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We discuss the molecular optimization problem of determining the optimal configurations of large, confined ionic systems This problem arises in the study of heavy ions in plasma physics, where there is interest in the evolution of the optimal configurations as the size of the system increases. In particular, we are interested in determining the phase transition of the ionic system from the shell structure to the BCC lattice. Based on experimental evidence, scientists expect the phase transition to occur at systems with 200,000 atoms.
We show that for this problem we are able to obtain sharp lower and upper bounds on the value of the potential energy for the optimal configurations. We also study the evolution of the optimal configurations. Our approach is based on using the Gaussian transform to map the original objective function into a smoother function with fewer minimizers, and using an optimization algorithm on the transformed function to trace the minimizers back to the original function.
We discuss the general geometrical properties of optimal ionic systems, and discuss our computational experience with small to medium-sized (2,000 atoms) problems. We present results obtained with the IBM SP and CAVE at Argonne's High-Performance Computing Research Facility.
This work is joint with Jorge Moré.
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