We note that this quantitative comparison and concomitant conclusions are only enabled by the use of the gigantic c(27 x 27√3) minimum-strain Cu(111) simulation cell. Figure shows the temperature dependence of the adsorption height of Gr on solid and liquid Cu, also including data generated in models with smaller Cu(111) cells with a concomitantly increased Gr strain. In particular for the smallest such cell with a strain of +3.6%, a strong temperature dependence of the "gap" is obtained. In contrast, the liquid Cu "gap" shows almost no temperature dependence with "gaps" varying by ∆ = 0.008 Å in the temperature range 1000 K to 1200 K. The latter invariance further supports our direct comparison to the experimental data, even in light of the uncertainty with regards to the computational melting temperature of Cu at the PBE+MBD level. We attribute the overall decrease of the computed "gap" at solid Cu(111) with increasing temperature to the thermal expansion of the Gr lattice in the extended periodic cell and a thus resulting additionally induced small strain. The stronger this strain, the stronger the temperature dependence. The small difference in this temperature dependence obtained Figure in for the solid Cu(111) computed in the c(24 x 24√3) cell model with -0.5% strain and the gigantic c(27x27√3) cell model with -0.1% strain suggests that the residual strain in the latter cell has no longer any significant effect on the deduced "gap". At least, the remaining variations cannot explain the small difference in the computed solid and liquid gap at elevated temperatures of the order of ∆ = 0.05 Å apparent in Figure . While we cannot exclude that this difference could indeed result from slightly different interactions, we emphasize that it may also result (at least partially) from sampling restrictions of the liquid state in the employed finite supercell. Even if the latter was the case though, its effect on the computed "gap" would thus be smaller than ∆ = 0.05 Å, showing that we indeed reached a quantitative agreement between the computed and measured "gap" at liquid Cu within the experimental uncertainty.