent minimization is sufficient to arrive at accurate and predictive models. It is hitherto unknown why deep neural networks are easily optimizable. We analyze the energy landscape of a spin glass model of deep neural networks using random matrix theory and algebraic geometry. We analytically show that the multilayered structure holds the key to optimizability: Fixing the number of parameters and increasing network depth, the number of stationary points in the loss function decreases, minima become more clustered in parameter space, and the trade-off between the depth and width of minima becomes less severe. Our analytical results are numerically verified through comparison with neural networks trained on a set of classical benchmark datasets. Our model uncovers generic design principles of machine learning models.
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Affiliation(s)
- Simon Becker
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Yao Zhang
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
| | - Alpha A Lee
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
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14
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Sharipov AS, Loukhovitski BI. Small atomic clusters: quantum chemical research of isomeric composition and physical properties. Struct Chem 2019. [DOI: 10.1007/s11224-019-01417-7] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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15
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Sharpe DJ, Wales DJ. Identifying mechanistically distinct pathways in kinetic transition networks. J Chem Phys 2019; 151:124101. [DOI: 10.1063/1.5111939] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- 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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16
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Jana G, Mitra A, Pan S, Sural S, Chattaraj PK. Modified Particle Swarm Optimization Algorithms for the Generation of Stable Structures of Carbon Clusters, C n ( n = 3-6, 10). Front Chem 2019; 7:485. [PMID: 31355182 PMCID: PMC6640203 DOI: 10.3389/fchem.2019.00485] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2019] [Accepted: 06/24/2019] [Indexed: 11/13/2022] Open
Abstract
Particle Swarm Optimization (PSO), a population based technique for stochastic search in a multidimensional space, has so far been employed successfully for solving a variety of optimization problems including many multifaceted problems, where other popular methods like steepest descent, gradient descent, conjugate gradient, Newton method, etc. do not give satisfactory results. Herein, we propose a modified PSO algorithm for unbiased global minima search by integrating with density functional theory which turns out to be superior to the other evolutionary methods such as simulated annealing, basin hopping and genetic algorithm. The present PSO code combines evolutionary algorithm with a variational optimization technique through interfacing of PSO with the Gaussian software, where the latter is used for single point energy calculation in each iteration step of PSO. Pure carbon and carbon containing systems have been of great interest for several decades due to their important role in the evolution of life as well as wide applications in various research fields. Our study shows how arbitrary and randomly generated small Cn clusters (n = 3-6, 10) can be transformed into the corresponding global minimum structure. The detailed results signify that the proposed technique is quite promising in finding the best global solution for small population size clusters.
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Affiliation(s)
- Gourhari Jana
- Department of Chemistry and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur, India
| | - Arka Mitra
- Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Kharagpur, India
| | - Sudip Pan
- Fachbereich Chemie, Philipps-Universität Marburg, Marburg, Germany
| | - Shamik Sural
- Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, India
| | - Pratim K. Chattaraj
- Department of Chemistry and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur, India
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai, India
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17
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Sturniolo S, Liborio L, Jackson S. Comparison between density functional theory and density functional tight binding approaches for finding the muon stopping site in organic molecular crystals. J Chem Phys 2019; 150:154301. [PMID: 31005103 DOI: 10.1063/1.5085197] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Finding the possible stopping sites for muons inside a crystalline sample is a key problem of muon spectroscopy. In a previous study, we suggested a computational approach to this problem when dealing with muonium, the pseudoatom formed by a positive muon that has captured an electron, using density functional theory software in combination with a random structure searching approach that relies on a Poisson sphere distribution. In this work, we test this methodology further by applying it to muonium in three organic molecular crystal model systems: durene, bithiophene, and tetracyanoquinodimethane. Using the same sets of random structures, we compare the performance of density functional theory software CASTEP and the much faster lower level approximation of Density Functional Tight Binding provided by DFTB+ combined with the use of the 3ob-3-1 parameter set. We show the benefits and limitations of such an approach, and we propose the use of DFTB+ as a viable alternative to more cumbersome simulations for routine site-finding in organic materials. Finally, we introduce the Muon Spectroscopy Computational Project software suite, a library of Python tools meant to make these methods standardized and easy to use.
