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Monolayer graphene grown on Ru(0001) surfaces forms a superstructure with periodic modulations in its geometry and electronic structure. The large dimension and inhomogeneous features of this superstructure make its description and subsequent analysis a challenge for theoretical modeling based on density functional theory. In this work, we compare two different approaches to describe the same physical properties of this surface, focusing on the geometry and the electronic states confined at the surface. In the more complex approach, the actual moiré structure is taken into account by means of large unit cells, whereas in the simplest one, the graphene moiré is completely neglected by representing the system as a stretched graphene layer that adapts pseudomorphicallyto Ru(0001). As shown in previous work, the more complex model provides an accurate description of the existing experimental observations. More interestingly, we show that the simplified stretched models, which are computationally inexpensive, reproduce qualitatively the main features of the surface electronic structure. They also provide a simple and comprehensive picture of the observed electronic structure, thus making them particularly useful for the analysis of these and maybe other complex interfacesWe thank Barcelona Supercomputing Center–Spanish SupercomputingNetwork (BSC-RES) and Centro de Computación Científica – Universidad Autónoma de Madrid (CCC-UAM) for allocation of computer time. Work supported by the MICINN Projects No. FIS2010-15127, No.FIS2010-18847, No. CTQ2010-17006, No. FIS-2010-19609- C09-00, No. ACI2008-0777, No. 2010C-07-25200, and No. CSD2007-00010, the CAM program NANOBIOMAGNET S2009/MAT1726 and the Gobierno Vasco-UPV/EHU Project No. IT-366-07. S.B. acknowledges financial support from MEC under FPU Grant No. AP-2007-00157. D.S. acknowledges financial support from the FPI-UAM grant progra

Lattice-matched versus lattice-mismatched models to describe epitaxial monolayer graphene on Ru(0001)