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We describe recent advances in the theoretical description of bimolecular reactions involving four or more atoms based on quantum scattering theory and quasiclassical trajectory methods. The application of these methods to several reactions is described in detail along with relevant experimental results. The discussion emphasizes the use of reduced dimensionality quantum scattering methods and quasiclassical trajectory methods to describe quantum state-resolved effects, including state-specific reaction rate enhancements and product state distributions. Also considered are thermal rate constants, the lifetimes of intermediate complexes, and the branching between multiple reaction pathways.
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