Symmetry allowed reactions, definition

The available experimental information does not warrant any definitive distinction between these four possibilities. However, some indirect evidence allows for some choices. Regardless of the 66 kcal/mol of strain embodied in the bicyclobutane ring, it has been shown to be a relatively stable system in the gas phase or in hydrocarbon solvents. Nevertheless, when bicyclobutane is heated at 200 C two of the peripheral C-C bonds are broken, while the central bond remains intact during the purely thermal, symmetry controlled reactions. This relative stability has been associated with the predominantly rr character of this... 

While photocycloadditions are typically not concerted, pericyclic processes, our analysis of the thermal [2+2] reaction from Chapter 15 is instructive. Recall that suprafacial-suprafacial [2+2] cycloaddition reactions are thermally forbidden. Such reactions typically lead to an avoided crossing in the state correlation diagram, and that presents a perfect situation for funnel formation. This can be seen in Figure 16.17, where a portion of Figure 15.4 is reproduced using the symmetry and state definitions explained in detail in Section 15.2.2. The barrier to the thermal process is substantial, but the first excited state has a surface that comes close to the thermal barrier. At this point a funnel will form allowing the photochemical process to proceed. It is for this reason that reactions that are thermally forbidden are often efficient photochemical processes. It is debatable, however, whether to consider the [2+2] photochemical reactions orbital symmetry "allowed". Rather, the thermal forbiddenness tends to produce energy surface features that are conducive to efficient photochemical processes. As we will see below, even systems that could react via a photochemically "allowed" concerted pathway, often choose a stepwise mechanism instead. 

The main effect is already taken into account if symmetry numbers are included in the densities of states. The symmetry number is a correction to the density of states that allows for the fact that indistinguishable atoms occupy symmetry-related positions and these atoms have to obey the constraints of the Pauli principle (i.e. the wave function must have a definite symmetry with respect to any permutation), whereas the classical density of states contains no such constraint. The density of states is reduced by a factor that is equal to the dimension of the rotational subgroup of the molecule. When a molecule is distorted, its symmetry is reduced, and so its symmetry number changes by a proportion that is equivalent to the number of indistinguishable ways in which the distortion may be produced. For example, the rotational subgroup of the methane molecule is T, whose dimension is 12, whereas the rotational subgroup of a distorted molecule in which one bond is stretched is C3, whose dimension is 3. The ratio of these symmetry numbers, 4, is the number of ways in which the distortion can occur, i.e. the reaction path degeneracy. 

One of the crucial points in the recent developments of coordination compound photochemistry has been the debate concerning the identity of the excited state(s) responsible for the photosolvation reactions that are obtained by irradiating Cr(III) complexes in their ligand field bands (5,8), Direct photolysis experiments revealed that the most likely candidates (see e.g,. Figures 2 and 3) are the lowest spin-allowed excited state ( T2ff in octahedral symmetry) and the lowest spin-forbidden excited state ( Eg). Such experiments, however, did not warrant any definite conclusion about the actual role of each of these two states (5). 

With these descriptors in hand, we can look at the generalized orbital symmetry rule. There is a definite binary nature to the theory of pericyclic reactions. For cycloadditions, [2-f2] is forbidden (all suprafacial), whereas [4-F2] is allowed (all suprafacial). Continuing with the series, [6+2] is forbidden, and [8+2] is allowed. We will also encounter patterns in the other kinds of pericyclic reactions presented electrocyclic reactions, sigmatropic shifts, etc. Based on patterns such as these. Woodward and Hoffmann proposed the following rule for all pericyclic reactions ... 

When Woodward and Hoffmann developed the conservation of orbital symmetry, they introduced the terms "allowed" and "forbidden" to describe reactions such as the [4+2] and [2+2] cycloadditions, respectively. This terminology caught on, and has become fairly standard in the field. With the benefit of a historical perspective, though, we can now see that these terms are too definitive. 

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