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.