Comparison of performance of van der Waals-corrected exchange-correlation functionals for interlayer interaction in graphene and hexagonal boron nitride

Abstract

Exchange-correlation functionals with corrections for van der Waals interactions (PBE-D2, PBE-D3, PBE-D3(BJ), PBE-TS, optPBE-vdW and vdW-DF2) are tested for graphene and hexagonal boron nitride, both in the form of bulk and bilayer. The characteristics of the potential energy surface, such as the barrier to relative sliding of the layers and magnitude of corrugation, and physically measurable properties associated with relative in-plane and out-of-plane motion of the layers including the shear modulus and modulus for axial compression, shear mode frequency and frequency of out-of-plane vibrations are considered. The PBE-D3(BJ) functional gives the best results for the stackings of hexagonal boron nitride and graphite that are known to be ground-state from the experimental studies. However, it fails to describe the order of metastable states of boron nitride in energy. The PBE-D3 and vdW-DF2 functionals, which reproduce this order correctly, are identified as the optimal choice for general studies. The vdW-DF2 functional is preferred for evaluation of the modulus for axial compression and frequency of out-of-plane vibrations, while the PBE-D3 functional is somewhat more accurate in calculations of the shear modulus and shear mode frequency. The best description of the latter properties, however, is achieved also using the vdW-DF2 functional combined with consideration of the experimental interlayer distance. In the specific case of graphene, the PBE-D2 functional works very well and can be further improved by adjustment of the parameters.

Stacking in incommensurate graphene/hexagonal-boron-nitride heterostructures based on ab initio study of interlayer interaction

“…41 The calculations of the optimal size of the commensurate unit cell of the graphene/boron-nitride heterostructure and potential energy surface are performed at a fixed interlayer distance d = 3.33Å, which is close to the experimentally measured interlayer distances in bulk boron nitride [51][52][53][54][55][56][57][58][59] and graphite. 53,[60][61][62][63][64][65] It has been shown previously 47,66 that our appoach based on the combination of the vdW-DF2 functional 43 and the use of the experimental interlayer distance allows to describe adequately such properties of purely graphene or boron ni-tride systems related to in-plane relative motion of the layers as the shear mode frequency, shear modulus, barrier to relative sliding of the layers and width of stacking dislocations. The DFT calculations using the experimental interlayer distance were found to be much more accurate than the ones using the optimized interlayer distance, while at the experimental interlayer distance the vdW-DF2 functional was demonstrated to perform better than the PBE-D2, PBE-D3, PBE-D3(BJ), PBE-TS, PBE-TS/HI, PBE-TS+SCS, optPBE-vdW functionals.…”

Commensurate-incommensurate phase transition and a network of domain walls in bilayer graphene with a biaxially stretched layer

“…(11). Still this error is acceptable given that the barrier to relative sliding of the layers is not known with a high precision (the DFT values for the barrier lie in the range of 0.5 -2.1 meV/atom, [26][27][28][29][30]34,35 although the interval can be reduced if the experimental interlayer distance is used, 34 and the estimates of the barrier from the experimental measurements of the shear mode frequencies 25 and dislocation width 2 correspond to 1.7 meV/atom and 2.4 meV/atom, respectively). It can be expected that our model used to analyze the triangular network of domain walls in bilayer graphene with a biaxially stretched bottom layer has a similar accuracy.…”

Energetics and Structure of Domain Wall Networks in Minimally Twisted Bilayer Graphene under Strain

“…Unfortunately, the magnitude of the barrier V max is not known with certainty. Because of the difficulty in description of long-range interactions in DFT, the corresponding values from literature lie in the wide range from 0.5 meV/atom to 2.1 meV/atom 37,38,[41][42][43][44][45][46] (in meV per atom of the upper/adsorbed layer, see Supporting Information). After comparison of a number of properties of bilayer graphene, graphite and boron nitride, such as shear and bulk moduli, shear mode frequencies, etc.…”