Visualizing lone pairs and quantifying their bonding in solids with tight-binding Wannier models from first principles

Abstract Lone pairs critically influence material properties, from local structure to bonding interactions, yet their direct visualization in solids has remained elusive. We address this gap with a method using Wannier functions and Hamiltonian rotation. Bonding analyses have also been constrained by the use of spherical s-orbitals derived from orbital projectors. In this study, we directly visualize lone pair orbitals using first-principles calculations and Wannier functions obtained through a simple Hamiltonian rotation via a similarity transform. This method offers a direct understanding of their role in solids through the resulting tight-binding model and qualitative information from the resulting 3D representation of the wavefunctions. We apply our approach to two materials from the bismuth oxyhalide family, confirming previous findings from the Revised Lone Pair Model. Additionally, our model enables us to manipulate inter-orbital hopping, highlighting the significant role of lone pairs in shaping the materials’ electronic structure and band gap.