Binding of polycyclic aromatic hydrocarbons and graphene dimers in density functional theory

An early van der Waals density functional (vdW-DF) described layered systems (such as graphite and graphene dimers) using a layer-averaged electron density in the evaluation of nonlocal correlations. This early vdW-DF version was also adapted to approximate the binding of polycyclic aromatic hydrocarbons (PAHs) (Chakarova S D and Schroeder E 2005 J. Chem. Phys. 122 054102). In parallel to that PAH study, a new vdW-DF version (Dion M, Rydberg H, Schroeder E, Langreth D C and Lundqvist B I 2004 Phys. Rev. Lett. 92 246401) was developed that provides accounts of nonlocal correlations for systems of general geometry. We apply here the latter vdW-DF version to aromatic dimers of benzene, naphthalene, anthracene and pyrene, stacked in sandwich (AA) structure, and the slipped-parallel (AB) naphthalene dimer. We further compare the results of the two methods as well as other theoretical results obtained by quantum-chemistry methods. We also compare calculations for two interacting graphene sheets in the AA and the AB structures and provide the corresponding graphene-from-graphite exfoliation energies. Finally, we present an overview of the scaling of the molecular-dimer interaction with the number of carbon atoms and with the number of carbon rings.