Corrigendum to: ¿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 inthe form of bulk and bilayer. The characteristics of the potential energy surface, such as the barrier to rel-ative sliding of the layers and magnitude of corrugation, and physically measurable properties associatedwith relative in-plane and out-of-plane motion of the layers including the shear modulus and modulusfor 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 graphitethat are known to be ground-state from the experimental studies. However, it fails to describe the orderof metastable states of boron nitride in energy. The PBE-D3 and vdW-DF2 functionals, which reproducethis order correctly, are identified as the optimal choice for general studies. The vdW-DF2 functional ispreferred 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 shearmode 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 caseof graphene, the PBE-D2 functional works very well and can be further improved by adjustment of theparameters.