  The adsorption of metal atoms on nanostructures, such as graphene and
nanotubes, plays an important role in catalysis, electronic doping, and tuning
material properties. Quantum chemical calculations permit the investigation of
this process to discover desirable interactions and obtain mechanistic insights
into adsorbate behavior, of which the binding strength is a central quantity.
However, binding strengths vary widely in the literature, even when using
almost identical computational methods. To address this issue, we investigate
the adsorption of a variety of metals onto graphene, carbon nanotubes, and
boron nitride nanotubes. As is well-known, calculations on periodic structures
require a sufficiently large system size to remove interactions between
periodic images. Our results indicate that there are both direct and indirect
mechanisms for this interaction, where the latter can require even larger
system sizes than typically employed. The magnitude and distance of the effect
depend on the electronic state of the substrate and the open- or closed-shell
nature of the adsorbate. For instance, insulating substrates (e.g., boron
nitride nanotubes) show essentially no dependence on system size, whereas
metallic or semi-metallic systems can have a substantial effect due to the
delocalized nature of the electronic states interacting with the adsorbate. We
derive a scaling relation for the length dependence with a representative
tight-binding model. These results demonstrate how to extrapolate the binding
energies to the isolated-impurity limit.
