Nonlocal Correlations in Density Functional Theory

Abstract: In Density Functional Theory, the widely used local and semilocal approximations to the exchange-correlation energy, the local density approximation (LDA) and the generalized gradient approximations (GGAs), lack a physical description of truly nonlocal correlation effects, which are absolutely essential for a proper description of soft matter. A scheme is proposed that provides a basis for systematic improvements beyond LDA and GGA, including correlations at intermediate and long range, giving rise to bonds of pure van der Waals type as well as more intricate, intermediate-range correlation bonds. The scheme is developed with regard to computational efficiency as well as physical soundness, and incorporated into the standard DFT formalism. The method is applied to a generic set of systems, illuminating different aspects of nonlocal correlations. Studies of van der Waals interactions in molecules, of nonlocal correlations between surfaces, and of bonds in graphite and between graphene layers are included. Successful account of energetics, bond lengths and compressibilities of graphitic systems clearly illustrates the significance of using approximate exchange-correlation energy functionals that are based on the true physics of the system. Finally an explicit formula is given for a general nonlocal correlation density functional, suitable for incorporation into standard DFT schemes.