A Twisted σ-Bond Mediated by a Lone-Pair in Elemental Sulfur

Abstract

The lone pair is a foundational concept in chemistry, classically regarded as a localized, nonbonding entity. However, a persistent anomaly in elemental sulfur (S8) challenges this view: the observed electron density along the S–S bond shows a bimodal distribution that is irreconcilable with a single-peak theoretical prediction. This suggests that lone pairs may actively bond─a possibility that remains overlooked and unverified. Here, using high-resolution electron density analysis and quantum chemical topology, we visualize that sulfur lone pairs can delocalize spatially up to ∼1.3 Å from the nucleus. This delocalization enables mixing between π-type lone-pair orbitals and bonding orbitals, inducing a twisted σ-bond with substantial π-character, which exhibits strong anisotropic deformation and highly twisted orbital alignment. This picture quantitatively explains the bimodal anomaly. Our findings revise the nonbonding paradigm of lone pairs, showing that their delocalization actively reshapes covalent interactions, a new bonding motif with broad implications for main-group chemistry, especially for those with stereochemically active lone pairs.