Uchida and co-workers reported on the preparation of biphenalenylidene 1 and its interesting electrocyclization to dihydroperopyrene 2.¹ The experimental barrier they find by experiment for the conversion of 1-Z to 1-E is only 4.3 kcal mol^-1. Secondly, the photochemical electrocyclization of 2-anti to 1-Z proceeds rapidly, through an (expected) allowed conrotatory pathway. However, the reverse reaction did not occur photochemically, but rather did occur thermally, even though this is formally forbidden by the Woodward-Hoffman rules.

To address these issues, they performed a number of computations, with geometries optimized at UB3LYP(BS)/6-31G**. First, CASSCF computations indicated considerable singlet diradical character for 1-Z. Both 1-Z and 1-E show significant twisting about the central double bond, consistent with the singlet diradical character. 1-Z is 1.8 kcal mol^-1 lower in energy than 1-E, and the barrier for rotation interconverting these isomers is computed to be 7.0 kcal mol^-1, in reasonable agreement with the experiment. These geometries are shown in Figure 1.

1-Z	1-E
TS (Z→E)

Figure 1. UB3LYP(BS)/6-31G** optimized geometries of 1-Z and 1- and the transition state to interconvert these two isomers.

The conrotatory electrocyclization that takes 1-Z into 2-anti has a barrier of 26.0 kcal mol^-1 and is exothermic by 3.4 kcal mol^-1. The disrotatory process has a higher barrier (34.2 kcal mol^-1) and is endothermic by 8.4 kcal mol^-1. These transition states and products are shown in Figure 2. So, despite being orbital symmetry forbidden, the conrotatory path is preferred, and this agrees with their experiments.

TS (con)	TS (dis)
2-anti	2-syn

Figure 2. UB3LYP(BS)/6-31G** optimized geometries of 2-anti and 2-syn and the transition states leading to them.

The authors argue that the large diradical character of 1 leads to both its low Z→E rotational barrier, and the low barrer for electrocyclization. The Woodward-Hoffmann allowed disrotatory barrier is inhibited by its highly strained geometry, making the conrotatory path the favored route.

References

(1) Uchida, K.; Ito, S.; Nakano, M.; Abe, M.; Kubo, T. "Biphenalenylidene: Isolation and Characterization of the Reactive Intermediate on the Decomposition Pathway of Phenalenyl Radical," J. Am. Chem. Soc. 2016, 138, 2399-2410, DOI: 10.1021/jacs.5b13033.

InChIs

1-E: InChI=1S/C26H16/c1-5-17-9-3-11-23-21(15-13-19(7-1)25(17)23)22-16-14-20-8-2-6-18-10-4-12-24(22)26(18)20/h1-16H/b22-21+
InChIKey=LOZZANITCNALJB-QURGRASLSA-N

1-Z: InChI=1S/C26H16/c1-5-17-9-3-11-23-21(15-13-19(7-1)25(17)23)22-16-14-20-8-2-6-18-10-4-12-24(22)26(18)20/h1-16H/b22-21-
InChIKey=LOZZANITCNALJB-DQRAZIAOSA-N

2-anti: InChI=1S/C26H18/c1-3-15-7-11-19-21-13-9-17-5-2-6-18-10-14-22(26(21)24(17)18)20-12-8-16(4-1)23(15)25(19)20/h1-14,19,21,25-26H/t19-,21-,25?,26?/m0/s1
InChIKey=BZIOOLOJBUBMSS-ATJINXRDSA-N

2-syn: InChI=1S/C26H18/c1-3-15-7-11-19-21-13-9-17-5-2-6-18-10-14-22(26(21)24(17)18)20-12-8-16(4-1)23(15)25(19)20/h1-14,19,21,25-26H/t19-,21+,25?,26?
InChIKey=BZIOOLOJBUBMSS-YXGNQKCYSA-N