| A global optimization algorithm was developed to locate the lowest energy structure of atomic clusters. This algorithm implements the main ideas of the Tabu Search method, in addition to a number of “sub-algorithms” specific to cluster structure optimization. In particular, we developed a new way to represent cluster structures using the structure descriptors.; The algorithm begins by generating a series of possible cluster structures. Using deMon, a molecular orbital (MO) Kohn-Sham density functional theory (KS-DFT) program, the energy of each generated structure is calculated. Next, the algorithm selects among the lowest energy structures and modifies them randomly to create the next generation of ten to twenty new clusters; this generally leads to more stable structures. This procedure of obtaining an energetically biased selection of structures and modifying them is repeated many times. Finally a local optimization procedure is used to obtain the apparent global minimum.; In this thesis, we discuss the details of our algorithm, tests of its performance, and our findings about the structure of silicon (Si n) and lithium (Lin) clusters. Our algorithm is able to find the lowest known global minimum for Si 10 to Si12. The Sin cluster geometries tend to be prolate and trigonal prismatic. The Lin clusters have a general tendency to minimize the surface area. This gives compact structures with pentagonal bipyramid and icosahedral building blocks. We discovered new, and qualitatively different structures for Li n clusters. We also found that some Lin clusters have high spin magnetic moments. This is different from previous studies on Lin clusters and other metal clusters (i.e. Nan, Agn,…), where the ground state of the stable structures is generally a singlet or doublet state. |
