Inversion symmetry, reaction paths

These rules show that the G<- G transition, in contrast with the others, is purely rotational. In the coordinate system shown in Figure 8.20, the transition states for the cis and trans paths of interconversion have symmetry axes and C2y and relate to the symmetry groups and C2h, respectively. The different symmetries of the transition states results from the fact that the same permutation relates to different symmetry operations in C2v and C2h. For example, (ab)(14)(28)(36) is equivalent to inversion in C2h, while in it corresponds to the reflection in the axy plane. The symmetry of the reaction path does not affect the symmetry of states with even Ka (and Ka = 0). However, the selection rules for transitions Ka = 1 0 are different for cis and trans paths. The classifica-... 

The criteria of allowedness discussed in the preceding two sections do not require the explicit consideration of orbital symmetry, in the sense that the symmetry elements retained along the reaction path do not enter directly into the analysis consequently, they were not drawn in the figures. However, it is easy to ascertain from Fig. 1.1, for example, that two ethylene molecules in either the coplanar or [s -f s] orientation have three perpendicular mirror planes one common to the four carbon atoms, another reflecting one molecule into the other, and a third bisecting both of them three twofold axes of rotation (one at the intersection of each pair of mirror planes) and a center of inversion at the point where the three rotational axes intersect. After both molecules have been twisted so as to react in the [a + a] mode (Fig. 1.1c), only the rotational axes remain, whereas the off-orthogonal orientation of Fig. 1.4b retains a single twofold rotational axis and no other element of symmetry. 

During conversion of santonin to lumisantonin antara-addition.at double bond occurs alongwith inversion at the migrating saturated carbon atom. In this conversion alternative symmetry-forbidden change will occur with retention at C - 4 and will lead to sterically-forbidden trans-ring fusion. Therefore, path of the reaction will be decided by the geometry of the system. 

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