Relative Efficiency of Stochastic and Genetic Algorithms for Characterizing Clusters with Unique Bonding Patterns

This thesis investigates the relative efficiencies of two isomeric search procedures to survey potential energy surfaces with the objective of rapidly assessing the relevancy of compounds possessing atypical structural patterns. Variants of both the standard stochastic procedure and the genetic algorithm (GA) were implemented, benchmarked, and compared using a series of homoatomic silicon clusters and hypercoordinated planar-carbon containing species. Both of these approaches emerge as valuable tools for the objective of locating small low-lying energy clusters on the potential energy surface. For systems with ten or fewer atoms, the stochastic search locates every global and low-lying minima for reference cluster compounds. For larger systems, the GA surpasses stochastic approaches as the best alternative. Geometry optimization of the generated structures performed at the quantum chemistry level represents, by far, the most time-consuming step. Replacement of preliminary density functional computations with a semi-empirical alternative results in a dramatic reduction (∼20x) in the time needed to achieve final results. The benchmarking of the two search procedures is followed by explorations authenticating that high-symmetry (Be, B+, C2+)@Si6-10 clusters correspond to low-lying energy isomers. This emerging class of endohedral silicon-based structures, whose stability depends upon the nature of the doping atom, represents an intriguing alternative to their carbon analogues. Extensive analysis of the electronic structure of these compounds corroborates a reverse charge transfer (i.e. away from the cage) as compared to the archetypal metal-containing endohedral fullerenes. The key factors leading to enhanced stabilization can be attributed to a maximization of multicenter-type bonding along with an appropriate balance between electronegativity and atom size. Overall, the methodologies proposed throughout this thesis provide general guidelines on the best ways to validate computational structural design.


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