An accurate DFT-based method for the treatment of weak and van der Waals
interactions : the LCAO-S2+vdW formalism

Y.J. Dappe

Institut de Physique et Chimie des Matériaux de Strasbourg

Recent achievements in the field of the Nanotechnology have opened a wide range
of powerful technological applications. These strong developments in
nanomolecular systems have reinforced the importance of weak and van der Waals
interactions. The need to understand these phenomena at a microscopic level by
the mean of accurate methods becomes of fundamental importance. However, it has
been demonstrated that standard Density Functional Theory (DFT) is unable to
describe correctly these kind of interactions. This is mainly due to the local
character of the standard functional approximations (LDA,GGA, ...), in
opposition with the long range behaviour of the van der Waals interaction.

In this presentation, I will mainly focus on the important role played by weak
interactions-among them the so called van der Waals interaction-in Carbon based
Nanostructures, like the interaction between two graphene sheets for example.
These interactions are fundamental to the stability of such structures.
Here we present a DFT based formalism, the LCAO-S2+vdW method, which is an
intermolecular perturbation theory coupled with the use of the dipolar
approximation, in order to treat weak and van der Waals interactions.
The first contribution, due to the electronic densities overlaps between the
interacting subsystems, is a repulsive energy that we call “chemical”
interaction. We treat it by expanding the electronic wavefunctions with respect
to the electronic overlaps. The second contribution is the so called van der
Waals interaction, originating from charge fluctuations which lead to
interacting electronic dipoles. This energy is treated in the frame of the
dipolar approximation and gives rise to an attractive contribution. The balance
of these two energies gives the binding energy of the system as well as the
equilibrium position.
This method has already been applied giving good results to the study of
graphene-graphene interaction [1], and to more graphitic materials like Carbon
Nanotubes or fullerenes [2]. I will detail these results and present some new
perspectives for molecular Hydrogene dimer and adsorption on Carbon Nanotubes.

[1] Y. J. Dappe, M. A. Basanta, F. Flores, and J. Ortega, Phys. Rev. B 74,
205434 (2006).

[2] Y. J. Dappe, J. Ortega, and F. Flores, Phys. Rev. B 79, 165409 (2009).