Prediction of the lowest energy configuration for Lennard-Jones clusters

Lai, Xiangjing; Xu, Ran; Huang, Wenqi

doi:10.1007/s11426-011-4280-4

Cited by 12 publications

(6 citation statements)

References 40 publications

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“…[27][28][29] The LJ pair potential can be defined as follows: The main interaction potential we adopt is the LJ pair potential, which for several decades has been used as a benchmark for cluster energy minimization methods, and which even today constitutes a challenging and active area of research.…”

Section: The Fire Methodsmentioning

confidence: 99%

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A strategy to find minimal energy nanocluster structures

et al. 2013

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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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Section: The Fire Methodsmentioning

confidence: 99%

“…The main interaction potential we adopt is the LJ pair potential, which for several decades has been used as a benchmark for cluster energy minimization methods, and which even today constitutes a challenging and active area of research. [27][28][29] The LJ pair potential can be defined as follows:…”

Section: The Fire Methodsmentioning

confidence: 99%

A strategy to find minimal energy nanocluster structures

et al. 2013

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“…No symmetry constraints are imposed during the minimisations. This approach is therefore related to lattice-based approaches, 8,9,[17][18][19][20][21]43,44 but with sites defined by incomplete orbits of G core , which change throughout a run depending upon the current configuration.…”

Section: Overview Of the Core Orbits Symmetrisationmentioning

confidence: 99%

“…The best previous published results for optimisation of Lennard-Jones clusters involve particle swarm optimisation with symmetrical structures used to initialise the search. 13 Lattice-based searches have also proved to be effective, 8,9,[19][20][21]43,44 so long as a lattice that supports the true global minimum structure is included in the analysis. The core orbits approach described in the present contribution does not assume any particular point group symmetry, but instead searches for approximate symmetry operations in a general way.…”

Section: Introductionmentioning

confidence: 99%

Symmetrisation schemes for global optimisation of atomic clusters

Oakley

Johnston

Wales³

2013

Phys. Chem. Chem. Phys.

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Locating the global minima of atomic and molecular clusters can be a difficult optimisation problem. Here we report benchmarks for procedures that exploit approximate symmetry. This strategy was implemented in the GMIN program following a theoretical analysis, which explained why high-symmetry structures are more likely to have particularly high or particularly low energy. The analysis, and the corresponding algorithms, allow for approximate point group symmetry, and can be combined with basin-hopping and genetic algorithms. We report results for 38-, 75-, and 98-atom Lennard-Jones clusters, which are all multiple-funnel systems. Exploiting approximate symmetry reduces the mean time taken to locate the global minimum by up to two orders of magnitude, with smaller improvements in efficiency for LJ(55) and LJ(74), which correspond to simpler single-funnel energy landscapes.

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“…− Lai et al (2011a) found best solutions for N = 533 and 536 using the dynamic lattice searching method with two-phase local search and interior operation [31,32,55].…”

Section: Introductionmentioning

confidence: 99%

The Hybrid Idea of (Energy Minimization) Optimization Methods Applied to Study PrionProtein Structures Focusing on the beta2-alpha2 Loop

Zhang¹

2015

Biochem Pharmacol (Los Angel)

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In molecular mechanics, current generation potential energy functions provide a reasonably good compromise between accuracy and effectiveness. This paper firstly reviewed several most commonly used classical potential energy functions and their optimization methods used for energy minimization. To minimize a potential energy function, about 95% efforts are spent on the Lennard-Jones potential of van der Waals interactions; we also give a detailed review on some effective computational optimization methods in the Cambridge Cluster Database to solve the problem of Lennard-Jones clusters. From the reviews, we found the hybrid idea of optimization methods is effective, necessary and efficient for solving the potential energy minimization problem and the Lennard-Jones clusters problem. An application to prion protein structures is then done by the hybrid idea. We focus on the β2-α2 loop of prion protein structures, and we found (i) the species that has the clearly and highly ordered β2-α2 loop usually owns a 3 10 -helix in this loop, (ii) a "π-circle" Y128-F175-Y218-Y163-F175-Y169-R164-Y128(-Y162) is around the β2-α2 loop.

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Prediction of the lowest energy configuration for Lennard-Jones clusters

Cited by 12 publications

References 40 publications

A strategy to find minimal energy nanocluster structures

A strategy to find minimal energy nanocluster structures

Symmetrisation schemes for global optimisation of atomic clusters

The Hybrid Idea of (Energy Minimization) Optimization Methods Applied to Study PrionProtein Structures Focusing on the beta2-alpha2 Loop

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