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Affiliation(s)
| | - Leandro Liborio
- Scientific Computing Department, UKRI, Swindon,United Kingdom
| | - Samuel Jackson
- Scientific Computing Department, UKRI, Swindon,United Kingdom
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18
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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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19
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Mallory JD, Mandelshtam VA. Quantum-induced solid-solid transitions and melting in the Lennard-Jones LJ 38 cluster. J Chem Phys 2018; 149:104305. [DOI: 10.1063/1.5050410] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Joel D. Mallory
- Department of Chemistry, University of California, Irvine, California 92617, 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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Mehta D, Zhao X, Bernal EA, Wales DJ. Loss surface of XOR artificial neural networks. Phys Rev E 2018; 97:052307. [PMID: 29906831 DOI: 10.1103/physreve.97.052307] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2017] [Indexed: 11/07/2022]
Abstract
Training an artificial neural network involves an optimization process over the landscape defined by the cost (loss) as a function of the network parameters. We explore these landscapes using optimization tools developed for potential energy landscapes in molecular science. The number of local minima and transition states (saddle points of index one), as well as the ratio of transition states to minima, grow rapidly with the number of nodes in the network. There is also a strong dependence on the regularization parameter, with the landscape becoming more convex (fewer minima) as the regularization term increases. We demonstrate that in our formulation, stationary points for networks with N_{h} hidden nodes, including the minimal network required to fit the XOR data, are also stationary points for networks with N_{h}+1 hidden nodes when all the weights involving the additional node are zero. Hence, smaller networks trained on XOR data are embedded in the landscapes of larger networks. Our results clarify certain aspects of the classification and sensitivity (to perturbations in the input data) of minima and saddle points for this system, and may provide insight into dropout and network compression.
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Affiliation(s)
- Dhagash Mehta
- Systems Department, United Technologies Research Center, East Hartford, Connecticut 06108, USA
| | - Xiaojun Zhao
- Systems Department, United Technologies Research Center, East Hartford, Connecticut 06108, USA
| | - Edgar A Bernal
- Systems Department, United Technologies Research Center, East Hartford, Connecticut 06108, USA
| | - David J Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK
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23
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Liborio L, Sturniolo S, Jochym D. Computational prediction of muon stopping sites using ab initio random structure searching (AIRSS). J Chem Phys 2018; 148:134114. [DOI: 10.1063/1.5024450] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Leandro Liborio
- Scientific Computing Department, Rutherford Appleton Laboratory, STFC, Didcot OX11 0DE, United Kingdom
| | - Simone Sturniolo
- Scientific Computing Department, Rutherford Appleton Laboratory, STFC, Didcot OX11 0DE, United Kingdom
| | - Dominik Jochym
- Scientific Computing Department, Rutherford Appleton Laboratory, STFC, Didcot OX11 0DE, United Kingdom
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24
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Lee AA, Brenner MP, Colwell LJ. Optimal Design of Experiments by Combining Coarse and Fine Measurements. PHYSICAL REVIEW LETTERS 2017; 119:208101. [PMID: 29219382 DOI: 10.1103/physrevlett.119.208101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2017] [Indexed: 06/07/2023]
Abstract
In many contexts, it is extremely costly to perform enough high-quality experimental measurements to accurately parametrize a predictive quantitative model. However, it is often much easier to carry out large numbers of experiments that indicate whether each sample is above or below a given threshold. Can many such categorical or "coarse" measurements be combined with a much smaller number of high-resolution or "fine" measurements to yield accurate models? Here, we demonstrate an intuitive strategy, inspired by statistical physics, wherein the coarse measurements are used to identify the salient features of the data, while the fine measurements determine the relative importance of these features. A linear model is inferred from the fine measurements, augmented by a quadratic term that captures the correlation structure of the coarse data. We illustrate our strategy by considering the problems of predicting the antimalarial potency and aqueous solubility of small organic molecules from their 2D molecular structure.
