Lenosky’s energy and the phonon dispersion of graphene

We calculate the phonon spectrum for a graphene sheet resulting from the model proposed by Lenosky et al. [Nature (London) 355, 333 (1992)] for the free energy of the lattice. This model takes into account not only the usual bond-bending and stretching terms, but it also captures the possible misalignment of the pz orbitals. We compare our results with previous models used in the literature and with available experimental data. We show that while this model provides an excellent description of the flexural modes in graphene, an extra term in the energy is needed for it to be able to reproduce the full phonon dispersion correctly beyond the Γ point.