Anatomy of Classical Boron-Boron Bonding: Overlap and sp Dissonance

Classical bonding is predominantly understood using the insipid spⁿ hybridization for σ-bonds as well as π bonds and their delocalized variants. Because hybridization ignores intricate differences in the energy and size of valence atomic orbitals, its naïve application to classically bonded boron atoms leads to numerous surprises in bond strengths, frontier MOs/bands, and even geometry. Here we show that the sp dissonance caused by size mismatch between the valence s and p orbitals of boron plays a crucial role in its bonding, subtly distinct from that of carbon and silicon. Unlike the heavier p block elements, boron prefers to actively engage its compact 2s orbitals in bonding. This leads to the overreach of p-p σ-type overlap that reduces its magnitude in the entire B─B bonding range. Consequently, the π-type overlap remains substantial, making its electronic structure visibly distinct in saturated and unsaturated regimes. The deltahedral frameworks offer a compromise by breaking this symmetry-enforced dichotomy of classical σ- and π-type bonding and following alternate electron counts that suit the electron deficiency of the boron. The pathological anatomy of classical B─B σ-bonding also explains the origins of puzzling metallic character and disorder in their classical boride networks even with ideal electron count, unlike deltahedral borides. The implications of sp dissonance are illustrated in classical boron networks of various hybridizations, explaining the unusual preference for unique sp³ lattice with strained four-membered rings in CrB₄, origins of observed σ holes in MgB₂ that lead to its superconducting nature, and the absence of Peierls distortion in LiB.