The transition state of a chemical reaction is the lowest barrier separating reactants and products on a potential en- ergy surface. As such it is a critical point on the surface and its force constant matrix has exactly one negative eigenvalue. The corresponding eigenvector is defined to be the transition vector for the reaction. Schur’s lemma implies that the transi- tion vector will belong to one of the symmetry species of the transition state point group provided sufficient care is taken in the choice of the coordinate system. Consideration of the effect of transition state symmetry operations on the reactants and products and on the paths joining them to the transition state leads to a series of theorems governing the transformation properties of the transition vector. In some cases these requirements are incompatible with the known transformation proper- ties of the available symmetry species for the proposed transition state. It is shown that such “transition states” are forbid- den; i.e., they cannot be the lowest barriers separating reactants from products. The concept of symmetry forbidden transi- tion states is applied to a series of reactions of gradually increasing complexity. Included (among others) are the classic H + HZ exchange reaction, the T + CH4 displacement reaction. the olefin metathesis reaction, the inversion of cyclohexane, and the Cope reaction.
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