van der Waals Interactions in Density Functional Theory Using Wannier Functions

van der Waals interactions between atoms and molecules are ubiquitous and very important for many molecular and condensed-matter structures. These systems are often studied from first principles using the density functional theory (DFT), because this approach often represents a good compromise between accuracy and efficiency. However, the commonly used DFT functionals are not able to describe properly van der Waals effects. Most attempts to correct for this problem have a basic semiempirical character, although computationally more expensive first principles schemes have been recently developed. Of course, the key issue is finding a way to include van der Waals interactions in DFT without dramatically increasing the computational cost. We here describe in detail the recently developed scheme, based on the use of the maximally localized Wannier functions, that combines the simplicity of the semiempirical formalism with the accuracy of the first principles approaches and appears to be promising., being simple, efficient, accurate, and transferable (for instance, charge polarization effects are naturally included). The results of successful applications to small molecules, bulk Ar, and the interaction of Ar, He, and H(2) with two different Al surfaces are presented. Directions for further improvements of the method are finally suggested.