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In recent years, quantum dynamics scattering theory§has been well developed for small systems, such as§three or four atom systems. In this book, based on§the author's Ph.D. dissertation, the Reactant Product§Decoupling§approach has been developed for photodissociation§systems to save the computational§effort in dynamics calculations without losing the§computational accuracy. Another challenging aspect is§how to correct available but not accurate potential§energy surfaces (PES) to experimentally accurate ones§that are crucial to§the accuracy of the dynamics calculations. The§Inverse Perturbation via Singular Value Decomposition§method has been proposed to correct the§available PES by using the experimental data as input. §For polyatomic systems, Semi-rigid Vibrating Rotor§Target model has been developed to deal with§polyatomic reactions on a rigid surface. This model§surpasses the diatomic model for polyatomic molecule§reactions on surfaces, especially for the rotational§motion which is treated accurately. Applications of§the above theories to specific chemical reactions are§presented in this book.