N-heterocyclic carbenes (NHCs) bind very strongly to transition metals due to their unique electronic structure featuring a divalent carbon atom with a lone pair in a highly directional sp2-hybridized orbital. As such, they can be assembled into monolayers on metal surfaces that have enhanced stability compared to their thiol-based counterparts. The utility of NHCs to form such robust self-assembled monolayers (SAMs) was only recently recognized and many fundamental questions remain. Here we investigate the structure and geometry of a series of NHCs on Au(111) using high-resolution X-ray photoelectron spectroscopy and density functional theory calculations. We find that the N-substituents on the NHC ring strongly affect the molecule-metal interaction and steer the orientation of molecules in the surface layer. In contrast to previous reports, our experimental and theoretical results provide unequivocal evidence that NHCs with N-methyl substituents bind to undercoordinated adatoms to form flat-lying complexes. In these SAMs, the donor-acceptor interaction between the NHC lone pair and the undercoordinated Au adatom is primarily responsible for the strong bonding of the molecules to the surface. NHCs with bulkier N-substituents prevent the formation of such complexes by forcing the molecules into an upright orientation. Our work provides unique insights into the bonding and geometry of NHC monolayers; more generally, it charts a clear path to manipulating the interaction between NHCs and metal surfaces using traditional coordination chemistry synthetic strategies.