Abstract
We have designed a simple method to place particles on lattices, concentric shells and icosahedral concentric layers for minimizing the total energy of Lennard-Jones clusters, approximately, by analytical means. The most significant difference of our schemes from others is the dramatic reduction of parameters, which allows the study of large clusters, not possible otherwise. We present the derivation of formulae for minimal per-particle energy and for inter-particle distance. We also present their asymptotic values for large number of particles.
Original language | English (US) |
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Pages (from-to) | 325-341 |
Number of pages | 17 |
Journal | Journal of Global Optimization |
Volume | 16 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2000 |
Keywords
- Asymptotic convergence
- Global optimization
- Lennard-Jones clusters
ASJC Scopus subject areas
- Computer Science Applications
- Management Science and Operations Research
- Control and Optimization
- Applied Mathematics