To characterize the adsorption height of Gr on the solid Cu(111), we also compute the gap by a direct method. Here, the gap is determined as the distance between the (center of) the top surface atoms of the solid Cu slab and those of the Gr layer. Since the surface atoms are clearly defined for the solid slab, we can easily determine the average value and standard deviation of all the "direct" distances (see Figure ) and sample them analog to the inflection-point "gap". This gap value corresponds to the experimentally determined distances for solid Cu (and other metals). An inflection-point "gap" on the solid slab is in contrast not reported to our knowledge. Therefore, a straightforward comparison cannot be easily done based on literature data. On the other hand, such a direct "gap" for the liquid case is vague since a peak position is not sharp (see Figure ). Fortunately, through our simulations we can provide a comparison of the different "gaps" which is justified by the excellent agreement of both, the inflection-point gap for Gr on liquid Cu (see main text) and the direct gap for Gr on Cu(111). We determine this latter as 3.287(±0.0001) Å at 300K , which compares well to the experimental values of as 3.34 ± 0.06 Å and 3.0 ± 0.2 Å measured via ex situ total-reflection high-energy positron diffraction (TRHEPD) and atomic force microscopy (AFM) at room temperature. The direct value and the inflection-point determined gap in our simulations differ consistently by 𝛿𝐷 ≈ 1 Å at the employed 𝜎 values used for the electron density. This 𝛿𝐷 roughly stays constant with temperature and ML potential used. We therefore use this value (1 Å) to freely translate between the two "gap" definitions.