Symmetry Rules for the Reaction Coordinate

Symmetry rules to predict reaction mechanisms through the analysis of the reacton coordinate were first applied by Bader [36] (see, also, Reference [37]) and were further developed by Pearson [38], 

The energy variation along the reaction path can be characterized in the following way. The energy of all vibrational modes except the reaction coordinate is minimal all along the path, i.e., 

The energy variation of the reaction coordinate is different. At every point, except at the maximum and minimum values, it is nonzero, 

In order to predict reaction mechanisms and to estimate energy barriers, the energy can be expressed in terms of the reaction coordinate using second-order perturbation theory in such a way that the expression contains symmetry-dependent terms (see References [39] and [40] for details). 

The expression of energy contains two different types of energy integrals  

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