Comparative study of van der Waals corrections to the bulk properties of graphite.

Graphite is a stack of honeycomb (graphene) layers bound together by nonlocal, long-range van der Waals (vdW) forces, which are poorly described by density functional theory (DFT) within local or semilocal exchange-correlation functionals. Several approximations have been proposed to add a vdW correction to the DFT total energies (Stefan Grimme (D2 and D3) with different damping functions (D3-BJ), Tkatchenko-Scheffler (TS) without and with self-consistent screening (TS  +  SCS) effects). Those corrections have remarkly improved the agreement between our results and experiment for the interlayer distance (from 3.9 to 0.6%) [corrected] and high-level random-phase approximation (RPA) calculations for interlayer binding energy (from 69.5 to 1.5%). [corrected]. We report a systematic investigation of various structural, energetic and electron properties with the aforementioned vdW corrections followed by comparison with experimental and theoretical RPA data. Comparison between the resulting relative errors shows that the TS  +  SCS correction provides the best results; the other corrections yield significantly larger errors for at least one of the studied properties. If considerations of computational costs or convergence problems rule out the TS  +  SCS approach, we recommend the D3-BJ correction. Comparison between the computed π(z)Γ-splitting and experimental results shows disagreements of 10% or more with all vdW corrections. Even the computationally more expensive hybrid PBE0 has proved unable to improve the agreement with the measured splitting. Our results indicate that improvements of the exchange-correlation functionals beyond the vdW corrections are necessary to accurately describe the band structure of graphite.