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Affiliation(s)
- Alpha A Lee
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom and School of Engineering and Applied Sciences and Kavli Institute of Bionano Science and Technology, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Michael P Brenner
- School of Engineering and Applied Sciences and Kavli Institute of Bionano Science and Technology, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Lucy J Colwell
- Department of Chemistry, University of Cambridge, CB2 1EW Cambridge, United Kingdom
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25
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Mallory JD, Mandelshtam VA. Quantum Melting and Isotope Effects from Diffusion Monte Carlo Studies of p-H2 Clusters. J Phys Chem A 2017; 121:6341-6348. [DOI: 10.1021/acs.jpca.7b06649] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Joel D. Mallory
- Department of Chemistry, University of California, Irvine, California 92697, United States
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26
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Wales DJ. Decoding heat capacity features from the energy landscape. Phys Rev E 2017; 95:030105. [PMID: 28415307 DOI: 10.1103/physreve.95.030105] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2017] [Indexed: 04/28/2023]
Abstract
A general scheme is derived to connect transitions in configuration space with features in the heat capacity. A formulation in terms of occupation probabilities for local minima that define the potential energy landscape provides a quantitative description of how contributions arise from competition between different states. The theory does not rely on a structural interpretation for the local minima, so it is equally applicable to molecular energy landscapes and the landscapes defined by abstract functions. Applications are presented for low-temperature solid-solid transitions in atomic clusters, which involve just a few local minima with different morphologies, and for cluster melting, which is driven by the landscape entropy associated with the more numerous high-energy minima. Analyzing these features in terms of the balance between states with increasing and decreasing occupation probabilities provides a direct interpretation of the underlying transitions. This approach enables us to identify a qualitatively different transition that is caused by a single local minimum associated with an exceptionally large catchment volume in configuration space for a machine learning landscape.
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Affiliation(s)
- David J Wales
- University Chemical Laboratories, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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27
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Husic BE, Schebarchov D, Wales DJ. Impurity effects on solid-solid transitions in atomic clusters. NANOSCALE 2016; 8:18326-18340. [PMID: 27775141 DOI: 10.1039/c6nr06299g] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We use the harmonic superposition approach to examine how a single atom substitution affects low-temperature anomalies in the vibrational heat capacity (CV) of model nanoclusters. Each anomaly is linked to competing solidlike "phases", where crossover of the corresponding free energies defines a solid-solid transition temperature (Ts). For selected Lennard-Jones clusters we show that Ts and the corresponding CV peak can be tuned over a wide range by varying the relative atomic size and binding strength of the impurity, but excessive atom-size mismatch can destroy a transition and may produce another. In some tunable cases we find up to two additional CV peaks emerging below Ts, signalling one- or two-step delocalisation of the impurity within the ground-state geometry. Results for Ni74X and Au54X clusters (X = Au, Ag, Al, Cu, Ni, Pd, Pt, Pb), modelled by the many-body Gupta potential, further corroborate the possibility of tuning, engineering, and suppressing finite-system analogues of a solid-solid transition in nanoalloys.
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Affiliation(s)
- B E Husic
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK. and Department of Chemistry, Stanford University, Stanford, CA 94305, USA.
| | - D Schebarchov
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK.
| | - D J Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, UK.
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28
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Yoshida Y, Sato H, Morgan JW, Wales DJ. Potential energy landscapes of tetragonal pyramid molecules. Chem Phys Lett 2016. [DOI: 10.1016/j.cplett.2016.09.058] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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29
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Schaefer B, Goedecker S. Computationally efficient characterization of potential energy surfaces based on fingerprint distances. J Chem Phys 2016; 145:034101. [DOI: 10.1063/1.4956461] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Affiliation(s)
- Bastian Schaefer
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Stefan Goedecker
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
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30
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Haber R, Hoffmann KH. Extending the parQ transition matrix method to grand canonical ensembles. Phys Rev E 2016; 93:063314. [PMID: 27415394 DOI: 10.1103/physreve.93.063314] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2015] [Indexed: 11/07/2022]
Abstract
Phase coexistence properties as well as other thermodynamic features of fluids can be effectively determined from the grand canonical density of states (DOS). We present an extension of the parQ transition matrix method in combination with the efasTM method as a very fast approach for determining the grand canonical DOS from the transition matrix. The efasTM method minimizes the deviation from detailed balance in the transition matrix using a fast Krylov-based equation solver. The method allows a very effective use of state space transition data obtained by different exploration schemes. An application to a Lennard-Jones system produces phase coexistence properties of the same quality as reference data.
