Dispersion Interactions with Density-Functional Theory: Benchmarking Semiempirical and Interatomic Pairwise Corrected Density Functionals

We present a comparative assessment of the accuracy of two approaches for evaluating dispersion interactions: inter-atomic pair-wise corrections and semi-empirical meta-generalized-gradient-approximation (meta-GGA) based functionals. This is achieved by employing conventional (semi-)local and (screened-)hybrid functionals, as well as semi-empirical hybrid and non-hybrid meta-GGA functionals of the M06 family, with and without pair-wise Tkatchenko-Scheffler corrections. All those are tested against the benchmark S22 set of weakly bound systems, a representative larger molecular complex, and a representative dispersively bound solid. We also compare our results with those obtained from Grimme's pair-wise correction (DFT-D3) and Langreth-Lundqvist functionals (vdW-DF1/2). We find that the semi-empirical kinetic-energy-density dependence of the M06 functionals mimics some of the non-local correlation needed to describe dispersion. However, long-range contributions are still missing. Pair-wise corrections provide for a satisfactory level of accuracy irrespectively of the underlying functional.