Density-Energy Balanced Selection of Chiral Honeycomb Superstructures from Deprotonated Carboxylate Molecules on Ag(111).

Here, we investigate the self-assembly of 4,4',4″-(1,3,3a1,4,6,7,9-heptaazaphenalene-2,5,8-triyl) tribenzoic acid on Ag(111) by scanning tunneling microscopy. Upon annealing, complete deprotonation drives the formation of a family of periodic honeycomb superstructures, denoted as HCN (N = 1-8), which are composed of triangular molecular sublattices and exhibit pronounced organizational chirality. By controlling the molecular coverage and annealing conditions, we identify the coexistence of HC4 and HC5 as the thermodynamically favored state near equilibrium. An analytical model incorporating the coupled contributions of molecular density and average intermolecular binding energy, supported by a rigorous convexity-based analysis, demonstrates that the ground state under a fixed density constraint corresponds to the coexistence of two adjacent HCN and HCN+1 phases. These results provide a unified thermodynamic framework for understanding and controlling surface-confined supramolecular networks.