Van der Waals Interactions in Density Functional Theory
Doctoral thesis, 1999
Density functional theory is a very important method for calculating ground-state properties for atoms, molecules and solids. Albeit exact in principle, its implementation requires an approximation for the so-called exchange-correlation energy. The most popular of these approximations, the local-density and generalized-gradient approximations, are local or semi-local and do not include the highly non-local van der Waals interaction.
In this thesis a density functional for calculating the asymptotic van der Waals interaction energy for objects of different sizes and geometries is proposed. It is based on the adiabatic-connection formula for the exchange-correlation energy, where two basic approximations are made. First, the density response function is calculated at the level of the random phase approximation. Second, a local approximation is made for the screened response.
In practice a doubly local approximation for the dielectric function is used when evaluating the interactions, together with a cutoff of each interacting object. This real-space cutoff prevents spurious overestimates of the response in the density tails otherwise caused by the local approximation. Explicit forms of the functional are derived for three model systems --- interacting atoms or molecules, an atom or molecule outside a surface and finally two interacting surfaces. Also the derivation of a correction to the 1 / z2-dependence for the asymptotic interaction between two surfaces is accounted for.
The functional is applied to and found very reasonable for a number of different objects, such as atoms, fullerenes, and other molecules. Surfaces at different levels of approximation are treated successfully, from jellium surfaces to low-indexed Al surfaces calculated within a plane-wave pseudopotential code, with both surface structure and relaxation of the outermost atomic layers. Anisotropic effects for interacting molecules and molecules outside a surface are also considered.
In summary, this thesis demonstrates that it is indeed possible to restore van der Waals interactions in density functional theory. An explicit van der Waals density functional that is proposed for long-ranged interactions is successfully applied to a range of test cases with mutual interactions of atoms, molecules, and surfaces. The prospects for a working van der Waals functional, applicable to problems within solid state physics, chemistry, and biology look very good.
van der Waals interaction
density functional theory