To understand sparse systems we must account for both strong local atom bonds and weak nonlocal van der Waals forces between atoms separated by empty space. A fully nonlocal functional form [H. Rydberg, B.I. Lundqvist, D.C. Langreth, and M. Dion, Phys. Rev. B 62, 6997 (2000)] of density-functional theory (DFT) is applied here to the layered systems graphite, boron nitride, and molybdenum sulfide to compute bond lengths, binding energies, and compressibilities. These key examples show that the DFT with the generalized-gradient approximation does not apply for calculating properties of sparse matter, while use of the fully nonlocal version appears to be one way to proceed.PACS numbers: 71.15. Mb, 61.50.Lt, 31.15.Ew, Calculations of structure and other properties of sparse systems must account for both strong local atom bonds and weak nonlocal van der Waals (vdW) forces between atoms separated by empty space. Present methods are unable to describe the true interactions of sparse systems, abundant among materials and molecules. Key systems, like graphite, BN, and MoS 2 , have layered structures. While today's standard tool, density-functional theory (DFT), has broad application, the common local (LDA) and semilocal density approximations (GGA) [1,2,3,4] for exchange and correlation, E xc [n], fail to describe the interactions at sparse electron densities. Here we show that the recently proposed density functional [5] with nonlocal correlations, E nl c [n], gives separations, binding energies, and compressibilities of these layered systems in fair agreement with experiment. This planar case bears on the development of vdW density functionals for general geometries [6,7], as do asymptotic vdW functionals [8].Figure 1 with its 'inner surfaces' defines the problem: voids of ultra-low density, across which electrodynamics leads to vdW coupling. This coupling depends on the polarization properties of the layers themselves, and not on small regions of density overlap between the layers, excluding proper account in LDA or GGA. For large interplanar separation d the vdW interaction energy between planes behaves as −c 4 /d 4 , while LDA or GGA necessarily predicts an exponential falloff. Layers rolled up to form two (i) nanotubes with parallel axes a distance l apart interact as −c 5 /l 5 , or (ii) balls (e.g., C 60 ), a distance r apart, as −c 6 /r 6 . If by fluke an LDA or GGA were to give the correct equilibrium for one shape, it would necessarily fail for the others. The simple expedient of adding the standard asymptotic vdW energies as corrections to the correlation energy of LDA or GGA also fails. The true vdW interaction between two close sheets must be (i) substantially stronger (Fig. 1), (ii) seamless, and (iii) saturate as d shrinks (Fig. 2).Like earlier work directly calculating nonlocal correlations between two jellium slabs [9], the vdW density functional (vdW-DF) theory [5] used here exploits assumed planar symmetry. It divides the correlation energy functional into two pieces,, where E nl c [n] is defined to in...

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Magnesium, nanotubes, graphitic nanofibers, and graphite represent interesting opportunities for efficient hydrogen storage applications and motivate first-principle investigations of the hydrogen energetics and dynamics that describe such potential technological usage. We present spin-polarized electron-density calculations of adsorption energies and diffusion barriers for both chemisorbed and physisorbed hydrogen atoms to provide a detailed description of the important hydrogen dynamics.

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