We have developed a genetic algorithm (GA) for the global geometry optimization of fully and partially H-passivated Si clusters. Since. it is not obvious how many H atoms will bind to a Si cluster, one important feature of our GA is that it can automatically select between different amounts of H passivation. The GA uses the AM1 semiempirical method for the fast calculation of individual locally optimized geometries for use in the GA, evolution process. Although the AM1 method produces reasonable Si,,H, optimized geometries, we perform a more accurate energy ranking of the low energy structures generated by the GA with B3LYP density functional theory and MP2 calculations. We use the GA to determine the low energy structures for the clusters Si10Hm, with m = 4, 8, 12, 16, 20, and Si14H20. The Si-10 framework evolves from compact structures to, more open structures with increasing numbers of H atoms, and we find Silo is essentially fully passivated with 16 H. atoms. Adding H atoms causes substantial changes in the Silo framework once all the Si atoms are four coordinate. We also find the Si framework in the global geometry of the fully H passivated clusters such as Si10H16 and Si14H20 to adopt the structure of a bulk Si lattice fragment providing B3LYP and MP2 energy Calculations are performed.