  Vertical stacking of two-dimensional (2D) crystals, such as graphene and
hexagonal boron nitride, has recently lead to a new class of materials known as
van der Waals heterostructures (vdWHs) with unique and highly tunable
electronic properties. Abinitio calculations should in principle provide a
powerful tool for modeling and guiding the design of vdWHs, but in their
traditional, form such calculations are only feasible for commensurable
structures with a few layers. Here we show that the dielectric properties of
realistic, incommensurable vdWHs comprising hundreds of layers can be
calculated with ab-initio accuracy using a multi-scale approach where the
dielectric functions of the individual layers (the dielectric building blocks)
are coupled simply via their long-range Coulomb interaction. We use the method
to illustrate the 2D- 3D dielectric transition in multi-layer MoS2 crystals,
the hybridization of quantum plasmons in large graphene/hBN heterostructures,
and to demonstrate the intricate effect of substrate screening on the
non-Rydberg exciton series in supported WS2.
