  The stacking of different 2D materials provides a promising approach to
realize new states of quantum matter. In this combined scanning tunneling
microscopy (STM) and density functional theory (DFT) study we show that the
structure in weakly bound, purely van der Waals (vdW) interacting systems is
strongly influenced by screening and relaxation. We studied in detail the
physisorption of lead phthalocyanine (PbPc) molecules on epitaxial monolayer
graphene on SiC(0001) as well as on highly ordered pyrolytic graphite (HOPG),
resembling truly 2D and anisotropic, semi-infinite 3D supports. Our analysis
demonstrates that the different deformation ability of the vdW coupled systems,
i.e. their actual thickness and buckling, triggers the molecular morphology and
exhibits a proximity coupled band structure. It thus provides important
implications for future 2D design concepts.
