DFT-GGA calculations, enhanced to include effects of dispersion, are used to investigate the adsorption process of corannulene on a Cu(111) surface In accord with experiments, we consider the dynamics of corannulene approaching the surface in a tilted fashion, concave side-up, enabling interactions between one of the six-membered rings and the surface over a 3-fold hollow site Electronic structure analyses, including projected density of states and detection of work function modification, are used to aid in the understanding of the specific nature of the interaction between the corannulene and the metal surface in the complex system Results show substantial charge rearrangement at the interface, the net effect being a large interface dipole that, added to the intrinsic molecular dipole, causes a significant decrease of the surface work function. Despite the charge rearrangement, no appreciable charge transfer occurs, and the general orbital structure of the individual components is retained The analysis suggests that the adsorption of corannulene on Cu(111) is not a chemisorption process Increased packing of corannulene on the surface leads to progressively smaller adsorption-induced interface dipoles, clue to the depolarizing field created by the molecules.