▎ 摘　　要

We present an ab initio analysis of the impact of edge shape and graphene-molecule anchor coupling on the electronic and transport functionalities of graphene-based molecular electronics devices. We analyze how Fano-like resonances, spin filtering, and negative differential resistance effects may or may not arise by modifying suitably the edge shapes and the terminating groups of simple organic molecules. We show that the spin filtering effect is a consequence of the magnetic behavior of zigzag-terminated edges, which is enhanced by furnishing these with a wedge shape. The negative differential resistance effect is originated by the presence of two degenerate electronic states localized at each of the atoms coupling the molecule to graphene which are strongly affected by a bias voltage. The effect could thus be tailored by a suitable choice of the molecule and contact atoms if edge shape could be controlled with atomic precision.