Dissecting the single-electron C–C bond: NBO and AIM perspectives

carbon atoms (C1 and C2), which has been characterized as an allegedly single electron sigma C-C bond. Our NCI analysis reveals that the interaction between the tricyclic moieties is weak and predominantly van der Waals in character (regardless of the counterion). AIM theory identifies a persistent bond critical point between C1 and C2 across all structures, albeit with low electron density indicative of a weak interaction. A comparison of the Laplacian density contour between C1-C2 and a previously reported B-B single-electron σ-bond (herein labeled as 1p-B), shows charge depletion between C1-C2 whereas in B1-B2 there is charge accumulation, characteristic of a σ-bond. The spin density population shows that half the radical is distributed among the two tricyclic structures. Our NBO and NRT analyses indicate that a single-electron σ-bond is present in some resonance structures, although its overall contribution is minimal. The calculated natural bond order for C1-C2 in the cationic form is only 0.066, suggesting limited bond character. Finally, NBO deletion analysis quantifies the interaction energy between the rings, showing that the C1-C2 interaction contributes only ∼9.5% to the total π-π interaction energy, primarily through donor-acceptor interactions between bonding orbitals and Rydberg orbitals. These results converge to show that the C1-C2 interaction is a weak, highly delocalized interaction governed by subtle electronic effects rather than a single electron σ-bond.