Aromaticity reversals and their effect on bonding in the low-lying electronic states of cyclooctatetraene

Aromaticity Reversal Induced by Vibrations in Cyclo[16]carbon

Aromaticity is typically regarded as an intrinsic property of a molecule, correlated with electron delocalization, stability, and other properties. Small variations in the molecular geometry usually result in small changes in aromaticity, in line with Hammond's postulate. For example, introducing bond-length alternation in benzene and square cyclobutadiene by modulating the geometry along the Kekulé vibration gradually decreases the magnitude of their ring currents, making them less aromatic and less antiaromatic, respectively. A sign change in the ring current, corresponding to a reversal of aromaticity, typically requires a gross perturbation such as electronic excitation, addition or removal of two electrons, or a dramatic change in the molecular geometry. Here, we use multireference calculations to show how movement along the Kekulé vibration, which controls bond-length alternation, induces a sudden reversal in the ring current of cyclo[16]carbon, C16. This reversal occurs when the two orthogonal π systems of C16 sustain opposing currents. These results are rationalized by a Hückel model which includes bond-length alternation, and which is combined with a minimal model accounting for orbital contributions to the ring current. Finally, we successfully describe the electronic structure of C16 with a "divide-and-conquer" approach suitable for execution on a quantum computer.

How Different are the Diamagnetic and Paramagnetic Contributions to Off-Nucleus Shielding in Aromatic and Antiaromatic Rings?

The spatial variations in the diamagnetic and paramagnetic contributions to the off-nucleus isotropic shielding, σ i s o r = σ i s o d r + σ i s o p r ${\ {{\sigma }_{{\rm i}{\rm s}{\rm o}}\left({\bf r}\right)=\ \sigma }_{{\rm i}{\rm s}{\rm o}}^{{\rm d}}\left({\bf r}\right)+{\sigma }_{{\rm i}{\rm s}{\rm o}}^{{\rm p}}\left({\bf r}\right)}$ , and to the zz component of the off-nucleus shielding tensor, σ z z r = σ z z d r + σ z z p r ${{{\sigma }_{zz}\left({\bf r}\right)=\sigma }_{zz}^{{\rm d}}\left({\bf r}\right)+{\sigma }_{zz}^{{\rm p}}\left({\bf r}\right)}$ , around benzene (C₆ H₆ ) and cyclobutadiene (C₄ H₄ ) are investigated using complete-active-space self-consistent field wavefunctions. Despite the substantial differences between σ i s o r ${{\sigma }_{{\rm i}{\rm s}{\rm o}}\left({\bf r}\right)}$ and σ z z r ${{\sigma }_{zz}\left({\bf r}\right)}$ around the aromatic C₆ H₆ and the antiaromatic C₄ H₄ , the diamagnetic and paramagnetic contributions to these quantities, σ i s o d r ${{\sigma }_{{\rm i}{\rm s}{\rm o}}^{{\rm d}}\left({\bf r}\right)}$ and σ z z d r ${{\sigma }_{zz}^{{\rm d}}\left({\bf r}\right)}$ , and σ i s o p r ${{\sigma }_{{\rm i}{\rm s}{\rm o}}^{{\rm p}}\left({\bf r}\right)}$ and σ z z P r ${{\sigma }_{zz}^{{\rm P}}\left({\bf r}\right)}$ , are found to behave similarly in the two molecules, shielding and deshielding, respectively, each ring and its surroundings. The different signs of the most popular aromaticity criterion, the nucleus-independent chemical shift (NICS), in C₆ H₆ and C₄ H₄ are shown to follow from a change in the balance between the respective diamagnetic and paramagnetic contributions. Thus, the different NICS values for antiaromatic and antiaromatic molecules cannot be attributed to differences in the ease of access to excited states only; differences in the electron density, which determines the overall bonding picture, also play an important role.

Magnetic Shielding Analysis of Bonding in [1.1.1]Propellane

The bonding in [1.1.1]propellane, bicyclo[1.1.0]butane, bicyclo[1.1.1]pentane, tetrahedrane, and cyclopropane is investigated by analyzing changes in the off-nucleus isotropic magnetic shielding within the space surrounding each of these molecules and, for [1.1.1]propellane, by examining also the diamagnetic and paramagnetic contributions to this shielding. Any shielding arising from the two "exo" sp³-like hybrid atomic orbitals on the bridgehead carbon atoms that have been used to support the idea of an inverted bond between these two atoms is found to be almost entirely contained within the [1.1.1]propellane cage and to contribute to a strongly shielded central region. This strongly shielded region suggests the establishment of a mainly covalent bonding interaction involving all carbon atoms that cannot be straightforwardly decomposed into contributions from individual carbon-carbon bonds. The emergence of the strongly shielding central region is traced by comparing the shielding variations in and around molecules with one three-membered carbon ring (cyclopropane), two fused three-membered carbon rings (bicyclo[1.1.0]butane), and three fused three-membered carbon rings ([1.1.1]propellane).