Long-range van der Waals attraction and alkali-metal lattice constants

While the short-range part of the van der Waals (vdW) interaction can be described by semilocal density functionals, the long range cannot. By respecting two uniform electron gas and other exact limits, we construct a nonlocal density functional for the long-range coefficient ${C}_{6}$. ${C}_{8}$ and ${C}_{10}$ may be determined empirically from ${C}_{6}$. Then we estimate the effect of the core-core vdW attraction upon the lattice constants of the alkali metals, including dynamic valence-electron screening. This attraction is important for the softest metals, shrinking the lattice constant of Cs by $0.1\text{ }\text{\AA{}}$.