Structures and Energies of C₄H₂²⁺¹

At the MP3/6-31G*//HF/6-31G* level of ab initio theory, the lowest energy C₄H₂²⁺ dication is indicated to have a linear (D_∞h) structure; the four-membered-ring (D_2h) alternative is 13.3 kcal/mol less stable. At MP4SDQ/6-31G*//3-21G the linear C₄H⁺(C_∞h) monocation is only 3.6 kcal/mol more stable than its four-membered-ring (C_2v) isomer. These stability orders differ from those of the C₄ structures where the cyclic isomer (D_2h) is 0.7 kcal/mol (MP4SDQ/6-31G*//6-31G*) more stable than the linear (D_∞h) structure. Despite the estimated very large heat of formation of C₄H₂²⁺ of 733 kcal/mol, all the modes of dissociation explored are calculated to be endothermic. In particular, the surprisingly large proton affinity of C₄H⁺, 63.1 kcal/mol, may be attributed to the diminution of electrostatic repulsion in the long, linear structure. In agreement with gas-phase studies, we find the most favorable C₄H₂²⁺ dissociations to be into C₃H⁺+ CH⁺(endothermic by 36.7 kcal/mol for 1) and into C₃H₂⁺ + C⁺ (endothermic by 14.7 kcal/mol for 2). All the four-membered-ring structures, C₄H₂²⁺, C₄H⁺, and C₄, show σ-deficient character for the bridging carbons. In these cases the HOMO’s are σ orbitals of nonbonding nature with the significant stabilization resulting from 4-center, 2-electron aromatic π bonding. This result is contrary to intuition, which suggests double bond character between the bridging carbons as allowed for by an inverted geometry of the two sp¹²-hybridized carbons.