2.1, orbital symmetry allows the disrotatory cyclizations in the ground states from 9o to 9c and from 11o to 11c. The relative ground state energies of the closed‐ring isomers of 9 and 11 are, however, 175 and 113 kJ/mol higher than the respective energies of the open‐ring isomers. This indicates that the open‐ring isomers are stable and the thermal cyclization reaction does not take place practically in both cases.
Figure 2.1 State correlation diagrams for the electrocyclic reactions in disrotatory mode. 9c and 11c are the closed‐ring isomers, in which two hydrogens attached to the reactive central carbons are in a cis configuration.
Figure 2.2 State correlation diagrams for the electrocyclic reactions in conrotatory mode. 9c and 11c are closed‐ring isomers, in which two hydrogens attached to the reactive central carbons are in a trans configuration.
Table 2.1 Relative ground state energy differences between the open‐ and closed‐ring isomers.
| Compound | Disrotatory (kJ/mol) | Conrotatory (kJ/mol) |
|---|---|---|
| 1,2‐Diphenylethene (9) | 175 | 114 |
| 1,2‐Di(3‐pyrrolyl)ethene (10) | 135 | 65 |
| 1,2‐Di(3‐furyl)ethene (11) | 113 | 38 |
| 1,2‐Di(3‐thienyl)ethene (12) | 51 | −14 |
On the contrary, orbital symmetry forbids the conrotatory cyclizations in the ground states from 9o to 9c and from 11o to 11c, because each S0 open‐ring isomer state correlates with a highly excited state of the closed‐ring isomer, as shown in Figure 2.2. On the other hand, no such large barrier exists in the S1 state for 9o and the S2 state for 11o. This indicates that electrocyclic reactions of both 1,2‐diphenylethene and 1,2‐bis(3‐furul)ethene are allowed in the photochemically excited states.
What should be discussed here is the stability of the closed‐ring isomers. Figure 2.2 shows that in both 9c and 11c, the cycloreversion reactions in the ground state have to overcome energy barriers, and the barriers correlate with ground state energy differences between the open‐ and closed‐ring isomers. The calculated energy differences are shown in Table 2.1. When the energy difference is large, as in the case of 9, the energy barrier becomes small and the cycloreversion reaction takes place readily. On the other hand, the energy barrier becomes large when the energy difference is small. In this case, the cycloreversion reaction hardly takes place. The correlation between the ground state energy difference and the energy barrier is well explained by the Horiuti–Polanyi rule as shown in Figure 2.3. The energy difference in the ground states between the open‐ and closed‐ring isomers controls the stability of the closed‐ring isomers.
Figure 2.3 Correlation between the ground state energy difference between open‐ and closed‐ring isomers and the energy barrier.
The next question is what causes the difference in the ground state energy levels of the two isomers. First, strain energies of the six‐membered rings of the closed‐ring isomers were compared. The optimized geometries of the closed‐ring isomers, 9c and 11c, however, showed almost identical six‐membered ring structures and the ring‐strain could not explain the energy difference. Next, the aromaticity change from the open‐ to the closed‐ring isomers was examined. During the cyclization reaction, phenyl and heterocyclic rings change the structures as shown in Scheme 2.3. The aromaticity of the rings is lost during the cyclization reactions. The energy differences between the right‐ and left‐side groups were calculated and are shown in Table 2.2. The aromatic stabilization energy of the aryl groups correlates well with the ground state energy difference. The highest energy difference was calculated for the phenyl group and the lowest one for the thienyl group. Destabilization due to destruction of the aromatic ring during the cyclization reaction increases the energy of the closed‐ring form. The aromaticity is the key molecular property that controls the thermal stability of the closed‐ring isomers.
Scheme 2.3 The structure changes of phenyl and five‐membered heterocyclic rings along with the cyclization reactions.
Table 2.2 Aromatic stabilization energy differences.
| Group | Energy (kJ/mol) |
|---|---|
| Phenyl | 116 |
| Pyrrol | 58 |
| Furyl | 38 |
| Thienyl | 20 |
The theoretical prediction was confirmed by the synthesis of diarylethene derivatives with various types of aryl groups as shown in Figure 2.4. When the aryl groups are thiophene, benzothiophene, thiazole, or oxazole rings, which have low aromatic stabilization energy, the closed‐ring isomers are stable (more than 12 hours at 80 °C). On the other hand, photogenerated closed‐ring isomers of diarylethenes with indole rings, which have intermediate aromatic stabilization energy, undergo thermally reversible photoswitching (half‐life
