On simple saddle points of a potential surface, the conservation of nuclear symmetry along paths of steepest descent, and the symmetry of transition states

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Abstract
We show that if the transition state of a chemical reaction is a simple saddle point of the potential surface linked directly with reactants and products by paths of steepest descent, then the symmetry of the transition state is limited to the joint symmetry of reactant and product, unless reactant and product are physically indistinguishable and themselves symmetry related, in which case the transition state may have those additional symmetries that interchange reactant and product. We outline some of the general consequences of this symmetry restriction on transition states.

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