Extended Data Fig. 6: Formation energies of freestanding (infinite) NHC sheets as a function of intermolecular separation.

Dashed lines indicate vdW contributions. Molecules are fixed at the gas-phase geometry, but rotated according to the adsorbed geometry at full coverage, as determined from the calculations (Supplementary Fig. 5). IPr^2D and IMe^2D are arranged on a hexagonal grid; IMe^1D corresponds to a face-on geometry, as shown. The Si(111)-B \(\sqrt{3}\)a lattice spacings are indicated. The IPr^2D data show an attractive potential well (due to strong vdW interactions) in coincidence with the spacing of the \(2\sqrt{3}\times 2\sqrt{3}\) Si(111)-B lattice. This indicates that IPr molecules moving across the surface are energetically favoured to assemble at specific sites near adsorbed molecules as part of a commensurate island or domain (epitaxial growth). The IMe^2D curve instead is repulsive at a molecular spacing of \(\sqrt{3}\ a\) (the minimum adatom-adatom distance), suggesting that larger spacings may be more favoured for IMe. Actually, the face-on alignment represented by IMe^1D indicates that a close packing (up to ~0.4 nm) is possible along one specific direction. However, the minimum intermolecular distance possible within the adsorbed layer is determined by the spacing of adatom sites (that is \(\sqrt{3}\ a\)), as they yield the largest adsorption energy. Thus, local assembly of IMe molecules near an adsorbed molecule or island is expected to be anisotropic. In an optimally packed configuration, IMe molecules align face-on at a \(\sqrt{3}\ a\) distance, with larger spacings in other directions due to steric repulsion of side groups (Supplementary Fig. 5). This configuration is consistent with the observation in STM of small \(2\sqrt{3}\times \sqrt{3}\) islands.