Heat-to-connect: surface commensurability directs organometallic one-dimensional self-assembly

Recent experiments demonstrated the assembly of unfunctionalized porphyrin molecules into organometallic wires on the Cu(110) surface through the formation of stable C-Cu-C bonds involving Cu adatoms. The remarkable property of the observed structures is that they adopt a clear direction, despite the lack of functional ligands to direct the assembly. Here we use density functional theory calculations and scanning tunneling microscopy to clarify the mechanism for the highly one-dimensional assembly of the observed nanostructures. An energetic preference for the formation of C-Cu-C bonds is found in several lattice directions, but self-assembly critically relies on the commensurability of appropriate adsorption sites for the Cu atoms involved in the coupling. The experimentally observed structures arise from a geometric self-limitation of the assembly process, which proceeds in the energetically and geometrically most preferred direction. A further extension of the structure in the orthogonal dimension to form 2D assemblies is prevented by the lattice mismatch between the repeat lengths in the 001 and 110 directions of the underlying (110) lattice and the apparent rigidity of the molecules involved. However, the fusing of two parallel chains is geometrically allowed and leads to some of the energetically most favorable configurations. Finally, the role of van der Waals forces is investigated for the covalent couplings and chemisorbed interactions found in this system.