Density functional theory (DFT) calculations can be a rewarding and pliable tool in the investigation of material, yet the insufficient knowledge of the necessary exchange-correlation term casts a shadow on the accuracy and that way to the "predictive power" of such simulations.

Here we combine DFT theoretical studies with experimental determination of the structure of single atom layer, two dimensional material hexagonal boron nitride, h-BN, and graphene, gr. On transition and coinage metal surfaces these form either a commensurate structure or, already at tiny mismatches, modulated, periodically repeating Moiré structures. Usually the wave length of the modulation is in the range of few nano-metres, and these structures can act as templates for adsorbed atoms and molecules, allowing for controlled modulation of the structures formed. As in the Moiré structure there are different lateral registries between the over-layer and the substrate there are different strengths of interactions too, ranging from covalent bonds to weak, van der Waals or London dispersion forces.

Such a wide range of qualitatively different interactions sets a high target bar to the approximations to the exchange-correlation term in DFT, and on the experimental side the large unit cells require also special care in the analysis of the microscopic structural information.  Here we claim that the two approaches can meet in the middle, if care is taken on both sides. We further discuss molecular adsorbates on the h-BN "nanomeshes" on transition metal substrates.