• Corpus ID: 16318727

A Brief Review on Results and Computational Algorithms for Minimizing the Lennard-Jones Potential

@article{Zhang2011ABR,
  title={A Brief Review on Results and Computational Algorithms for Minimizing the Lennard-Jones Potential},
  author={Jiapu Zhang},
  journal={ArXiv},
  year={2011},
  volume={abs/1101.0039}
}
  • Jiapu Zhang
  • Published 29 December 2010
  • Computer Science
  • ArXiv
The Lennard-Jones (LJ) Potential Energy Problem is to construct the most stable form of $N$ atoms of a molecule with the minimal LJ potential energy. This problem has a simple mathematical form $f(x) = 4\sum_{i=1}^N \sum_{j=1,j<i}^N (\frac{1}{\tau_{ij}^6} - \frac{1}{\tau_{ij}^3} {subject to} x\in \mathbb{R}^n$, where $\tau_{ij} = (x_{3i-2} - x_{3j-2})^2 + (x_{3i-1} - x_{3j-1})^2 + (x_{3i} - x_{3j})^2$, $(x_{3i-2},x_{3i-1},x_{3i})$ is the coordinates of atom $i$ in $\mathbb{R}^3$, $i,j=1,2,...,N… 

Tables from this paper

Comparative study of population-based metaheuristic methods in global optimization

This thesis studies so-called population-based metaheuristics, especially Nature-inspired evolutionary algorithms and swarm intelligence, and studies their capabilities of solving a difficult real-world optimization problem, the Lennard-Jones cluster structure problem.

References

SHOWING 1-10 OF 46 REFERENCES

Improvement on the northby algorithm for molecular conformation: Better solutions

  • G. Xue
  • Computer Science
    J. Glob. Optim.
  • 1994
Simple data structures are introduced which reduce the time complexity of the Northby algorithm for lattice search from O(n5/3) per move toO(n2/3" per move for ann-atom cluster involving full Lennard-Jones potential function and show that in some cases, the relaxation of a lattice local minimizers with a worse potential function value may lead to a local minimizer with a better potential functionvalue.

The optimal geometry of Lennard-Jones clusters: 148-309

Structure and binding of Lennard‐Jones clusters: 13≤N≤147

An efficient lattice based search and optimization procedure has been developed and used with various assumed pair potentials to find minimal energy structures on an icosahedrally derived lattice.

Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms

We describe a global optimization technique using “basin-hopping” in which the potential energy surface is transformed into a collection of interpenetrating staircases. This method has been designed

Morphology and statistical statics of simple microclusters

Abstract In this paper we discuss the statics of small assemblies of soft, rare-gas type atoms (N=4 to 13) interacting under simple two-body central forces such as the Lennard-Jones and Morse type.

Molecular conformation on the CM-5 by parallel two-level simulated annealing

  • G. Xue
  • Computer Science
    J. Glob. Optim.
  • 1994
A two-level simulated annealing algorithm for solving certain class of hard combinatorial optimization problems is proposed and the full Lennard-Jones potential function is presented, with satisfactory results for problems for cluster sizes as large as 100,000.

Physical cluster mechanics: Statics and energy surfaces for monatomic systems

Abstract The potential energy surfaces for clusters of some three to sixty atoms under Lennard-Jones forces have been systematically explored using numerical optimization techniques. In searching for

An Infeasible Point Method for Minimizing the Lennard-Jones Potential

The Lennard-Jones potential problem is reformulated as an equality constrained nonlinear programming problem with only linear constraints, which allows the solution to approached through infeasible configurations, increasing the basin of attraction of the globalsolution.

Thermodynamics and the Global Optimization of Lennard-Jones clusters

Theoretical design of global optimization algorithms can profitably utilize recent statistical mechanical treatments of potential energy surfaces (PES’s). Here we analyze the basin-hopping algorithm

A parallel build-up algorithm for global energy minimizations of molecular clusters using effective energy simulated annealing

The algorithm was effective for relatively large test problems, and also very suitable for massively parallel computation, and for the 72-atom Lennard-Jones microcluster, the algorithm found a structure whose energy is lower than any others found in previous studies.