  The equilibrium binding energy is an important factor in the design of
materials and devices. However, it presents great computational challenges for
materials built up from nanostructures. Here we investigate the binding-energy
scaling law from first-principles calculations. We show that the equilibrium
binding energy per atom between identical nanostructures can scale up or down
with nanostructure size. From the energy scaling law, we predict finite
large-size limits of binding energy per atom. We find that there are two
competing factors in the determination of the binding energy: Nonadditivities
of van der Waals coefficients and center-to-center distance between
nanostructures. To uncode the detail, the nonadditivity of the static multipole
polarizability is investigated. We find that the higher-order multipole
polarizability displays ultra-strong intrinsic nonadditivity, no matter if the
dipole polarizability is additive or not.
