Nature of partial sigma bond

This study investigates the formation of partial sigma (σ) covalent bonds in experimentally synthesizable biradicals formed from hydrogenated and fluorinated C₈, C₂₀, and C₆₀ cage structures, by assessing their stability, geometry, and bonding character in singlet and triplet states using restricted B3LYP-D3/6–31+G(d,p) theory, natural bond orbital (NBO) analysis, and complete active space self-consistent field (CASSCF) method. The results show that these partial σ_CC bonds have Wiberg bond orders of 0.38 to 0.48 and bond lengths ranging from 2.62 Å to 5.93 Å. Cage size influences the characteristics of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), with electrons favoring more antibonding orbitals in smaller cages where electrons reside more on the exterior of the cage and favoring bonding orbitals in larger ones where electrons are more in the interior. Fluorination enhances electron density on bonding orbitals. The analysis further clarified that the differentiation between antibonding and bonding features of HOMOs and LUMOs extends beyond merely electron transfer from s- to p-atomic orbitals, also noting possible interactions of the same symmetry repel. The study also introduces hyperconjugation from α-position CH bonds as a factor in stabilizing partial σ-bond formation. The results also caution against the use of broken symmetry methodology in unrestricted SCF wavefunctions for biradicals, such as those in this study as it may cause large spin contamination and thus errors in the calculated electronic properties results.