  There is enormous recent interest in weak, van der Waals-type (vdW)
interactions due to their fundamental relevance for two-dimensional materials
and the so-called vdW heterostructures. Tackling this problem using computer
simulation is very challenging due to the non-trivial, non-local nature of
these interactions. We benchmark different treatments of London dispersion
forces within the density functional theory (DFT) framework on hexagonal boron
nitride or graphene monolayers on Ir(111) by comparing the calculated
geometries to a comprehensive set of experimental data. The geometry of these
systems crucially depends on the interplay between vdW interactions and wave
function hybridisation, making them excellent test cases for vdW-treated DFT.
Our results show strong variations in the calculated atomic geometry. While
some of the approximations reproduce the experimental structure, this is rather
based on \textit{a posteriori} comparison with the ``target results''. General
predictive power in vdW-treated DFT is not achieved yet and might require new
approaches.
