Forbidden and allowed reaction

Most of the reactions involving multiple it bonds can be classified by the number of Jt-electrons in each reaction partner. A single it bond (2 n electrons) can interact with another single it bond of an alkene or a 

Woodward and Hoffman described addition modes based on the facial approach of the reactive termini as suprafacial and antarafacial. A suprafacial process is one in which bonds made or broken lie on the same face of the system undergoing reaction , as in 11. 2 antarafacial process has the newly formed or broken bonds on opposite sides of the reaction system, as in 12. 2 Woodward and Hoffman then described several 

With these tools in hand, the Woodward-Hoffman rules of cycloaddition can be presented. Two Jt systems of m JT electrons and n it electrons, 4 q and 4 q+2 systems ( = 0, 1,2, 3, 4, 5,. ) can be classified as thermally and photochemically allowed or forbidden, as presented in Table 11.3.5 For suprafacial interactions, the thermally allowed reactions involve one 4 + 2 molecule and one 4 q molecule [an alkene q = I for Aq) 

Allowed (ground state, thermal) Forbidden iexcited state. hv  

Allowed (excited state, hv) Forbidden tground state, thermall 

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In previous sections we have seen how the CM model may be utilized to generate reaction profiles for ionic reactions, and it is now of interest to observe whether the same general principles may be applied to the class of pericyclic reactions, the group of reactions that is governed by the Woodward-Hoffmann (1970) rules. In other words, the question we ask is whether the concept of allowed and forbidden reactions may be understood within the CM framework. 

The essential point that distinguishes between allowed and forbidden reactions is the role of the D+A configuration. If the D+A configuration is allowed by symmetry to mix into the transition state wave-function then the transition state will be stabilized and will take on character associated with that configuration. For the ethylene dimerization, D+A is precluded from mixing with DA due to their opposite symmetries. As was discussed in detail in Section 2 (p. 130), DA cannot mix with D+A" since and n orbitals are orthogonal (106). Thus for ethylene dimerization the concerted process... 

This intuitive parallel can be best demonstrated by the example of electrocye-lic reactions for which the values of the similarity indices for conrotatory and disrotatory reactions systematically differ in such a way that a higher index or, in other words, a lower electron reorganisation is observed for reactions which are allowed by the Woodward-Hoffmann rules. In contrast to electrocyclic reactions for which the parallel between the Woodward-Hoffmann rules and the least motion principle is entirely straightforward, the situation is more complex for cycloadditions and sigmatropic reactions where the values of similarity indices for alternative reaction mechanisms are equal so that the discrimination between allowed and forbidden reactions becomes impossible. The origin of this insufficiency was analysed in subsequent studies [46,47] in which we demonstrated that the primary cause lies in the restricted information content of the index rRP. In order to overcome this certain limitation, a solution was proposed based on the use of the so-called second-order similarity index gRP [46]. This... 

Let us discuss now the most important conclusions that can be deduced from these figures. First, the most important conclusion concerns the comparison of the values of functional L along the optimal allowed and forbidden reaction paths. As can be seen, the value for the allowed conrotatory cyclisation is lower in absolute value than in the forbidden one. This confirms the intuitive expectation of the least motion principle that the extent of electron reorganisation should be smaller in allowed reactions than in the forbidden ones. On the basis of this primary test of reliability of the proposed model it is, in the next step, possible to start with the analysis and the classification of the reaction mechanisms for both individual reactions. Especially interesting in this connection is again the thermally forbidden disrotatory cyclisation. The reason for this... 

Of course, formally allowed and forbidden reactions, in the Woodward—Hoffmann sense, must be considered separately, as distinct reaction families, when correlating barriers to the G parameter. This happens because, as a rule, allowed reactions have comparatively larger resonance energies B relative to forbidden reactions, as will be shown below. 

Perhaps the most important consequence of the Woodward-Hoffman rules is its predictions of allowed and forbidden reactions. In particular, reactions involving An (An + 2) electrons are allowed if there are an odd (even) number of antarafacial two-electron components. A conseqnence of this symmetry property is that changing the number of electrons will alter whether the reaction is allowed or forbidden. 

Another bridge in the VBSCD is to orbital symmetry effects [6] and to frontier orbital theory [36]. The effect of orbital symmetry and frontier orbitals is implicit in the expression for B. It is the factor B that makes distinction between allowed and forbidden reactions, and determines the preferred trajectory of the reaction, thereby forming bridges between the VB diagram and MO-derived concepts of reactivity. This has been elaborated amply in previous reviews of the field [7,11,13,14,28], and a brief discussion, by way of an example, is given later. 

Allowed and forbidden reactions were defined by Woodward and Hoffman as those that proceed without and with a change in the orbital occupancies, respectively. This simple picture is only strictly applicable withinpoinf groups that do not allow the two orbitals to interact, but is still a good interpretative framework. 

The distinction between allowed" and "forbidden" reactions... seems to be one of topology rather than symmetry, there being a qualitative distinction between pairs of isomers that can be interconverted by a pericyclic reaction without a HOMO-LUMO crossing and pairs that cannot be so interconverted without a HOMO-LUMO crossing. ... 

ReaxFF [50] provides a generally valid and accurate way to capture the barriers for various chemical reaction processes (allowed and forbidden reactions) into the force fields needed for large-scale MD simulation. ReaxFF is parameterized exclusively from QM calculations, and has been shown to reproduce the energy surfaces, structures, and reaction barriers for reactive systems at nearly the accuracy of QM but at costs nearly as low as conventional FFs. 

The application of this matrix to concrete pericyclic reactions has revealed that the difference between the allowed and forbidden reactions, manifesting itself on the differences in the values of overlap integrals, finds its reflection also in the topological density matrices, where its manifestations are reflected by the specific differences in the character of the electron reorganization. These differences can be very simply demonstrated with the occupation numbers of natural orbitals resulting... 

As can be seen from this Table, the original insufficiency of the index r is indeed remedied by the index g p. This result is very interesting since if we realize that the primary source of the increased information content of the index g p is the partial inclusion of electron correlation, then the discrimination between the allowed and forbidden reactions in these cases seems to suggest that certain delicateness of cycloadditions and sigmatropic reactions, which both belong to the class of the so-called multibond reactions [99], can be apparently related to the greater sensitivity of these reactions to the effects of electron correlation. This conclusion, together with the systematic analysis of the role of correlation effects in pericyclic reactivity will be discussed in more details in chapter 8. 

Although the correct description of forbidden reaction generally requires the variation of the reaction coordinate within the range (0, -x/2), the second order similarity index (116) is independent of the direction of the reaction path and both the allowed and forbidden reactions can be described by cp varying within (0, tc/2)... 

This difference in the form of the matrix Q(9) then leads to the observed specific differences in the character of the electron reorganization between allowed and forbidden reactions. 

It is therefore inaccurate and misleading to talk about allowed and forbidden pericyclic reactions. The terms aromatic and antiaromatic pericyclic reaction are much more appropriate. It is also clear that the distinction between them has nothing to do with symmetry. It depends on the topology of overlap of the AOs in pericyclic transition states, not on the symmetries of MOs. If symmetry were involved, the distinction between allowed and forbidden reactions would be attenuated as symmetry was lost. This is not the case. The Woodward-Hoffmann rules, or the equivalent statement embodied in Evans principle, hold just as strongly in systems lacking symmetry as in symmetric systems. Indeed, if this were not the case, they would be far less useful and important. 

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