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.
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References
Leary, R.H. (1997), Global optima of Lennard-Jones clusters, Journal of Global Optimization 11: 35–53.
Leary, R.H. (1996), A robust gradient descent algorithm for the global optimization of Lennard-Jones clusters. San Diego Supercomputer Center, San Diego, Technical Report GA-A-22514.
Northby, J.A. (1987), Structure and binding of Lennard-Jones clusters: 13 ⩽ N ⩽ 147, Journal of Chemical Physics 87: 6166–6178.
Pardalos, P.M., Shalloway, D., Xue, G.L. (1994), Optimization methods for computing global minima of non-convex potential energy functions, Journal of Global Optimization 4: 117–133.
Raoult, B., Farges, J., De Feraudy, M.F., Torchet, G. (1989), Comparison between icosahedral, decahedral, and crystalline Lennard-Jones models containing 500 to 6000 atoms, Philosophical Magazine B 60: 881–906
Xie, J., Northby, J.A., Freeman, D.L., Doll, J.D. (1989), Theoretical studies of the energetics and structure of atomic clusters, Journal of Chemical Physics 91: 612–619.
Xue, G.L. (1994), Improvement of the Northby algorithm for molecular conformation: better solutions, Journal of Global Optimization 4: 425–440.
Byrd, R.H., Eskow, E., Schnabel, R.B. (1995), A new large-scale global optimization method and its application to Lennard-Jones problems. Technical Report CU-CS-630–92, Department of Computer Science, University of Colorado, revised 1995; also in P.M. Pardalos, D. Shalloway, and G. Xue (eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 23, American Mathematical Society, Providence, R.I., 1995.
Coleman, T.E., Shalloway, D., Wu, Z. (1994), A parallel build-up algorithm for global energy minimizations of molecular clusters using effective energy simulated annealing, Journal of Global Optimization 4: 171–185.
Deng, Y., Rivera, C. (1999), Simple energy minimization for huge Lennard-Jones clusters by dramatic parameter reduction, Appl. Math. Lett. 12: 119.
Pardalos, P.M., Shalloway, D., Xue, G. (1995), Global minimization of nonconvex energy functions: molecular conformation and protein folding. DIMACS workshop, vol. 23.
Hargittai, I. (1990), Quasicrystals, Networks, and Molecules of Fivefold Symmetry. VCH Publishers.
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Deng, Y., Rivera, C. Approximate energy minimization for large Lennard-Jones clusters. Journal of Global Optimization 16, 325–341 (2000). https://doi.org/10.1023/A:1008306325145
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DOI: https://doi.org/10.1023/A:1008306325145