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Affiliation(s)
- René Haber
- Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany
| | - Karl Heinz Hoffmann
- Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany
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31
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Marks LD, Peng L. Nanoparticle shape, thermodynamics and kinetics. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:053001. [PMID: 26792459 DOI: 10.1088/0953-8984/28/5/053001] [Citation(s) in RCA: 99] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
Nanoparticles can be beautiful, as in stained glass windows, or they can be ugly as in wear and corrosion debris from implants. We estimate that there will be about 70,000 papers in 2015 with nanoparticles as a keyword, but only one in thirteen uses the nanoparticle shape as an additional keyword and research focus, and only one in two hundred has thermodynamics. Methods for synthesizing nanoparticles have exploded over the last decade, but our understanding of how and why they take their forms has not progressed as fast. This topical review attempts to take a critical snapshot of the current understanding, focusing more on methods to predict than a purely synthetic or descriptive approach. We look at models and themes which are largely independent of the exact synthetic method whether it is deposition, gas-phase condensation, solution based or hydrothermal synthesis. Elements are old dating back to the beginning of the 20th century-some of the pioneering models developed then are still relevant today. Others are newer, a merging of older concepts such as kinetic-Wulff constructions with methods to understand minimum energy shapes for particles with twins. Overall we find that while there are still many unknowns, the broad framework of understanding and predicting the structure of nanoparticles via diverse Wulff constructions, either thermodynamic, local minima or kinetic has been exceedingly successful. However, the field is still developing and there remain many unknowns and new avenues for research, a few of these being suggested towards the end of the review.
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Affiliation(s)
- L D Marks
- Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208, USA
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32
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Fournier R, Mohareb A. Optimizing molecular properties using a relative index of thermodynamic stability and global optimization techniques. J Chem Phys 2016; 144:024114. [PMID: 26772561 DOI: 10.1063/1.4939530] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We devised a global optimization (GO) strategy for optimizing molecular properties with respect to both geometry and chemical composition. A relative index of thermodynamic stability (RITS) is introduced to allow meaningful energy comparisons between different chemical species. We use the RITS by itself, or in combination with another calculated property, to create an objective function F to be minimized. Including the RITS in the definition of F ensures that the solutions have some degree of thermodynamic stability. We illustrate how the GO strategy works with three test applications, with F calculated in the framework of Kohn-Sham Density Functional Theory (KS-DFT) with the Perdew-Burke-Ernzerhof exchange-correlation. First, we searched the composition and configuration space of CmHnNpOq (m = 0-4, n = 0-10, p = 0-2, q = 0-2, and 2 ≤ m + n + p + q ≤ 12) for stable molecules. The GO discovered familiar molecules like N2, CO2, acetic acid, acetonitrile, ethane, and many others, after a small number (5000) of KS-DFT energy evaluations. Second, we carried out a GO of the geometry of CumSnn (+) (m = 1, 2 and n = 9-12). A single GO run produced the same low-energy structures found in an earlier study where each CumSnn (+) species had been optimized separately. Finally, we searched bimetallic clusters AmBn (3 ≤ m + n ≤ 6, A,B= Li, Na, Al, Cu, Ag, In, Sn, Pb) for species and configurations having a low RITS and large highest occupied Molecular Orbital (MO) to lowest unoccupied MO energy gap (Eg). We found seven bimetallic clusters with Eg > 1.5 eV.
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Affiliation(s)
- René Fournier
- Department of Chemistry, York University, Toronto, Ontario M3J 1P3, Canada
| | - Amir Mohareb
- Department of Chemistry, York University, Toronto, Ontario M3J 1P3, Canada
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33
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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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34
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Wilson HF, Barnard AS. Water bilayers on ZnO(101̄0) surfaces: data-driven structural search. RSC Adv 2016. [DOI: 10.1039/c5ra26874e] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
We demonstrate an approach for the use of data science methods for structural search for high-stability atomic structures in ab initio simulation, via the analysis of a large set of candidate structures.
