Abstract
This paper presents a three-phase computational procedure for minimizing molecular energy potential functions of the pure Lennard-Jones type. The first phase consists of a special heuristic for generating an initial atomic configuration. In the second phase a global minimization method is applied to compute a configuration close to the optimal solution. Finally, the third phase uses this configuration as the starting point for a local minimization method. Since the second and third phases are very suitable for parallel implementation, we describe briefly our implementation of the method in a parallel version of C on a transputer network, and we exhibit numerical results for approximate optimization of clusters with up to 20,000 atoms.
The research reported here was sponsored in part by the Air Force Systems Command, USAF, under Grant F49620-95-1-0222. The U. S. Government has certain rights in this material, and is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the sponsoring agencies or the U. S. Government.
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References
R.H. Byrd, E. Eskow, and R.B. Schnabel, A new large-scale global optimization method and its application to Lennard-Jones problems, Technical report, University of Colorado at Boulder (1992).
T. Coleman, D. Shalloway, and Z. Wu, Isotropic effective energy simulated annealing searches for low energy molecular cluster states, Technical Report, Cornell Theory Center, Cornell University, Ithaca, NY (1992).
T. Coleman, D. Shalloway, and Z. Wu, A parallel build-up algorithm for global energy minimization of molecular clusters using effective energy simulated an-nealing,Technical Report, Cornell Theory Center, Cornell University, Ithaca, NY (1993).
M.R. Hoare and P. Pal, Physical cluster mechanics: statics and energy surfaces for monatomic systems Adv. Phys. 20, pp. 161–196 (1971).
I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus, Springer-Verlag, New York, Berlin, Heidelberg (1991).
R.S. Maier, J.B. Rosen, and G.L. Xue, A discrete-continuous algorithm for molecular energy minimization,Technical report, U. S. Army High-Performance Computing Research Center, University of Minnesota, Minneapolis, MN (1992).
J.A. Northby, Structure and binding of Lennard-Jones clusters: 13 ≤N ≤147, J. Chem. Phys. 87, pp. 6166–6177 (1987).
P. Protter, Stochastic Integration and Differential Equations, Springer-Verlag, New York, Berlin, Heidelberg (1990).
S. Schäppler, Unconstrained global optimization using stochastic integral equations, Optimization 35, pp. 43–60 (1995).
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© 1997 Springer Science+Business Media New York
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Ritter, K., Robinson, S.M., Schäffler, S. (1997). Global Minimization of Lennard-Jones Functions on Transputer Networks. In: Biegler, L.T., Conn, A.R., Coleman, T.F., Santosa, F.N. (eds) Large-Scale Optimization with Applications. The IMA Volumes in Mathematics and its Applications, vol 94. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0693-4_7
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DOI: https://doi.org/10.1007/978-1-4612-0693-4_7
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