The Poincareacute; classification theory of the singularities of the equations of motion of a classical mechanical system are suitably modified to describe the singularities in the motion of an arbitrary quantumhyphen;mechanical system, derivable from a timehyphen;independent Hamiltonian. Dynamical quantumhyphen;mechanical stability criteria are derived starting with the appropriate equations of motion satisfied by the Heisenberg position and momentum matrices of the system. These stability criteria are used to discuss and classify certain singular nuclear motions of molecular systems which are of some interest in the context of prevalent theories of chemical stability and chemical reaction kinetics. In particular we show that the singular nuclear motions of a molecular system whose electronic and nuclear motions can be assumed to be separable, reduce to the rolling motion of dynamically equivalent classical spheres on the electronic potential energy surface.
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