Numerical Study of INDO₄ Molecules: Ordering of Centered Honeycomb Structures and Central Molecule Switching

We simulate the ordering of centered honeycomb patterns formed by elongated s-indacene-1,3,5,7(2H,6H)-tetrone (INDO₄) molecules recently observed on Ag(100) and Ag(111) surfaces. Based on a detailed analysis of STM images and plausible intermolecular interactions, we propose a coarse-grained six-state model similar to multistate lattice models used in phase transition theory. Each state in our model corresponds to a distinct molecular orientation, while the ordering of the two centered honeycomb phases is governed by four main distance-dependent intermolecular interactions. The fundamental building block of these phases is a 7-molecule honeycomb with the central molecule adopting different angular positions. For INDO₄/Ag(111), this leads to switching of the central molecule between two orientations. Within our model, we derive ground-state phase diagrams and attribute this switching to degeneracy in the interaction energies of the two centered honeycomb phases. Our Monte Carlo simulations nicely corroborate these results. To quantify intermolecular interactions, we performed DFT calculations to obtain pair and trio interaction potentials. Furthermore, we computed the expansion energy of the centered honeycomb (7-molecule cluster) for both orientations of the central molecule and determined that the degeneracy occurs at the cluster expansion length of 1.3-1.4 Å.