Conrotatory/disrotatory rotation

Based on the product distribution of their computed trajectories. Doubleday and Hase found that = 2.3-3, depending on the initial state sampling. Borden and Carpenter obtained the following 12/ 1 ratio for trajectories initiated at the conrotatory, disrotatory, and monorotation TSs, 5.8-6,2.S-3.3, and 0.35-0.4, respectively, giving an overall value of 4.73. TST predicts a double-to-single rotation ratio of less than 1.5, dramatically lower than the value from two MD studies. 

The states involved in the photochemical butadiene-to-cyclobutene conversion are if/u ( 2, and il/ of the first excited state of butadiene, and a, tt, and tt for the lowest excited state of cyclobutene. The correlation diagram for this reaction is shown in Fig. 11.4. The appropriate elements of symmetry are the plane of symmetry and the axis of symmetry corresponding to conrotatory and disrotatory rotation ... 

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. 

Conservation of orbital symmetry is a general principle that requires orbitals of the same phase (sign) to match up in a chemical reaction. For example, if terminal orbitals are to combine with one another in a cyclixation reaction as in pattern. A, they must rotate in the same dii ection (conrotatory ovei lap). but if they combine according to pattern H. they must rotate in opposite directions (disrotatory). In each case, rotation takes place so that overlap is between lobes of the it orbitals that are of the same sign. 

Figure 11.3 illustrates the classification of the MOs of butadiene and cyclobutene. There are two elements of symmetry that are common to both s-cw-butadiene and cyclobutene. These are a plane of symmetry and a twofold axis of rotation. The plane of symmetry is maintained during a disrotatory transformation of butadiene to cyclobutene. In the conrotatory transformation, the axis of rotation is maintained throughout the process. Therefore, to analyze the disrotatory process, the orbitals must be classified with respect to the plane of symmetry, and to analyze the conrotatory process, they must be classified with respect to the axis of rotation. 

For the butadiene-cyclobutene interconversion, the transition states for conrotatory and disrotatory interconversion are shown below. The array of orbitals represents the basis set orbitals, i.e., the total set of 2p orbitals involved in the reaction process, not the individual MOs. Each of the orbitals is tc in character, and the phase difference is represented by shading. The tilt at C-1 and C-4 as the butadiene system rotates toward the transition state is different for the disrotatory and conrotatory modes. The dashed line represents the a bond that is being broken (or formed). 

This is an example of an electrocyclic reaction, and involves rotation of the terminal methylene groups either in the same way ( conrotatory ) or in opposite ways ( disrotatory ). 

The ring closure of a diene to a cyclobutene can occur with rotation of the two termini in the same conrotatory) or opposite disrotatory) directions. For suitable substituted compounds, these two reaction modes lead to products with different stereochemistry. 

As there are 6 ir electrons to accommodate—two per orbital—the HOMO will be ip3 (11). To form the C—C a bond on cyclisation, the orbital lobes on the terminal carbon atoms of the conjugated system (C2 and C7—the C atoms carrying the Me substituents) must each rotate through 90° if mutual overlap is to occur (p/sp2— sp3 re-hybridisation must also occur). This necessary rotation could be either (a) both in the same direction—conrotatory (12), or (b) each in opposite directions—disrotatory (13) ... 

The [2 + 2]-cycloaddition of allene proceeds via a stepwise diradical mechanism rather than a concerted one-step mechanism. The allenes come together in a crossed configuration. The bond formation between the central sp carbon atoms is accompanied by a simultaneous conrotatory twisting leading to a perpendicular 2,2 -bisallyl diradical 3. Rotation about the central bond of 3 gives the planar diradical and a disrotatory closure leads to the formation of dimer 2. The stereochemistry of some of the following examples is explained by this mechanism. 

Dynamics calculations have also provided new approaches to the stereochemical modes through which cyclopropanes and trimethylene intermediates may be related. Full quantum dynamics calculations for the trimethylene diradical based on a reduced dimensionality model that followed wave packet densities and time constants for formation of products led to the conclusion that conrotatory and disrotatory double rotations of both terminal methylene groups are favored over a single rotation of just one by a 2.2 1 ratio." °... 

To achieve this stereospecificity, both terminal C s rotate 90° in the same direction, called a conrotatory motion. Movement of these C s in opposite directions (one clockwise and one counterclockwise) is termed disrotatory. 

Answer to 2(d). This question illustrates that it is the number of electrons, not the number of nuclei, that is important. The orbital correlation diagram is shown in Figure 14.2. In disrotatory opening, a mirror plane of symmetry is preserved. This correlation is with bold symmetry labels and solid correlation lines. Italic symmetry labels and dotted correlation lines denote the preserved rotational axis of symmetry for conrotatory ring opening. For the cation, the disrotatory mode is the thermally allowed mode. It corresponds to a a2s + 05 pericyclic reaction. 

For a second example I take the ring opening of butene to cis butadiene. Considerations of symmetry allow a distinction to be made between paths which are distinguished by the modes of rotation of the CHj groups conrotatory and dis-rotatory as shown in Fig. 9. In the conrotatory mode the molecule retains a 2-fold axis of symmetry so that orbitals or states can be characterized by the symmetry labels A or 5, and in the disrotatory mode there is a plane of symmetry so that the symmetry labels. <4 and A , can be used. 

In the case of conrotatory mode, the symmetry is preserved with respeo to C2 axis of rotation. On 180° rotation along this axis, F goes to H. and H2 to H, and the new configuration is indistinguishable from the original. An orbital symmetric with respect to rotation is called a and antisymmetric as b. On the other hand, in the case of disrotatory moot-the elements of symmetry are described with respect to a mirror plane. Tilt symmetry and antisymmetry of an orbital with respect to a mirror plant of reflection is denoted by a and a" respectively (Section 2.9). The natun of each MO of cyclobutene with respect to these two operations is shov. n in the Table 8.4 for cyclobutene and butadiene. 

Ab initio MRCI calculations showed that the barrier from trimethylene to propene is 7.9kcalmol 1 higher than that from trimethylene to cyclopropane.11 Thus, cyclopropane stereomutation may occur through trimethylene as an intermediate (Chart 3). Trimethylene biradical may cyclize by double rotation of the two C C bonds in conrotatory or disrotatory fashion or successive single rotation. The calculations showed that the PES at the... 

---