Quantum-mechanical calculations of the stabilities of fluxional isomers of C₄H₇⁺ in solution

Although numerous quantum calculations have been made over the years of the stabilities of the fluxional isomers of C₄H₇⁺, none have been reported for other than the gas phase (which is unrealistic for these ionic species) that exhibit exceptional fluxional properties in solution. To be sure, quantum-mechanical calculations for solutions are subject to substantial uncertainties, but nonetheless it is important to see whether the trends seen for the gas-phase C₄H₇₊ species are also found in calculations for polar solutions. Of the C₄H₇⁺ species, commonly designated bisectedcyclopropylcarbinyl 1, unsym-bicyclobutonium 2, sym-bicyclobutonium 3, allylcarbinyl 4, and pyramidal structure 6, the most advanced gas-phase calculations available thus far suggest that the order of stability is 1 ≥ 2 ≥ 3 ≫4 ≫ 6 with barriers of only ≈1 kcal/mol for interconversions among 1, 2, and 3. We report here that, when account is taken of solvation, 2 turns out to be slightly more stable than 1 or 3 in polar solvents. The pattern of the overall results is unexpected, in that despite substantial differences in structures and charge distributions between the primary players in the C₄H₇⁺ equilibria and the large differences in solvation energies calculated for the solvents considered, the differential solvent effects from species to species are rather small.