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Using the normal incidence x-ray standing wave technique as well as low energy electron microscopy we have investigated the structure of quasi-freestanding monolayer graphene (QFMLG) obtained by intercalation of antimony under the $\left(6\sqrt{3}\times6\sqrt{3}\right)R30^\circ$ reconstructed graphitized 6H-SiC(0001) surface, also known as zeroth-layer graphene. We found that Sb intercalation decouples the QFMLG well from the substrate. The distance from the QFMLG to the Sb layer almost equals the expected van der Waals bonding distance of C and Sb. The Sb intercalation layer itself is mono-atomic, flat, and located much closer to the substrate, at almost the distance of a covalent Sb-Si bond length. All data is consistent with Sb located on top of the uppermost Si atoms of the SiC bulk.

The adsorption geometry, the electronic properties, and the adsorption energy of the prototype organic molecule 3,4,9,10-perylene tetracarboxylic dianhydride (PTCDA) on a monolayer of hexagonal boron nitride (hBN) grown on the Cu(111) surface were determined experimentally. The perylene core is at a large height of 3.37 $\AA{}$ and only a minute downward displacement of the functional anhydride groups (0.07 \AA{}) occurs, yielding adsorption heights that agree with the sum of the involved van der Waals radii. Thus, already a single hBN layer leads to a decoupled (physisorbed) molecule, contrary to the situation on the bare Cu(111) surface.

By means of low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS), we have investigated the adsorption of single Au atoms on a PTCDA monolayer physisorbed on the Au(111) surface. A chemical reaction between the Au atom and the PTCDA molecule leads to the formation of a radical that has an unpaired electron in its highest occupied orbital. This orbital is a $\ensuremath{\pi}$ orbital that extends over the whole Au-PTCDA complex. Because of the large Coulomb repulsion in this orbital, the unpaired electron generates a local moment when the molecule is adsorbed on the Au(111) surface. We demonstrate the formation of the radical and the existence of the local moment after adsorption by observing a zero-bias differential conductance peak that originates from the Kondo effect. By temperature dependent measurements of the zero-bias differential conductance, we determine the Kondo temperature to be ${T}_{\mathrm{K}}=(38\ifmmode\pm\else\textpm\fi{}8)\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. For the theoretical description of the properties of the Au-PTCDA complex we use a hierarchy of methods, ranging from density functional theory (DFT) including a van der Waals correction to many-body perturbation theory (MBPT) and the numerical renormalization group (NRG) approach. Regarding the high-energy orbital spectrum, we obtain an excellent agreement with experiments by both spin-polarized DFT/MBPT and NRG. Moreover, the NRG provides an accurate description of the low-energy excitation spectrum of the spin degree of freedom, predicting a Kondo temperature very close to the experimental value. This is achieved by a detailed analysis of the universality of various definitions of ${T}_{\mathrm{K}}$ and by taking into account the full energy dependence of the coupling function between the molecule-metal complex and the metallic substrate.