Oscillations in meta-generalized-gradient approximation potential energy surfaces for dispersion-bound complexes

Meta-generalized-gradient approximations (meta-GGAs) in density-functional theory are exchange-correlation functionals whose integrands depend on local density, density gradient, and also the kinetic-energy density. It has been pointed out by Johnson et al. Chem. Phys. Lett. 394, 334 (2004) that meta-GGA potential energy curves in dispersion-bound complexes are susceptible to spurious oscillations unless very large integration grids are used. This grid sensitivity originates from the saddle-point region of the density near the intermonomer midpoint. Various dimensionless ratios involving the kinetic-energy density, found in typical meta-GGAs, may be ill-behaved in this region. Grid sensitivity thus arises if the midpoint region is sampled by too sparse a grid. For most meta-GGAs, standard grids do not suffice. Care must be taken to avoid this problem when using, or constructing, meta-GGAs.