We have experimentally determined the lateral registry and geometric structure of free-base porphine (2H-P) and copper-metalated porphine (Cu-P) adsorbed on Cu(111), by means of energy-scanned photoelectron diffraction (PhD), and compared the experimental results to density functional theory (DFT) calculations that included van der Waals corrections within the Tkatchenko-Scheffler approach. Both 2H-P and Cu-P adsorb with their center above a surface bridge site. Consistency is obtained between

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... he experimental and DFT-predicted structural models, with a characteristic change in the corrugation of the four N atoms of the molecule's macrocycle following metalation. Interestingly, comparison with previously published data for cobalt porphine adsorbed on the same surface evidences a distinct increase in the average height of the N atoms above the surface through the series 2H-P, Cu-P, cobalt porphine. Such an increase strikingly anti-correlates the DFT-predicted adsorption strength, with 2H-P having the smallest adsorption height despite the weakest calculated adsorption energy. In addition, our findings suggest that for these macrocyclic compounds, substrate-to-molecule charge transfer and adsorption strength may not be univocally correlated.