Delocalization-ratio analysis of 3-center bonding in position-space for closo-boranes and related systems: Approaching the styx picture and beyond

Closo-boron hydrides B_nH_n²⁻ (n = 5–12) are a conceptually well understood class of compounds. For these and a few related prototype compounds, both the local and the global picture of 3-center bonding are extracted from position-space quantities based on the electron density and the pair density. For this purpose, three-center delocalization indices between quantum theory of atoms in molecules (QTAIM) atoms in position space are used to develop a consistent set of local bond and triangle, and global cluster delocalization ratios (DRs), which are quantitatively compared with conceptual Γ values derived from the styx code for each cluster. Combination of the cluster DRs with associated effective numbers of skeletal electron sharing (SES) for selected cluster surface edges, triangles, or the whole cluster yields effective styx type values describing the trend and even the size of the conceptual styx codes for closo-boranes B_nH_n²⁻ and related systems with increasing cluster size n reasonably well. For nonuniform cluster topologies, the different vertex degrees are shown to cause systematic 3-center wise bond delocalization effects for the associated edges and triangles of different average vertex degrees. Extension of DR analysis beyond the styx type triangular cluster-surface bonding corresponds to a triangulation of multicentric bonding. The cluster-wise results keep indicating consistency with the mixed 2- and 3-center bonding approach. The successfully established chemical meaning of the local edge, triangle, and global cluster DRs and their associated SES values constitutes the basis for systematic investigations of mixed 2- and 3-center bonding scenarios in particular in intermetallic and related (endohedral) cluster compounds in the future.