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Nonlinear dynamics plays a dominant role in a variety of important problems in chemical physics. Examples are unimolecular reactions,’ infrared multiphoton decomposition of molecules,’ the pumping process of the gamma ray laser,’ dissociation of vibrationally excited state-selected van der Waals’s complexes,’ and many other chemical and atomic processes. The present article discusses recent theoretical studies on the quasi-periodic and chaotic dynamical aspects of vibrational-rotational states of atomic, nuclear, and molecular systems using the semiclassical spectral method (SSM).’ We note that the coordinates, momenta, and so on, are found using classical mechanics in the studies included in this review. Consequently, certain processes of quantum mechanical origin, such as tunneling, have not been investigated in this framework. However, the projects to be described, undertaken using classical or semiclassical techniques, yield excellent results and explain many aspects of the underlying dynamics.

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