Intended correlations

The photochemical disrotatory closure of butadiene to cyclobutene has been described with a state-correlation diagram, like that shown in Figure 21.4. It is based on the familiar orbital-correlation diagram of Woodward and Hoffmann," from which the intended correlations indicated by the dashed lines can readily be deduced. The solid lines indicate that there is an avoided crossing, which is put in as a result of the quantum mechanical noncrossing rule. It says that two states of the same total symmetry cannot cross. Instead, as they approach each other in energy, they will mix and separate, as the solid lines indicate. 

Inspection of the orbital make-up of reactant and product states may imply intended correlations which would lead to state crossings. If the states involved may not cross by rule 3, an avoided crossing occurs. The intention to cross is often depicted by dashed lines. 

Figure 14.9. (a) Orbital correlation diagram for the direct insertion of carbene into an olefin to form cyclopropane. Symmetry classification is with respect to the vertical bisecting mirror plane. (b) State correlation diagram showing the intended correlations and the avoided crossing of states So and S2. 

Figure 4.11. Derivation of the orbital correlation diagram for the conrotatory ring opening of cyclobutene a) intended correlation, b) correlation including interaction between a and n and between and o MO s, respectively. Orbiial symmetry labels n and a apply strictly only at the planar cyclobutene and butadiene geometries. Labels S and A, or solid and broken correlation lines respectively, indicate the symmetry behavior with respect to the twofold-symmetry axis (by permission from Michl, 1974b).

If a correlation diagram is constructed by connecting reactant and product orbitals of equal symmetry that are localized in the same spatial region of the molecule and that show the same sign relations for the LCAO coefficients, crossings of correlation lines of equal symmetry may occur. The natural orbital correlations (Devaquet et al., 1978) obtained in this way are very similar to the intended correlations described earlier. The main difference is that in the first step the orbitals of the product are now not taken to be the AOs of the bond that is being broken, but rather MOs constructed from them. 

TABLE 14-4 Symmetries and Intended Correlations of Some Configurations of Butadiene and Cyclobutene... 

Figure 15-14 Band diagram for a linear chain of carbon atoms showing some COs and intended correlations. Positive and negative phases are indicated by shading or lack of shading. (From Hoffmann et al. [1].)...

The dashed lines in Fig. 15-14 are the bands for Bloch sums of pure 2s and 2po- AOs. They differ from the bands for variational COs, where the Bloch sums are mixed. Even though they are not real bands, these dashed lines are nevertheless useful for guessing in advance of calculation what a band diagram will look like. The dashed lines are sometimes referred to as intended correlations because they show where the band that starts out as 2s, for instance, intends to be at A = yr/a. These two dashed lines are forced to cross at some value of k, but we have seen (Section 7-6) that such crossings... 

The band diagram is identical to the one in Fig. 15-23 except that the o + 6 level at A = 0 has an intended correlation with o — at A = jr/a, and vice versa. However, these have the same symmetry (anti for (72), hence avoid crossing. The resulting diagram is identical to that in Fig. 15-23 except that band 7T2 has an intermediate hill and its an intermediate valley—height and depth unknown until a variational calculation is performed. 

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