Optimization of configurations of atomic species on two-dimensional hexagonal lattices for copper-based systems

We explore the stable configurations of atomic species on a hexagonal plane in two-dimensional (2D) binary systems. We investigate configurations for 9 and 16 atomic sites in the unit cell (3 × 3 and 4 × 4 supercells) by using the density-functional theory approach, where the configuration search is accelerated by the Bayesian optimization. Our results, which assume the 2D copper-based systems of Cu–X, show that the structures having a hexagonal or elongated ring of Cu (or X) atoms containing a X (or Cu) cluster in the unit cell are relatively stable, in particular, for X = Be, Pd, and Au. Assuming a 4 × 4 supercell, we also find such structures in binary Lennard-Jones crystals with moderately weak bonding between different atomic species. The present finding indicates that binary systems may show complex crystal structures if they are neither phase-separated nor strongly bonded systems.