Correlation between bowl-inversion energy and bowl depth in substituted sumanenes

The correlation between the bowl-inversion energy and the bowl depth for sumanenes monosubstituted with an iodo, formyl, or nitro group was investigated experimentally and by theoretical calculations. The bowl-inversion energies of the substituted sumanenes were determined experimentally by two-dimensional NMR exchange spectroscopy measurements. Various density functional theory methods were examined for the calculation of the structure and the bowl-inversion energy of sumanene, and it was found that PBE0, omega B97XD, and M06-2X gave better fits of the experimental value than did B3LYP. The experimental value was well reproduced at these levels of theory. The bowl structures and bowl-inversion energies of monosubstituted sumanenes were therefore calculated at the omega B97XD/6-311+ G(d, p) level of theory. In both the experiments and the calculations, the correlation followed the equation Delta E = acos(4)theta, where a is a coefficient, Delta E is the bowl-inversion energy, and cos theta is the normalized bowl depth, indicating that the bowl inversion follows a double-well potential energy diagram.