Cyclization of Butadiene to Cyclobutene

At this level of analysis, it is sufEcient to include in Fig. 5.1 the doubly-occupied MOs that appear in Fig. 19 of Reference [1] xi. nd X2 of butadiene and a and 7T of cyclobutene. The latter molecule has C2v symmetry, so the former is put into the same symmetry point group by adopting the s-cis conformation, on the reasonable assumption that the attainment of conformational equilibrium is a much faster process than cyclization. Xi and tt have the same irrep (6i), so they remain in correlation whether C y symmetry is retained or not. However, in order to deliver a pair of electrons from X2(fl2) to the reaction has 

Only two sym-ops, E and 6 2(2 ), have the character 1 in A2] therefore, the reaction will become allowed if the pathway is desymmetrized to C2, the kernel of A2, in which A and A2 both map onto the same irrep (A). The conrotatory pathway, along which the two sym-ops that comprise C are the only ones retained, is therefore selected. 

In analogy with Equation 4.1, the pathway must be displaced away from C y along a symmetry coordinate of the same irrep as the direct product of the irreps of the two orbitals between which the correspondence has to be induced  

The reaction coordinate along the allowed pathway must therefore include, in addition to totally symmetric displacements, such as decreasing the C1C4 distance and shortening the C2C3 bond, at least one 02 symmetry coordinate Conrotation of the methylene groups evidently fulfills this requirement. 

Any 02 displacement desymmetrizes the pathway to so the two ways of reading the Character Table are completely equivalent their common conclusion is symbolized in Fig. 5.1, as in Fig. 4.7, by a two-headed arrow - here labeled U2- It indicates that the reaction, which is forbidden in C yj is made allowed by an induced correspondence between the non-correlating orbitals of the reactant (02) and product (ai) that is produced when the pathway is desymmetrized to C2 by a conrotation (02). 

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Electi ocyclic reactions are examples of cases where ic-electiDn bonds transform to sigma ones [32,49,55]. A prototype is the cyclization of butadiene to cyclobutene (Fig. 8, lower panel). In this four electron system, phase inversion occurs if no new nodes are fomred along the reaction coordinate. Therefore, when the ring closure is disrotatory, the system is Hiickel type, and the reaction a phase-inverting one. If, however, the motion is conrotatory, a new node is formed along the reaction coordinate just as in the HCl + H system. The reaction is now Mdbius type, and phase preserving. This result, which is in line with the Woodward-Hoffmann rules and with Zimmerman s Mdbius-Huckel model [20], was obtained without consideration of nuclear symmetry. This conclusion was previously reached by Goddard [22,39]. 

This reasoning was used by the author in 1961 to rationalize the ubiquitous photochemical cyclization of butadienes to cyclobutenes here it was noted that the excited state has a high 1,4-bond order. The same reasoning was applied 6,12) to understanding the key step of cyclohexadienone rearrangements (vide infra). Still another example is the decreased central bond order in the excited state of stilbene which, as Daudel has noted 13), is in accord with photochemical cis-trans interconversion. 

The question posed in the preceding paragraphs as to the need for a reevaluation of the concept of allowedness , can be dismissed as a non-problem as long as it is taken as axiomatic that, for an orbital symmetry analysis to be of any use, the symmetry elements [retained along the pathway] must bisect bonds made or broken in the process . In contrast to the allowed conrotatory cyclization of butadiene to cyclobutene, in which the C2 axis bisects a newly formed cr bond, the only bond bisected by the axis in its conversion to bicyclobutane is the one between C2 and C3, which is essentially single in both the reactant and the product. 

The crucial moment in the formulation of the systematic theory of pericyclic reactions is undoubtedly represented by the advent of the so-called Woodward-Hoffmaim rules [20-22], on the basis of which it was possible to explain and to rationalize the remarkable stereospecificily of these reactions. This specificity manifests itself in the predominant formation of only one stereoisomer as well as by the dramatic change of the preferred reaction mechanism depending on whether the reaction proceeds under the conditions of thermal or photochemical initiation. Thus, e.g., the thermal cyclization of butadiene to cyclobutene proceeds by the conrotatory mechanism, while for the photochemical reaction the disrotatory reaction is prefened. 

Figure 1 Occupation numbers of natural orbitals in thermally allowed cyclization of butadiene to cyclobutene in dependence on the value of the generalized reaction coordinate cp.

Figure 11 The partitioning of the modified More O Ferrall diagram with the corresponding reaction path for thermally forbidden disrotatoiy cyclization of butadiene to cyclobutene. The extent of electron reorganization measured by the value of the fimctional L is -0.48 along this reaction path.