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Affiliation(s)
- Hugh F. Wilson
- CSIRO Virtual Nanoscience Laboratory
- Australia
- Department of Applied Physics
- RMIT University
- Melbourne
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35
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Pini D, Parola A, Reatto L. An unconstrained DFT approach to microphase formation and application to binary Gaussian mixtures. J Chem Phys 2015. [DOI: 10.1063/1.4926469] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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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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37
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Shang C, Wales DJ. Communication: optimal parameters for basin-hopping global optimization based on Tsallis statistics. J Chem Phys 2015; 141:071101. [PMID: 25149766 DOI: 10.1063/1.4893344] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A fundamental problem associated with global optimization is the large free energy barrier for the corresponding solid-solid phase transitions for systems with multi-funnel energy landscapes. To address this issue we consider the Tsallis weight instead of the Boltzmann weight to define the acceptance ratio for basin-hopping global optimization. Benchmarks for atomic clusters show that using the optimal Tsallis weight can improve the efficiency by roughly a factor of two. We present a theory that connects the optimal parameters for the Tsallis weighting, and demonstrate that the predictions are verified for each of the test cases.
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Affiliation(s)
- C Shang
- 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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38
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Exploiting the potential energy landscape to sample free energy. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2015. [DOI: 10.1002/wcms.1217] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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39
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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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40
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Asgari M, Behnejad H, Fortunelli A. Composition-dependent melting behaviour of Na xK 55–xcore–shell nanoalloys. Mol Phys 2014. [DOI: 10.1080/00268976.2014.919039] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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41
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Cameron MK. Metastability, spectrum, and eigencurrents of the Lennard-Jones-38 network. J Chem Phys 2014; 141:184113. [PMID: 25399138 DOI: 10.1063/1.4901131] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop computational tools for spectral analysis of stochastic networks representing energy landscapes of atomic and molecular clusters. Physical meaning and some properties of eigenvalues, left and right eigenvectors, and eigencurrents are discussed. We propose an approach to compute a collection of eigenpairs and corresponding eigencurrents describing the most important relaxation processes taking place in the system on its way to the equilibrium. It is suitable for large and complex stochastic networks where pairwise transition rates, given by the Arrhenius law, vary by orders of magnitude. The proposed methodology is applied to the network representing the Lennard-Jones-38 cluster created by Wales's group. Its energy landscape has a double funnel structure with a deep and narrow face-centered cubic funnel and a shallower and wider icosahedral funnel. However, the complete spectrum of the generator matrix of the Lennard-Jones-38 network has no appreciable spectral gap separating the eigenvalue corresponding to the escape from the icosahedral funnel. We provide a detailed description of the escape process from the icosahedral funnel using the eigencurrent and demonstrate a superexponential growth of the corresponding eigenvalue. The proposed spectral approach is compared to the methodology of the Transition Path Theory. Finally, we discuss whether the Lennard-Jones-38 cluster is metastable from the points of view of a mathematician and a chemical physicist, and make a connection with experimental works.
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Affiliation(s)
- Maria K Cameron
- Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015, USA
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42
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Schebarchov D, Wales DJ. Structure prediction for multicomponent materials using biminima. PHYSICAL REVIEW LETTERS 2014; 113:156102. [PMID: 25375724 DOI: 10.1103/physrevlett.113.156102] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2014] [Indexed: 06/04/2023]
Abstract
The potential energy surface of a heteroparticle system will contain points that are local minima in both coordinate space and permutation space for the different species. We introduce the term biminima to describe these special points, and we formulate a deterministic scheme for finding them. Our search algorithm generates a converging sequence of particle-identity swaps, each accompanied by a number of local geometry relaxations. For selected binary atomic clusters of size N = N(A) + N(B) ≤ 98, convergence to a biminimum on average takes 3 N(A)N(B) relaxations, and the number of biminima grows with the preference for mixing. The new framework unifies continuous and combinatorial optimization, providing a powerful tool for structure prediction and rational design of multicomponent materials.
