Testing the local density approximation with energy-versus-separation curves of jellium slab pairs

We explore the successes and failures of the local-density approximation (LDA) in predicting the attractive force and energetics of attraction between two jellium metals. We model the metals by two very thin slabs, and follow the energetics at all separations D from the van der Waals (vdW) regime at large D through to metallic bonding as D0. We compare LDA results with calculations including exact exchange and microscopic nonlocal random-phase-approximation-type correlation energy: only these latter calculations include dispersion (van der Waals) forces correctly. We show how this error of LDA at large separations leads also to errors even at smaller separations outside the vdW regime.