Reaction coordinate least motion path

The principal component of the reaction coordinate is the approach of the two ethylene molecules towards one another with retention of the full symmetry assumed in the construction of the correspondence diagram as Fig. 6.2 Wcts set up in D2/1, this least motion approach has the irrep ag. The diagram then tells us that the reaction coordinate for concerted conversion of the two tt bonds into the two (T bonds of cyclobutane also has to include a 625 component. Several symmetry coordinates, and the subgroups of D2/1 to which they desymmetrize the reaction path, are shown in Fig. 6.3. If the correspondence diagram had called for an displacement, the relatively facile formation of cyclobutane in its stable puckered D2 conformation would have been expected. If a b u component were required to induce the neccesary correspondence, the favored pathway would generate a cisoid biradical, which would immediately collapse to cyclobutane. The nominally stepwise reaction would then be kinetically indistinguishable from one in which the formation of both bonds is synchronous. 

This easy physical interpretation of natural collision coordinates, combined with the fact that the translational motion along the reaction path can be solved using essentially standard inelastic scattering techniques [112, 113], led to the success of the early H-I-P-H2 0-H2+H calculations and appeared to bode well for future applications of the approach [114]. Unfortunately, attempts to generalize methods based on these coordinates beyond the simplest 3D reaction soon ran into technical difficulties which seemed impossible to overcome. These difficulties are not immediately apparent in the simple collinear model of Fig. 1.2b, but the following two observations should at least give the general idea ... 

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