Fate of the resonating valence bond in graphene.

We apply a variational wave function capable of describing qualitatively and quantitatively the so-called "resonating valence bond" (RVB) in realistic materials, by improving standard ab initio calculations by means of quantum Monte Carlo methods. In this framework we clearly identify the Kekulé and Dewar contributions to the chemical bond of the benzene molecule and establish the corresponding RVB energy of these structures (≃0.01 eV/atom). We apply this method to unveil the nature of the chemical bond in undoped graphene, providing an estimate of the RVB energy gain, and show that this picture remains only within a small "resonance length" of a few atomic units.