Noncrossing rule avoided crossing

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. 

The Ay state arising from 3B1 and the Ax state arising from 1A1 may now mix, since the noncrossing rule applies.128 Thus in the presence of spin interactions there is an avoided crossing as indicated in Figure 5. This noncrossing implies that in the isolated CH2 molecule there is a finite transition probability between the nonstationary zero-order states. If we... 

For diatomic systems that have only one degree of freedom, it is not possible for two electronic states of the same symmetry to become degenerate and as a consequence of the well-known noncrossing rule an avoided crossing results. However, it stands only in field-free space. It was pointed out... 

---