In this work, we study the interlayer interactions between sheets of blue phosphorus with quantum Monte Carlo (QMC) methods. We find that as previously observed in black phosphorus, interlayer binding of blue phosphorus cannot be described by van der Waals (vdW) interactions alone within the density-functional theory framework. Specifically, while some vdW density functionals produced reasonable binding curves, none of them could provide a correct, even qualitatively, description of charge redistribution due to interlayer binding. We also show that small systematic errors in common practice QMC calculations, such as the choice of optimized geometry and finitesize corrections, are non-negligible given the energy and length scales of this problem. We mitigate some of the major sources of error and report QMC-optimized lattice constant, stacking, and interlayer binding energy for blue phosphorus. It is strongly suggested that these considerations are important and quite general in the modeling of two-dimensional phosphorus allotropes.

Structural properties and energetics of carbon rings are studied with the diffusion Monte Carlo (DMC) method. Our DMC-based geometry optimization reveals that both polyynic C 4n and cumulenic C 4n + 2 rings exhibit bond length alternations for n ≥ 3, which is understood to be due to Jahn−Teller distortions. The bond length alternation even in a cumulenic (4n + 2) carbon ring was experimentally observed in a recently synthesized C 18 molecule. From a comparison of the DMC cohesive energies of C 4n with those of C 4n + 2 , we present a comprehensive picture of the competition between Huckel's rule and Jahn−Teller distortion in small carbon rings; the former is more dominant than the latter for n < 5 where C 4n + 2 rings are more stable than C 4n , while C 4n rings are as stable as C 4n + 2 for n < 5 where dimerization effects due to Jahn−Teller distortion are more important.

Diffusion Monte Carlo (DMC) calculations have been performed to study the adsorption of a single Pt atom on pristine graphene. We obtain the adsorption energy curves of a single Pt...

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.

We have carried out diffusion Monte Carlo calculations for an A1B–1-stacked bilayer blue phosphorene to find that it undergoes a semiconductor–metal transition as the interlayer distance decreases. While the most stable bilayer structure is a semiconducting one with two monolayers coupled through a weak van der Waals interaction, the metallic bilayer at a shorter interlayer distance is found to be only metastable. This is in contrast to a recent theoretical prediction based on a random phase approximation that the metallic phase would be the most stable bilayer configuration of blue phosphorene. Our analysis of charge density distributions reveals that the metastable metallic phase is induced by interlayer chemical bonding and intralayer charge redistributions. This study enriches our understanding of interlayer binding of a blue phosphorene and contributes to the establishment of correct energetic order between its different phases, which will be essential in devising an experimental pathway for a metallic phosphorene.