High-throughput computational search for two-dimensional binary compounds: Energetic stability versus synthesizability of three-dimensional counterparts

Using first-principles calculations, the energetic stability of two-dimensional (2D) binary compounds $XY$ is investigated, where $X$ and $Y$ indicate the metallic element from Li to Pb in the periodic table. Here, 1081 compounds in the buckled honeycomb (BHC), buckled square, B2, $\mathrm{L}{1}₀$, and ${\mathrm{B}}_h$ structures are studied. For the compounds that have negative formation energy in the BHC structure or the compounds that can have the ${\mathrm{B}}_h$ structure, the phonon dispersions of the 2D structures are also calculated. We demonstrate that (i) a negative formation energy is neither a sufficient nor necessary condition for yielding the dynamical stability of 2D compounds; and (ii) if a compound in the ${\mathrm{B}}_h$ structure has been synthesized experimentally, that in the BHC structure is dynamically stable.