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Affiliation(s)
- 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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43
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Mann M, Kucharík M, Flamm C, Wolfinger MT. Memory-efficient RNA energy landscape exploration. Bioinformatics 2014; 30:2584-91. [PMID: 24833804 PMCID: PMC4155248 DOI: 10.1093/bioinformatics/btu337] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2014] [Revised: 04/25/2014] [Accepted: 05/08/2014] [Indexed: 02/01/2023] Open
Abstract
MOTIVATION Energy landscapes provide a valuable means for studying the folding dynamics of short RNA molecules in detail by modeling all possible structures and their transitions. Higher abstraction levels based on a macro-state decomposition of the landscape enable the study of larger systems; however, they are still restricted by huge memory requirements of exact approaches. RESULTS We present a highly parallelizable local enumeration scheme that enables the computation of exact macro-state transition models with highly reduced memory requirements. The approach is evaluated on RNA secondary structure landscapes using a gradient basin definition for macro-states. Furthermore, we demonstrate the need for exact transition models by comparing two barrier-based approaches, and perform a detailed investigation of gradient basins in RNA energy landscapes. AVAILABILITY AND IMPLEMENTATION Source code is part of the C++ Energy Landscape Library available at http://www.bioinf.uni-freiburg.de/Software/.
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Affiliation(s)
- Martin Mann
- Bioinformatics Group, Department of Computer Science, University of Freiburg, 79110 Freiburg, Germany, Institute for Theoretical Chemistry, University of Vienna, 1090 Vienna, Center for Integrative Bioinformatics Vienna, Max F. Perutz Laboratories, University of Vienna, Medical University of Vienna, and Department of Biochemistry and Molecular Cell Biology, Max F. Perutz Laboratories, University of Vienna, A-1030 Vienna, Austria
| | - Marcel Kucharík
- Bioinformatics Group, Department of Computer Science, University of Freiburg, 79110 Freiburg, Germany, Institute for Theoretical Chemistry, University of Vienna, 1090 Vienna, Center for Integrative Bioinformatics Vienna, Max F. Perutz Laboratories, University of Vienna, Medical University of Vienna, and Department of Biochemistry and Molecular Cell Biology, Max F. Perutz Laboratories, University of Vienna, A-1030 Vienna, Austria
| | - Christoph Flamm
- Bioinformatics Group, Department of Computer Science, University of Freiburg, 79110 Freiburg, Germany, Institute for Theoretical Chemistry, University of Vienna, 1090 Vienna, Center for Integrative Bioinformatics Vienna, Max F. Perutz Laboratories, University of Vienna, Medical University of Vienna, and Department of Biochemistry and Molecular Cell Biology, Max F. Perutz Laboratories, University of Vienna, A-1030 Vienna, Austria
| | - Michael T Wolfinger
- Bioinformatics Group, Department of Computer Science, University of Freiburg, 79110 Freiburg, Germany, Institute for Theoretical Chemistry, University of Vienna, 1090 Vienna, Center for Integrative Bioinformatics Vienna, Max F. Perutz Laboratories, University of Vienna, Medical University of Vienna, and Department of Biochemistry and Molecular Cell Biology, Max F. Perutz Laboratories, University of Vienna, A-1030 Vienna, Austria Bioinformatics Group, Department of Computer Science, University of Freiburg, 79110 Freiburg, Germany, Institute for Theoretical Chemistry, University of Vienna, 1090 Vienna, Center for Integrative Bioinformatics Vienna, Max F. Perutz Laboratories, University of Vienna, Medical University of Vienna, and Department of Biochemistry and Molecular Cell Biology, Max F. Perutz Laboratories, University of Vienna, A-1030 Vienna, Austria Bioinformatics Group, Department of Computer Science, University of Freiburg, 79110 Freiburg, Germany, Institute for Theoretical Chemistry, University of Vienna, 1090 Vienna, Center for Integrative Bioinformatics Vienna, Max F. Perutz Laboratories, University of Vienna, Medical University of Vienna, and Department of Biochemistry and Molecular Cell Biology, Max F. Perutz Laboratories, University of Vienna, A-1030 Vienna, Austria
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44
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Kim Y, Choi S, Kim WY. Efficient Basin-Hopping Sampling of Reaction Intermediates through Molecular Fragmentation and Graph Theory. J Chem Theory Comput 2014; 10:2419-26. [DOI: 10.1021/ct500136x] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Affiliation(s)