The practical exploitation of the proposed criterion can be very simply demonstrated by the example of the electrocyclic transformation of butadiene to cyclobutene, for which the structure of the possible intermediates can be quite reliably estimated from the available results of quantum chemical calculations [123]. This reaction is especially convenient for the demonstration purposes since it displays both possible types of the dissection of the More O Ferrall diagrams [121] as schematically given in Figs. 9 and 10. Especially interesting is, above all, the case of forbidden disrotatory cyclization, for which the special form of the dissection allows the classification of the reaction mechanism even without the knowledge of the reaction path. As can be seen from the Fig. (9) no reaction path coimecting the reactant with the product can avoid the region of the intermediate so that the reaction has to be classified as nonconcerted. 

The temperature required for the conversion of butadienes to cyclobutenes depends on the substituents. Cyclization of butadi-enyl phosphine oxides require an elevated temperature, but at high... 

Let us return to Fig. 5.4 and compare two closely related synunetry coordinates illustrated in it (b) is the familiar conrotation that has been confirmed to be essential for allowing the cyclization of s-czs-butadiene to cyclobutene, whereas (c) leads directly to bicyclobutane. The irrep of both coordinates in is 02] i.e. both are conrotatory. They differ by virtue of the concerted out-of-plane motion of Ci and C4, which brings them within bonding distance of C3 and C2 respectively, rather than of each other. 

For the solution of this problem we proposed a simple numerical method [144] on the basis of which the above model was applied to several selected pericyclic reactions. In order to maintain the close correspondence with alrea presented example of the butadiene to cyclobutene cyclization discussed in coimection with the topological criterion of concertedness, the proposed formalism will be demonstrated first just for this specific pericyclic process. On the basis of the idealized reaction scheme the whole procedure is quite straightforward and consists in the conversion of the corresponding structural formulae into the approximate wave functions. 

As can be seen from this comparison, the resulting values are affected by the choice of the critical structure and on going from X(n/4) to X(-7t/4), the systematic shift of the dominant similarity from the zwitterionic state Z + Z2 to the state Zj -Z2 is observed. We can thus see that the predictions for both types of critical structures differ and the problem thus appears which of the above two critical structures should be regarded as a true model of the transition state in forbidden reactions. Similarly as in the case of allowed reactions such a decision does not arise from the approach itself, but some external additional information is generally required. This usually represents no problem since the desired information can be obtained, as in the case of allowed reactions, from the simple qualitative considerations based on the least motion principle [80,81], or from the direct quantum chemical calculations.This is also the case with us here, where the desired information is provided by the quantum chemical study [63] of the thermally forbidden cyclization of the butadiene to cyclobutene. From this shufy it follows that the ground state of the transition state should correspond to the ground state of the cyclobutadiene which is the Zj - Z2 state. 

From experiment one merely knows that the photochemical cyclization of butadiene starts from an excited singlet state and terminates at the ground state of the cyclobutene appropriate labelling indicates the cyclization to be stereospecific. What intervenes between start and finish is not clear, but it is certainly not excited singlet cyclobutene. What seems more likely is that at... 

SUBSTITUTED BUTADIENES. The consequences of p-type orbitals rotations, become apparent when substituents are added. Many structural isomers of butadiene can be foiined (Structures VIII-XI), and the electrocylic ring-closure reaction to form cyclobutene can be phase inverting or preserving if the motion is conrotatory or disrotatory, respectively. The four cyclobutene structures XII-XV of cyclobutene may be formed by cyclization. Table I shows the different possibilities for the cyclization of the four isomers VIII-XI. These structmes are shown in Figure 35. 

Electrocyclic ring closures are reversible, and only those which yield significant amounts of cyclic products at equilibrium have been studied. Most butadiene-cyclobutene equilibria greatly favor the butadienes (see below). An exception is the cyclization of irans, a.s-l,2,3,4-tetraphenyl-l-bromo-l,3-butadiene, which undergoes the predicted conrotatory cyclization to a significant extent. ... 

MO theory has been used to draw qualitative conclusions about the course of chemical reactions. The most fi-uitful applications have come from the Woodward-Hqffmemn rules, which predict the preferred path and stereochemistry for many important classes of organic reactions. As an example of the application of these rules, we consider the cyclization of a substituted 5-cis-butadiene to a substituted cyclobutene. There are two possible steric courses the reaction can take, described as con-rotatory or disrotatory, depending on whether the terminal groups rotate in the same or opposite senses as the reaction proceeds. Note the difference in products in Fig. 16.13. 

The electrocyclic reactions are intramolecular (n + a) cycloadditions, a most important example of which is provided by the cyclization of 1,3-butadiene XXI to cyclobutene XXIII ... 

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