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Ionic reactions are the most common reactions used in chemical synthesis. In relatively low dielectric constant solvents (e.g., dichloromethane, toluene), ions usually exist as ion pairs. Despite the importance of counterions, a quantitative description of how the paired ’counterion’ affects the reaction kinetic is still elusive. We introduce a general and quantitative model, namely transition-state expansion (TSE), that describes how the size of a counterion affects the transition- state structure and the kinetics of an ionic reaction. This model could rationalize the counterion effects in nucleophilic substitutions and gold-catalyzed enyne cycloisomerizations.more » « less
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Paths found on grid graphs are often unrealistic looking in the continuous environment that the grid graph represents and often need to be smoothed after a search. The well-known algorithm for path smoothing is greedy in nature and does not necessarily eliminate all heading changes in freespace. We present preliminary research toward a new path-smoothing algorithm based on 'string pulling' and show experimentally that it consistently finds shorter paths than the greedy path-smoothing algorithm and produces paths with no heading changes in freespace.more » « less
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