Rearrangements of C₇H₆ Isomers:  Computational Studies of the Interconversions of Bicyclo[3.2.0]hepta-1,3,6-triene, Bicyclo[3.2.0]hepta-3,6-diene-2-ylidene, Bicyclo[3.2.0]hepta-2,3,6-triene, and Cyclohepta-1,2,4,6-tetraene

The structures of several bicyclo[3.2.0] isomers on the C(7)H(6) potential energy surface, and the transition states which interconnect them, have been fully optimized using density functional theory (BLYP/6-31G). Relative energies were determined using single-point calculations at higher levels of theory (CCSD(T), CASPT2N). These calculations show that bicyclo[3.2.0]hepta-3,6-diene-2-ylidene (2) readily undergoes ring opening to cycloheptatetraene (4) with a barrier of 5 kcal/mol. The rearrangement of 2 to 4 occurs without intervention of bicyclo[3.2.0]hepta-1,3,6-triene (1). Triene 1 is much more stable than carbene 2, but faces a much higher barrier (35 kcal/mol) to rearrangement to cycloheptatetraene (4). The singlet and triplet states of carbene 2, along with the triplet state of triene 1 and the singlet state of bicyclo[3.2.0]hepta-2,3,6-triene (3), lie very close in energy, ca. 55 kcal/mol higher than the singlet state of 4. The computed transition states for the electrocyclic ring closure of cycloheptatetraene (4) to bicyclo[3.2.0]hepta-1,3,6-triene (1) and for the degenerate 1,5-sigmatropic H-shift in triene 1 occur at very similar energy. This finding provides a rationalization for the experimental observation of (13)C-label scrambling upon high-temperature pyrolysis of various C(7)H(6) isomers. The calculated IR frequencies and intensities for 1, (1)()2, (3)()2, and 3 may aid future identification of these species.