This article reviews the different density functional theory (DFT) methods available in the literature for dealing with dispersion interactions and recent applications of DFT approaches including van der Waals corrections in the study of the interaction of atoms and molecules with several different surfaces. Focus is given to the interaction of atoms and molecules with metal, metal oxide and graphite surfaces or more complex systems. It will be shown that DFT approaches including van der Waals corrections present significant advances over standard exchange–correlation functionals for treating systems dominated by weak interactions.

We compute, from first principles, the dispersion interaction between two and three fullerenes, in time-dependent density functional theory. These results, complemented with total energy calculations at small and intermediate distances, lead to a parameter-free determination of the interaction between fullerenes. Agreement with experiment, within $4\%$, is found for all quantities, computed via Monte Carlo simulations of fullerite. Inclusion of the three-body term is found to increase by $6\%$ the cohesive energy at equilibrium density.