Energetic stability of free-standing and metal-supported borophenes: Quantum Monte Carlo and density functional theory calculations

Quantum Monte Carlo (QMC) and density-functional theory (DFT) calculations were carried out to study cohesion energetics of two-dimensional (2D) sheets of boron atoms called borophenes. Our QMC calculations confirmed the polymorphism among free-standing borophenes that was reported in previous DFT studies. Although Perdew−Burke−Ernzerhof (PBE) calculations significantly overestimate the cohesive energies of 2D boron sheets, DFT-PBE relative energetics with respect to each other among various free-standing borophenes are found to be in quantitative agreement with the corresponding QMC results. This suggests that one can make reliable predictions for relative stability of different boron sheets through DFT-PBE calculations. Our analysis of PBE formation energies of borophenes on metal surfaces shows that the polymorphic range is extended for borophenes on the Ag(111) and the Au(111) surfaces beyond that of free-standing borophenes, reflecting recent experimental synthesis of β₁₂ and χ₃ boron sheets on the Ag(111) surface. We have also found that a hexagonal borophene can be stabilized through charge transfer from a metal surface and is energetically favored on the Al(111) surface over other borophene structures. Finally, it is found that the bilayer formation could be energetically favored over its monolayer form for the borophene−Au system, especially for borophenes with hexagonal hole densities η lower than 1/9. This leads to our prediction that in addition to its monolayer form, a bilayer η = 1/12 borophene can be synthesized on the Au(111) surface, opening a new possibility for borophene-based electronic devices.