- Yeonjoon Kim
- Department
of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Korea
| | - Sunghwan Choi
- Department
of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Korea
| | - Woo Youn Kim
- Department
of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Korea
- KAIST
Institute for NanoCentury, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Korea
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Sehgal RM, Maroudas D, Ford DM. Phase behavior of the 38-atom Lennard-Jones cluster. J Chem Phys 2014; 140:104312. [DOI: 10.1063/1.4866810] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Senn F, Wiebke J, Schumann O, Gohr S, Schwerdtfeger P, Pahl E. Melting of “non-magic” argon clusters and extrapolation to the bulk limit. J Chem Phys 2014; 140:044325. [DOI: 10.1063/1.4862906] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
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47
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Wales DJ. Surveying a complex potential energy landscape: Overcoming broken ergodicity using basin-sampling. Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2013.07.066] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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48
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Somani S, Wales DJ. Energy landscapes and global thermodynamics for alanine peptides. J Chem Phys 2013; 139:121909. [DOI: 10.1063/1.4813627] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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49
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Sarkar K, Bhattacharyya SP. Single string based global optimizer for geometry optimization in strongly coupled finite clusters: An adaptive mutation-driven strategy. J Chem Phys 2013; 139:074106. [PMID: 23968071 DOI: 10.1063/1.4818162] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
We propose and implement a simple adaptive heuristic to optimize the geometries of clusters of point charges or ions with the ability to find the global minimum energy configurations. The approach uses random mutations of a single string encoding the geometry and accepts moves that decrease the energy. Mutation probability and mutation intensity are allowed to evolve adaptively on the basis of continuous evaluation of past explorations. The resulting algorithm has been called Completely Adaptive Random Mutation Hill Climbing method. We have implemented this method to search through the complex potential energy landscapes of parabolically confined 3D classical Coulomb clusters of hundreds or thousands of charges--usually found in high frequency discharge plasmas. The energy per particle (EN∕N) and its first and second differences, structural features, distribution of the oscillation frequencies of normal modes, etc., are analyzed as functions of confinement strength and the number of charges in the system. Certain magic numbers are identified. In order to test the feasibility of the algorithm in cluster geometry optimization on more complex energy landscapes, we have applied the algorithm for optimizing the geometries of MgO clusters, described by Coulomb-Born-Mayer potential and finding global minimum of some Lennard-Jones clusters. The convergence behavior of the algorithm compares favorably with those of other existing global optimizers.
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Affiliation(s)
- Kanchan Sarkar
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
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50
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Grebner C, Pason LP, Engels B. PathOpt-A global transition state search approach: Outline of algorithm. J Comput Chem 2013; 34:1810-8. [DOI: 10.1002/jcc.23307] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2013] [Revised: 03/30/2013] [Accepted: 04/04/2013] [Indexed: 01/05/2023]
Affiliation(s)
- Christoph Grebner
- Institut für Physikalische und Theoretische Chemie, Fakultät für Chemie und Pharmazie; Julius-Maximilians-Universität Würzburg; Emil-Fischer-Straße 42 Würzburg D-97074 Germany
| | - Lukas P. Pason
- Institut für Physikalische und Theoretische Chemie, Fakultät für Chemie und Pharmazie; Julius-Maximilians-Universität Würzburg; Emil-Fischer-Straße 42 Würzburg D-97074 Germany
| | - Bernd Engels
- Institut für Physikalische und Theoretische Chemie, Fakultät für Chemie und Pharmazie; Julius-Maximilians-Universität Würzburg; Emil-Fischer-Straße 42 Würzburg D-97074 Germany
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