Generalized Coordination Numbers
The coordination number of a surface atom counts its nearest neighbors, and undercoordinated atoms tend to be more reactive. The generalized coordination number (GCN) refines this by summing the coordination numbers of an atom’s neighbors and dividing by the bulk maximum (12 for fcc), so it carries second-neighbor information and serves as a cheap structural descriptor of site reactivity on metal and alloy surfaces of arbitrary structure.
GCN features for enantiospecific kinetics on chiral Cu (2024)
Abdelmaqsoud and coworkers represented each Cu(hkl) orientation by the fraction of its surface atoms having each of the 58 distinct GCN values found over 270 slabs spanning the stereographic triangle, and regressed tartaric acid decomposition half-times on these vectors. Because GCN features are identical for the R and S forms of a surface, handedness was introduced by training separate models on the two diastereomeric pairings of molecule and surface. The model fit measured half-time differences with a test MAE of 138 s and, being interpretable, identified a kink motif (atoms with GCN 4.8, 5.6, 6.4 and 9.3) whose surface fraction tracks predicted enantiospecificity, peaking at Cu(11,3,1). A symmetry-only expansion in five chiral cubic harmonics fit slightly better (133 s) but offers no structural insight (Abdelmaqsoud et al. 2024). Summary: abdelmaqsoud2024; see also Chiral metal surfaces.