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. These were then taken as initial configurations and allowed to relax freely under the Lennardhyphen;Jones pair potential to the adjacent energy minimum. The initial configurations and relaxed energies of the most tightly bound structures found for eachNare presented for the range 13le;Nle;147. While the energies obtained are rigorously only upper bounds to the absolute minimal energy of anNhyphen;atom Lennardhyphen;Jones cluster, they appear to be less than or equal to that of any other structures proposed previously. They are believed to be the most tightly bound structures of the multilayer icosahedral type, and to be reasonable candidates for the absolutely minimal energy structures in this size range. The most tightly bound configuration found was the truncated icosahedral structure atN=135.
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