Abstract
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 Schröder E 2005 J. Chem. Phys. 122 054102). In parallel to that PAH study, a new vdW-DF version (Dion M, Rydberg H, Schröder 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.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Density functional theory (DFT) is a widespread method for calculating the atomic and electronic structure of materials on the atomic scale. It is based directly on the many-body Schrödinger equation and in principle it provides an exact account of ground state properties. However, in practice some approximations must be introduced. The most frequently used approximations do not describe the long-range van der Waals (or dispersion) forces well and in recent years there have been a number of methods that attempt to overcome this deficiency of common implementations of DFT.
Main results. Polycyclic aromatic hydrocarbon molecules (PAH) bind in pairs, much like the planes in graphite. We use and compare two recent, related, implementations of DFT that include the van der Waals forces to calculate the binding energies and separations of a number of small PAH molecule dimers and two sheets of graphite. Our results for the newer and more general method are in good agreement with more elaborate, highly accurate quantum-chemistry calculations, where those exist. We find that for linear PAH molecules (acenes) the binding energy scales linearly with the number of aromatic rings.
Wider implications. Whereas we find that the binding energy scales with the number of rings for linear PAH molecules (acenes), this is not the case for the PAH molecule included that is not linear (pyrene). This illustrates the intriguing complexity of the van der Waals interactions even in such simple systems.
Figure. Binding curve of the pyrene dimer, using two implementations of DFT with van der Waals forces.