We present a detailed first-principles investigation of the response of a free-standing graphene sheet to an external perpendicular static electric field E. The charge density distribution in the vicinity of the graphene monolayer that is caused by E was determined using the pseudopotential density-functional theory approach. Different geometries were considered. The centroid of this extra density induced by an external electric field was determined as zim = 1.048 Å at vanishing E, and its dependence on E has been obtained. The thus determined zim was employed to construct the hybrid one-electron potential which generates a new set of energies for the image-potential states.
Keywords: electric field; graphene; image potential; image-plane position; image-potential states; valence charge density.