I briefly review some of the methods, developed at the Naval Research Laboratory, that were used in a variety of collaborations with the Frauenheim group. To aid experimental understanding at that time, we attempted to predict equilibrium structures and also provide calculated vibrational spectra for direct comparison to experimental measurements. Most of our work was on carbon-based systems with a heavy focus on fullerenes and diamond. More recently another pure carbon compound, graphene, has received much attention. In this paper, I present applications of density-functional-based spectroscopic techniques to a single graphene nanofilm and confirm that spin polarization can occur at the edge states. However, antiferromagnetic ordering is preferred over ferromagnetic ordering. By extracting a Heisenberg Hamiltonian from the calculations the energy of the various spin multiplets can be estimated through diagonalization of this Hamiltonian. The Perdew–Burke–Ernzerhof–density-functional theory (PBE-DFT) results indicate that both antiferromagnetic and ferromagnetic graphene structures are vibrationally stable but that the lowest-energy eigenstate of the system is an open-shell singlet with a gap of approximately 14 cm−1 to the open-shell triplet state. Consistent with recent work that stabilizes graphene nanofilms via adsorption onto metal surfaces the density functional results presented here show that small graphene nanofilms, while vibrationally stable, will exothermically form previously identified fullerene structures. Vibrational excitation spectra for the 54-atom graphene and fullerene structures are calculated to provide spectroscopic means for distinguishing between the two structures.