Ab initio calculations were carried out on cyclopropenone, 1, benzocyclopropenone, 2, the benzocyclopropenone-containing [2.2]paracyclophane derivative tetracyclo[8.3.2.(4,7)O(11,13)]heptadeca-1(13),4,6,10,14,16-hexaen-12-one, 3, its decarbonylation product tricyclo[8.2.2.2(4,7)]hexadeca-1(12), 4,6,10,13-pentaen-15-yne, 5, a benzyne intermediate, and the bridged benzobarrelene derivative, pentacyclo[5.5.2.2.(1,4)O(4,14)O(10,13)]hexadeca-2,7,9,13,15-pentaene, 6. These calculations suggest that benzocyclopropenone-containing [2.2]paracyclophane, 3, and highly strained bridged benzobarrelene, 6, could exist as stable species. Both aryl rings of the benzocyclopropenone derivative 3 are predicted to be distorted from planarity. This distortion relieves some angle strain present in planar benzocyclopropenone due to the presence of the annulated three-membered ring. Calculations on benzobarrelene, 8, and [2.2]paracyclophane, 4, were performed for comparison to gain a better understanding of the strain borne in bridged benzobarrelene 6. The activation barrier for the intramolecular [4 + 2] cycloaddition of 5 to give 6 was estimated at 18.8 kcal/mol while that for the corresponding [2 + 2] cycloaddition, giving the less stable 9, was 54.5 kcal/mol. The [2 + 2] cycloaddition's transition state was twisted in a manner reminiscent of the conservation of orbital symmetry prediction for an unstrained system.