Translation Symmetry Breakdown in Low-Dimensional Lattices of Pentagonal Rings

The mechanism of translation symmetry breakdown in newly proposed low-dimensional carbon pentagon-constituted nanostructures (e.g., pentagraphene) with multiple sp²/sp³ sublattices was studied by GGA DFT, DFTB, and model potential approaches. It was found that finite nanoclusters suffer strong uniform unit cell bending followed by breaking of crystalline lattice linear translation invariance caused by structural mechanical stress. It was shown that 2D sp²/sp³ nanostructures are correlated transition states between two symmetrically equivalent bent structures. At DFT level of theory the distortion energy of the flakes (7.5 × 10^-2 eV/atom) is much higher the energy of dynamical stabilization of graphene. Strong mechanical stress prevents stabilization of the nanoclusters on any type of supports by either van der Waals or covalent bonding and should lead to formation of pentatubes, nanorings, or nanofoams rather than infinite nanoribbons or nanosheets. Formation of two-layered pentagraphene structures leads to compensation of the stress and stabilization of flat finite pentaflakes.